text:
# Why is calcium carbonate relatively insoluble in water?

In fact most carbonates are insoluble in water (the exceptions are?). Carbonate is a doubly charged negative ion that should form strong electrostatic bonds with metal ions - the doubly charged calcium ion, $C {a}^{2 +}$, should form strong ionic bonds, and indeed it does.
As physical scientists, however, we seek actual data, and I confess that I cannot find an appropriate table. I did find ${K}_{s p} = 3.3 \times {10}^{-} 9$, which corresponds to approx. 10 mg per litre at $25$ ""^@C.
Should the $p H$ of the solution be increased, would you expect the solubility of calcium carbonate to go up or down? Will the carbonate ion remain as carbonate at lower $p H$?

format: plain


text:
Enter the total number of tolls and the average cost per toll ($/toll) into the Toll Cost Calculator. The calculator will evaluate and display the Toll Cost. ## Toll Cost Formula The following formula is used to calculate the Toll Cost. TC = #T * CPT • Where TC is the Toll Cost ($)
• #T is the total number of tolls
• CPT is the average cost per toll ($/toll) ## How to Calculate Toll Cost? The following example problems outline how to calculate Toll Cost. Example Problem #1: 1. First, determine the total number of tolls. The total number of tolls is given as 3. 2. Next, determine the average cost per toll ($/toll). The average cost per toll ($/toll) is provided as 3. 3. Finally, calculate the Toll Cost using the equation above: TC = #T * CPT The values given above are inserted into the equation below: TC = 3* 3 = 9.00 ($)

Example Problem #2:

The variables needed for this problem are provided below:

total number of tolls = 6

average cost per toll ($/toll) = 5 Entering these values and solving gives: TC = #T * CPT = 30.00 ($)


text:
Vietoris-Rips complexes of metric spaces near a closed Riemannian manifold

Latschev, J (2001). Vietoris-Rips complexes of metric spaces near a closed Riemannian manifold. Archiv der Mathematik, 77(6):522-528.

Abstract

We show that for every closed Riemannian manifold X there exists a positive number¶ ε0>0 such that for all 0< there exists some¶ δ>0 such that for every metric space Y with Gromov-Hausdorff distance to X less than¶ δ the geometric ε -complex |Yε| is homotopy equivalent to X.¶ In particular, this gives a positive answer to a question of Hausmann.

Abstract

We show that for every closed Riemannian manifold X there exists a positive number¶ ε0>0 such that for all 0< there exists some¶ δ>0 such that for every metric space Y with Gromov-Hausdorff distance to X less than¶ δ the geometric ε -complex |Yε| is homotopy equivalent to X.¶ In particular, this gives a positive answer to a question of Hausmann.

Statistics

Citations

Dimensions.ai Metrics
25 citations in Web of Science®
30 citations in Scopus®


text:
# Rerunning a Pipelet#

Pipelets, just as other enrichments, are only executed on items that are loaded into a project after the pipelet has been configured. However, it is often desired to run the pipelet on all previously loaded items without having to reload the items into Squirro. Pipelets are either rerun from the command line or directly in the user interface.

## Command Line#

Warning

Pipelet rerunning using the command line tool is implemented using the Update Item API. Because of this, the only changes that can be applied to an item are changes in the keywords. It is currently not possible to update any of the other Item Fields when rerunning a pipelet.

You can use the rerun individual pipeline step functionality to work around this limitation.

The basic command to rerun a pipelet is:

pipelet rerun --cluster CLUSTER --token TOKEN --project-id PROJECT mypipelet.py

This executes the pipelet contained in mypipelet.py on all the items in the given project (see Connecting to Squirro for the cluster, token and project options).

It is possible to limit the rerunning to just a subset of the project’s items, by specifying a query (the connection options are now omitted for brevity):

pipelet rerun --query 'big data' mypipelet.py

To pass in configuration, that the pipelet needs, use the config parameter which is a JSON string:

pipelet rerun --config '{"file":"test.txt"}' mypipelet.py

## Versioning#

A common use of pipelet rerun is to change the way some keywords are calculated. To easily update the data, it is recommended to introduce a separate keyword for the pipelet’s version. This way, the version can be incremented when the logic is improved, and the rerun command can be applied to all older items.

Take for example this pipelet:

import re

from squirro.sdk import PipeletV1, require

VERSION = 1

@require('log')
class PricePipelet(PipeletV1):
"""Extract the price of the item from the body.

Searches for the first number prefixed with $and uses that as the price. """ def __init__(self, config): self.config = config def consume(self, item): body = item.get('body') kw = item.setdefault('keywords', {}) kw['price_version'] = [VERSION] if not body: return item match = re.search('\$(\d+)', body)
if not match:
return item

kw['price'] = int(match.group(1))
return item

This sets a price_version facet to the value 1 (the facet should be declared in the project as being a numeric facet).

When the pipelet is updated, increment the version to VERSION = 2. Then rerun is then called as follows:

pipelet rerun --cluster CLUSTER --token TOKEN --project-id PROJECT --query '-price_version:2' price_pipelet.py

This runs the pipelet on all items that do not have the price_version set to the value 2 - either the value hasn’t been set at all, or it’s still on a different version.

## User Interface#

To rerun a pipelet in the user interface, follow the explanations for rerunning an individual pipeline step in the pipeline editor.

Note

Using the rerun functionality in the pipeline editor changes are not limited to keywords. You can also change Item Fields like the title or the created_at field.

## Pipelet Features#

• Number of items: only pipelets that return exactly one item are supported. There is no support for pipelets that return None (to remove an item from the index) or that yield more than one item.


text:
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# State X's income-averaging law allows a portion of one's income to be

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State X's income-averaging law allows a portion of one's income to be taxed at lower rate than the rate based on one's total taxable income. To use income averaging, the taxpayer must have earned taxable income for a particular year that exceeds 140 percent of his or her average taxable income for the previous three years. People using income averaging owe less tax for that year than they would without income averaging.

Which of the following individuals would be most seriously affected if income averaging were not permitted in computing the taxes owed for current year?

(A) Individuals whose income has steadily decreased for the past three years
(B) Individuals whose income increased by 50 percent four years ago and has remained the same since then
(C) Individuals whose income has doubled this year after remaining about the same for five years
(D) Individuals who had no income this year, but did in each of the previous three years
(E) Individuals who are retired and whose income has remained about the same for the past ten years

Originally posted by arjsingh1976 on 27 Oct 2006, 08:19.
Last edited by Bunuel on 22 Feb 2019, 04:00, edited 3 times in total.
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Re: State X's income-averaging law allows a portion of one's income to be  [#permalink]

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29 Oct 2006, 22:30
Yes has to be (C).

The income in the present year in (C) would be 200% of the income in the last three years,thus making him eligible for tax averaging,

if that were removed he would have to pay much higher taxes.
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Re: State X's income-averaging law allows a portion of one's income to be  [#permalink]

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31 Oct 2006, 21:06
Looks like C. If salary changes from s to 2s that is a 200% of the original salary which is greater than 140%. Hence C
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11 Jul 2013, 12:01
arjsingh1976 wrote:
State Xâ€™s income-averaging law allows a portion of oneâ€™s income to be taxed at lower rate than the rate based on oneâ€™s total taxable income. To use income averaging, the taxpayer must have earned taxable income for a particular year that exceeds 140 percent of his or her average taxable income for the previous three years. People using income averaging owe less tax for that year than they would without income averaging.
Which of the following individuals would be most seriously affected if income averaging were not permitted in computing the taxes owed for current year?
(A) Individuals whose income has steadily decreased for the past three years
(B) Individuals whose income increased by 50 percent four years ago and has remained the same since then
(C) Individuals whose income has doubled this year after remaining about the same for five years
(D) Individuals who had no income this year, but did in each of the previous three years
(E) Individuals who are retired and whose income has remained about the same for the past ten years

I am lost in it. Please explain.

Guys,
It is saying "the taxpayer must have earned taxable income for a particular year that exceeds 140 percent of his or her average taxable income for the previous three years. "

Now, if the average taxable income for the previous three years is 100$, then the current taxable income should exceed 140% of 100$, that is total taxable income should be 240$. Then how is C correct, if 100$ is turning to 200$...????? _________________ MODULUS Concept ---> http://gmatclub.com/forum/inequalities-158054.html#p1257636 HEXAGON Theory ---> http://gmatclub.com/forum/hexagon-theory-tips-to-solve-any-heaxgon-question-158189.html#p1258308 VP Status: Far, far away! Joined: 02 Sep 2012 Posts: 1055 Location: Italy Concentration: Finance, Entrepreneurship GPA: 3.8 Re: State X's income-averaging law allows a portion of one's income to be [#permalink] ### Show Tags 11 Jul 2013, 12:10 1 jaituteja wrote: arjsingh1976 wrote: State Xâ€™s income-averaging law allows a portion of oneâ€™s income to be taxed at lower rate than the rate based on oneâ€™s total taxable income. To use income averaging, the taxpayer must have earned taxable income for a particular year that exceeds 140 percent of his or her average taxable income for the previous three years. People using income averaging owe less tax for that year than they would without income averaging. Which of the following individuals would be most seriously affected if income averaging were not permitted in computing the taxes owed for current year? (A) Individuals whose income has steadily decreased for the past three years (B) Individuals whose income increased by 50 percent four years ago and has remained the same since then (C) Individuals whose income has doubled this year after remaining about the same for five years (D) Individuals who had no income this year, but did in each of the previous three years (E) Individuals who are retired and whose income has remained about the same for the past ten years I am lost in it. Please explain. Guys, It is saying "the taxpayer must have earned taxable income for a particular year that exceeds 140 percent of his or her average taxable income for the previous three years. " Now, if the average taxable income for the previous three years is 100$, then the current taxable income should exceed 140% of 100$, that is total taxable income should be 240$.
Then how is C correct, if 100$is turning to 200$...?????

" 140 percent of his or her average taxable income "

the 100% of 100$is 100$ => the 140% of 100 $is 140$.

This is what the text meant, hope it's clear now.
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Re: State X's income-averaging law allows a portion of one's income to be  [#permalink]

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11 Jul 2013, 12:16
Zarrolou wrote:
jaituteja wrote:
arjsingh1976 wrote:
State Xâ€™s income-averaging law allows a portion of oneâ€™s income to be taxed at lower rate than the rate based on oneâ€™s total taxable income. To use income averaging, the taxpayer must have earned taxable income for a particular year that exceeds 140 percent of his or her average taxable income for the previous three years. People using income averaging owe less tax for that year than they would without income averaging.
Which of the following individuals would be most seriously affected if income averaging were not permitted in computing the taxes owed for current year?
(A) Individuals whose income has steadily decreased for the past three years
(B) Individuals whose income increased by 50 percent four years ago and has remained the same since then
(C) Individuals whose income has doubled this year after remaining about the same for five years
(D) Individuals who had no income this year, but did in each of the previous three years
(E) Individuals who are retired and whose income has remained about the same for the past ten years

I am lost in it. Please explain.

Guys,
It is saying "the taxpayer must have earned taxable income for a particular year that exceeds 140 percent of his or her average taxable income for the previous three years. "

Now, if the average taxable income for the previous three years is 100$, then the current taxable income should exceed 140% of 100$, that is total taxable income should be 240$. Then how is C correct, if 100$ is turning to 200$...????? " 140 percent of his or her average taxable income " the 100% of 100$ is 100$=> the 140% of 100$ is 140$. This is what the text meant, hope it's clear now. It states that-- taxable income for a particular year that exceeds 140 percent of his or her average taxable income for the previous three years. The word exceeds states that taxable income is 140% more than(exceeds) average taxable income forof previous 3 years. You are skipping the word "exceeds" _________________ MODULUS Concept ---> http://gmatclub.com/forum/inequalities-158054.html#p1257636 HEXAGON Theory ---> http://gmatclub.com/forum/hexagon-theory-tips-to-solve-any-heaxgon-question-158189.html#p1258308 VP Status: Far, far away! Joined: 02 Sep 2012 Posts: 1055 Location: Italy Concentration: Finance, Entrepreneurship GPA: 3.8 Re: State X's income-averaging law allows a portion of one's income to be [#permalink] ### Show Tags 11 Jul 2013, 12:22 2 1 jaituteja wrote: It states that-- taxable income for a particular year that exceeds 140 percent of his or her average taxable income for the previous three years. The word exceeds states that taxable income is 140% more than(exceeds) average taxable income forof previous 3 years. You are skipping the word "exceeds" The word exceeds makes no difference in the numbers. (C) Individuals whose income has doubled this year after remaining about the same for five years 100$,100$,100$,100$,100$ and now 200$average of the past 3 years is 100$ so if is income is greater than 140$, he can have less taxes. Which of the following individuals would be most seriously affected if income averaging were not permitted in computing the taxes owed for current year? This individual would be affected because he earned 200$, which is more than 140\$, so could have paid less taxes.

Hope this makes sense
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Re: State X's income-averaging law allows a portion of one's income to be  [#permalink]

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05 May 2017, 07:34
Took Some time for me to understand. But I feel all the cases other than choice C fails to stand in this scenario.

Lets see what the averaging method says.

Let income for last three years be a, b,c and current year d.

First and foremost thing, to apply this method, a tax payer's current year income should have satisfied the below case.

$$d > 1.4(\frac{(a+b+c)}{3})$$

If this method is applied then, taxpayer will pay less tax than state's current tax majors.

Now the questions stem says, In case if this method was not adapted, which of the following criteria would seriously would have affected?

Choice A - If the income of a person is steadily decreased, the the current year's income will be less than the average. Hence even this policy would be in force, this person was not eligible for income averaging.

Choice B - Even if the income has increased by 50% 4 years ago, we are considering the last 3 year's income which is same. So this person is also not eligible for the method.

Choice D - If this year's income is 0, the person is also not eligible

Choice E - If a person is retired, his current year's income would be 0.

Only choice C says Current year's income is doubled so this person is eligible for the policy. So this person will get benefit of it. If this policy was not in force, the person would be affected.
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Re: State X's income-averaging law allows a portion of one's income to be  [#permalink]

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12 Feb 2018, 10:21
arjsingh1976 wrote:
State X's income-averaging law allows a portion of one's income to be taxed at lower rate than the rate based on one's total taxable income. To use income averaging, the taxpayer must have earned taxable income for a particular year that exceeds 140 percent of his or her average taxable income for the previous three years. People using income averaging owe less tax for that year than they would without income averaging.

Which of the following individuals would be most seriously affected if income averaging were not permitted in computing the taxes owed for current year?

(A) Individuals whose income has steadily decreased for the past three years
(B) Individuals whose income increased by 50 percent four years ago and has remained the same since then
(C) Individuals whose income has doubled this year after remaining about the same for five years(D) Individuals who had no income this year, but did in each of the previous three years
(E) Individuals who are retired and whose income has remained about the same for the past ten years

I am lost in it. Please explain.

Managed to focus on the argument well this time. Income-averaging policy benefits those individuals who get 40% hike in their salaries allowing them to pay less taxes than that they would pay without the policy. Per choice C, individuals whose income doubled this year after remaining same for five years would be the most affected of all if the law is not permitted.
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Re: State X's income-averaging law allows a portion of one's income to be  [#permalink]

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22 Feb 2019, 03:13
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Re: State X's income-averaging law allows a portion of one's income to be   [#permalink] 22 Feb 2019, 03:13
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text:
# Render every Nth frame of an animation

I want to render every Nth frame of an animation, in this case every 12th frame. This way I can play back the animation at 2fps and see if everything is going correctly.

I'm a real novice with Blender Python and cobbled this together:

import bpy

for f in range(startframe,endframe,NthFrame):
bpy.context.scene.frame_current = f
bpy.ops.render.render()
bpy.data.images['Render Result'].save_render(filepath="" + str(f) + '.png')

This kind of works, the right images are rendered and saved. However it completely freezes up Blender, and after about an hour it crashes on windows due to being unresponsive I guess. How can I fix this? Preferably I'd like it to work like rendering an animation normally works, i.e. being able to still use Blender and seeing the progress of each rendered frame.


text:
How do the YAML Parameters relate to Pinhole-Model

I try to make sense of the YAML Matrixes below and so far know that
camera_matrix holds intrinsics
distortion_coefficient is vector for lens distortions and holds k and p parameters projection_matrix is for coordinate mapping world to camera. But why is it the same as the camera matrix and what does the rectification matrix hold. According to opencv-docs this matrix does not exist. Could someone shed some light into this, I feel confused.

image_width: 640 //Region of Interest
image_height: 480
camera_name: depth_A70774V01752221A //@do Seriennummer anpassen
camera_matrix:
rows: 3
cols: 3
data: [4827.94, 0, 1223.5, 0, 4835.62, 1024.5, 0, 0, 1]
distortion_model: plumb_bob
distortion_coefficients: //Korrektur der Linsenfehler
rows: 1
cols: 5
data: [-0.41527, 0.31874, -0.00197, 0.00071, 0]
rectification_matrix:
rows: 3
cols: 3
data: [1, 0, 0, 0, 1, 0, 0, 0, 1]
projection_matrix:
rows: 3
cols: 4
data: [4827.94, 0, 1223.5, 0, 0, 4835.62, 1024.5, 0, 0, 0, 1, 0]

EDIT So the projection_matrix is equal to the camera_matrix, just modified to comply with the rectification_matrix. No Rectification means projection_matrix equal to camera_matrix, which would explain why both have the same entries, as the rectification matrix is the identity.
But why do the dimensions not fit and also the principal point c0 c1 is zero.

Edit
I have read through this image_proc but the rectification process still does not make sense to me. If I perform correction with respect to the distortion coeff, the intrinsics and the extrinsics matrixes, I have a perfectly fine image. Ok it reveals having a look at this. (so good!) I made a flowchart, could someone correct me if sth is wrong? ( the x,y,z is camera coord., XYZ is world coord., ud for undistorted)

Furthermore is this tatement right: The mapping from depth to 3D point is only possible with depth-frames because there I still have the info to reverse the normalisation (division by z), because the z-coordinate is the depth-entry itself. In RGB the z is missing thus no reversing like: x' * z = x(in camera)
Maybe this makes it a little easier to imagine:

edit retag close merge delete

1

CameraInfo.msg has some documentation for projection matrices that might be useful. (e.g. /opt/ros/jade/share/sensor_msgs/msg/CameraInfo.msg)

( 2016-02-17 11:22:34 -0500 )edit

Sort by » oldest newest most voted

The projection matrix contains the intrinsic values for the rectified image. When you rectify your image (remove the distortion), you (in general) also modify the intrinsic calibration matrix (e.g. because you remove pixels at the edge of the image). So if your subscribe to the raw image, you need to use the coefficients from the camera_matrix, if you subscribe to the rect image, you use the projection_matrix.

The projection matrix can also be used in a Stereo Setup. It then contains not only the intrinsic calibration, but also the transformation between the two cameras.

more

So what your saying is the distortion coefficients modify the camera_matrix leading to the projection_matrix. In my case both are the same, which then must be false. How to get the projection matrix?

( 2016-05-08 11:40:36 -0500 )edit

I read this opposing your answer. Monocular case: *In this case, since there is no rotation, translation, or scaling from the original image, K = K' , and only the K and D elements of CameraInfo are needed.

( 2016-05-08 12:05:18 -0500 )edit

The difference between both matrices comes from the translation of the stereo setup you mentioned. The second paragraph is accepted.

( 2016-05-08 12:06:45 -0500 )edit


text:
# Thread: Could someone please check my math on this question involving equivalent rates?

1. ## Could someone please check my math on this question involving equivalent rates?

**Funny side note: While typing this up, as a question, half way through I think I figured it out, which is why this is now a "check my math" post**

Hello,

I'm currently getting my grade 11 college math (Functions and Applications, MCF3M) through a learn from home program. Unfortunately I ran into a little trouble with this problem, which had me stumped . I would be very thankful to anyone who could check my math

By the way, sorry if this is not a question involving equivalent rates but it's the title of the section this is in, in my book, and I wasn't sure what it is considered. :P

Nader plans to buy a used car. He can afford to pay $280 at the end of each month for three years. The best interest rate he can find is 9.8%/a, compounded monthly. For this interest rate, the most he could spend on a vehicle is$8702.85.

Determine the amount he could spend on the purchase of a car if the interest rate is 9.8%/compounded annually.

First of all, I understand the first part about him being able to spend $8702.85. I know this can be figured out using the present value formula: PV=R[1-(1+i)^-n]/i =$280[1-(1+[.098/12])^-36]/(.098/12)
=8702.849629
Which, rounded, gives you $8702.85 And I think this is how you figure out the question (though like I said I'm unsure): 1) Find the (monthly?) interest rate (of the compounded annually plan?) (1+i)^12=(1+[.098/12]) (1+i)^12=(1.008166667) 1+i=12√1.008166667 1+i=1.000678021 i=1.000678021-1 i=.000678021 2)Use this new interest rate in the present value formula used earlier PV=R[1-(1+i)^-n]/i =280[1-(1+.000678021)^-36]/.000678021 =9954.641382 Which, rounded, gives you$9954.64

Therefore Nate could spend \$9954.64 on the purchase of a car.

*NOTE: I am also unsure whether I should be using the future value formula in step 2 instead of the present value formula.*

Like I said, if someone could look this over and tell me if I did it right or what I did wrong I would be EXTREMELY thankful!

- Lliam

2. ## Re: Could someone please check my math on this question involving equivalent rates?

This question has been solved here: Could someone please check my math?

- Lliam


text:
unicode-transforms-0.3.5: Unicode normalization

Data.ByteString.UTF8.Normalize

Description

Deprecated: Convert ByteString to Text and then normalize

Unicode normalization for ByteString data type.

Synopsis

# Normalization Modes

Normalization transforms Unicode text into an equivalent composed or decomposed form, allowing for easier sorting and searching of text. Standard normalization forms are described in http://www.unicode.org/unicode/reports/tr15/, Unicode Standard Annex #15: Unicode Normalization Forms.

Characters with accents or other adornments can be encoded in several different ways in Unicode. For example, take the character A-acute. In Unicode, this can be encoded as a single character (the "composed" form):

     00C1    LATIN CAPITAL LETTER A WITH ACUTE

or as two separate characters (the "decomposed" form):

     0041    LATIN CAPITAL LETTER A
0301    COMBINING ACUTE ACCENT

To a user of your program, however, both of these sequences should be treated as the same "user-level" character "A with acute accent". When you are searching or comparing text, you must ensure that these two sequences are treated equivalently. In addition, you must handle characters with more than one accent. Sometimes the order of a character's combining accents is significant, while in other cases accent sequences in different orders are really equivalent.

Similarly, the string "ffi" can be encoded as three separate letters:

     0066    LATIN SMALL LETTER F
0066    LATIN SMALL LETTER F
0069    LATIN SMALL LETTER I

or as the single character

     FB03    LATIN SMALL LIGATURE FFI

The "ffi" ligature is not a distinct semantic character, and strictly speaking it shouldn't be in Unicode at all, but it was included for compatibility with existing character sets that already provided it. The Unicode standard identifies such characters by giving them "compatibility" decompositions into the corresponding semantic characters. When sorting and searching, you will often want to use these mappings.

Normalization helps solve these problems by transforming text into the canonical composed and decomposed forms as shown in the first example above. In addition, you can have it perform compatibility decompositions so that you can treat compatibility characters the same as their equivalents. Finally, normalization rearranges accents into the proper canonical order, so that you do not have to worry about accent rearrangement on your own.

The W3C generally recommends to exchange texts in NFC. Note also that most legacy character encodings use only precomposed forms and often do not encode any combining marks by themselves. For conversion to such character encodings the Unicode text needs to be normalized to NFC. For more usage examples, see the Unicode Standard Annex.

Constructors

 NFD Canonical decomposition. NFKD Compatibility decomposition. NFC Canonical decomposition followed by canonical composition. NFKC Compatibility decomposition followed by canonical composition.
Instances
 Source # Instance detailsDefined in Data.Unicode.Types Methods Source # Instance detailsDefined in Data.Unicode.Types Methods Source # Instance detailsDefined in Data.Unicode.Types MethodsshowList :: [NormalizationMode] -> ShowS #

# Normalization API

Perform Unicode normalization on a UTF8 encoded ByteString according to the specified normalization mode.


text:
# Gravitational time dilation

1. Jan 6, 2007

### actionintegral

Hello,

I am trying to learn about Gravitational Time Dilation. I came across the following formula for time dilation in a uniform gravitational field:

$$T_d = {1-} \frac{gh}{c^{2}}}$$

but I cannot find any derivation for this. Can someone point me in the right direction?

Thanks

Last edited: Jan 6, 2007
2. Jan 6, 2007

### cristo

Staff Emeritus
Take a look at http://hyperphysics.phy-astr.gsu.edu/hbase/relativ/gratim.html

Now, the time dilation factor you state above is $$\sqrt{1-\frac{2gh}{c^2}$$ (It's equal to T0/T, in the above link).

Using the binomial theorem $$\sqrt{1+x}=1+\frac{1}{2x}+\cdots$$

And hence, we obtain the result above $$T_d=1-\frac{gh}{c^2}$$

3. Jan 6, 2007

### Chris Hillman

cristo should have explained why we are supposed to take $2m/r = 2gh$ (in relativistic units in which G=c=1) in the Schwarzschild vacuum.

This takes some explaining! The idea is obvious enough: in a small box near the surface [itex]r=r_0[/tex] of a spherical massive isolated object, with the exterior gravitational field modeled by the Schwarzschild vacuum, right down to the surface, the "gravitational acceleration" is the acceleration of static observers sitting on the surface, which is radially outward with magnitude [itex]m/r^2[/tex], the same expression as in Newtonian gravitation, where needless to say I am using the exterior Schwarzschild coordinate chart. So the needed explanation concerns the "small box". I'll let readers think about that...

The notion of a "uniform gravitational field" in gtr is actually rather tricky. Since actionintegral didn't cite his source, I don't know if he misread something, or if the author was too careless to mention caveats (or wanted to avoid confusing his students), or if the source is a bad one (very possible for websites by someone who is not an acknowledged expert in gtr).


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# KS5. Coordinate Geometry

As you have learned previously, coordinate geometry was the brainchild of Rene Descartes (1596-1650), creating a permanent link between the topics of Euclidean geometry and algebra, both of which had previously been seen as separate unrelated topics. Below is the cover of the text he published introducing coordinate geometry.

In our AS level course, we will learn to understand and apply some algebraic formulae to represent lines and circles in cartesian space.

Given two points in cartesian space, we need to be able to find the following properties of the line segment joining them:

• Length;
• We can derive a formula for this by using Pythagoras’ Theorem;
• The gradient is the amount of units by which the line goes up for every 1 unit it goes across. Another way of saying this is the difference between the y-axis coordinates divided by the difference between the x-axis coordinate. This leads straight to the relevant formula;
• Midpoint.
• The midpoint between two coordinates has an x coordinate which is the average of the two x coordinate values, a y coordinate which is the average of the two y coordinate values.

Relevant formulae to copy down and memorise

$d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$

$M=( \frac{x_1 + x_2}{2} , \frac{y_1+y_2}{2} )$

$m = \frac{y_2 - y_1}{x_2 - x_1}$

Example

For each of the following pairs of points, calculate the length, gradient and midpoint of the line segments joining them:

1. (1,1) and (4,5);
2. (1,1) and (-4,-5);
3. (-1,0) and (-3,-5); and
4. (1,5) and (-3,-5).

Exercise

(14.) A triangle has vertices A:(-2,1), B:(3, -4) and C:(5,7)

(a.) Find the coordinates of M, the mid-point of AB, and N, the midpoint of AC.

(b) Show that MN is parallel to BC.

(15.) The points A:(2,1), B:(2,7) and C:(-4,-1) form a triangle. M is the midpoint of AB and N is the midpoint of AC.

(a) Find the lengths of MN and BC;

(b) Show that BC = 2MN.

(19.) The vertices of a quadrilateral PQRS are P(1,2), Q(7,0), R(6,-4) and S(-3,-1).

(b.) What type of quadrilateral is PQRS?

Solutions

Equation of a line – parallel and perpendicular lines

Given 2 points on a line, or 1 point and the gradient of the line, we need to identify the equation of the line. This equation then lets us calculate the coordinates where the line intersects axes, or where two lines intersect each other.

Relevant formulae to copy down and memorise

$y - y_1 = m(x - x_1)$

$y - y_1 = \frac{y_2 - y_1}{x_2 - x_1}(x - x_1)$

Examples (give all answers in the form: y=mx+c)

• Find the equations of the following lines:
• Passing through (4,5) with gradient 2;
• Passing through (-4,-5) with gradient 1/3; and
• Passing through (1/2, -1/3) with gradient -6.
• Find the equations of the lines with the following end-points:
• (1,0) and (3,5);
• (1,0) and (-3,-5);
• (-1,0) and (-3,-5); and
• (1,5) and (-3,-5)

We need to understand what parallel lines are, what perpendicular line are, and to calculate the gradient of one line from another if the two lines are parallel or perpendicular.

If we know the equations of two lines, we need to be able to find the coordinates of the point where they intersect.

Example

• Find the point of intersection of the following two lines:
• y = 2x+3; and
• 3x + 2y = 13.

Take care to always calculate both coordinates!!!

Exercise – Equation of a Line

Circles

Everything above has been about lines. Let’s think now about a slightly more difficult shape, a circle.

What is our standard definition of a circle (in Euclidean geometry)?

How can we adopt this definition to make it applicable to coordinate geometry?

In the above diagram (a,b) is the centre and (x,y) is any point on the circumference of a circle with radius r.

By Pythagoras’ Theorem, CL2+LP2=r2, and so we have the following which is the general formula for the equation of circle:

(x-a)2+(y-b)2=r2.

This formula must be memorised!!

Example

Find the centre and the radius of a circle whose equation is 3x2+3y2-5x-6y+4=0

Exercise

Solutions

Intersection of lines and circles

We can find the intersection points by solving simultaneous equations.

We do this by substituting the linear equation into the quadratic equation.

Note: If the equations have only one solution, then the line is a tangent.  If they have no solutions then they don’t intersect.

Examples

Exercise

Solutions

General coordinate geometry practice exercise

Solutions to general coordinate geometry practice exercise


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# Calculate the mass, in grams, of 2.54 times 10^{-2} mol of CdS.

## Question:

Calculate the mass, in grams, of {eq}\rm 2.54 \times 10^{-2}\ mol {/eq} of {eq}\rm CdS {/eq}.

## Finding Molar Mass of Compounds

The molar mass of an element can be directly obtained from a periodic table. It is typically given in units of g/mol. For compounds however, where two or more elements are chemically combined together, it is necessary to compute the molar mass by adding up the atomic masses of each of the elements, taking into consideration how many atoms are there in the molecule.

The molecule of interest is cadmium sulfide, CdS. The atomic mass of cadmium (Cd) is 112.4 and that of sulfur (S) is 32.1. Hence, the molar mass of this compound is:

{eq}112.4 + 32.1 = 144.5 \ g/mol {/eq}.

Now, we have {eq}2.54 \times 10^{-2} \ mol {/eq} of the compound. Its mass, in grams, would be:

{eq}2.54 \times 10^{-2} \ mol \times 144.5 \ g/mol = 3.67 \ g {/eq}.


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Tag Info

11

Substituting $t=|\frac {x-3}{x+1}|$ will help. Can you see it?

8

Note that $$\frac{1}{i+1}+\frac{1}{k-i+1}=\frac{k+2}{(i+1)(k-i+1)}$$ So, (because $(a+b)^2\leq 2a^2+2b^2$): $$\frac{(k+2)^2}{(i+1)^2(k-i+1)^2}\leq\frac{2}{(i+1)^2}+\frac{2}{(k-i+1)^2}$$ Adding we get $$\sum_{i=0}^{k}\frac{(k+2)^2}{(i+1)^2(k-i+1)^2} \leq 4\sum_{i=0}^{k}\frac{1}{(1+i)^2}\leq 4\zeta(2)=\frac{2\pi^2}{3}$$ So $$... 6 Using the substitution a=\frac xy, b=\frac yz and c=\frac zx, we want to prove that$$ \sum_{cyc}\frac {xy}{z^2}\geq \frac xy+\frac yz+\frac zx $$where we are taking cyclic sums. Using AM-GM, we find that$$ \frac{\frac{xy}{z^2}+\frac{xz}{y^2} +\frac{xz}{y^2}}3 \geq \sqrt[3]{\frac{x^3}{y^3}}=\frac xy $$Applying this three times yields the required ... 5 For any C, one can always find an X such that \det(X+iC)=0 : if C is not invertible, simply take X=0. If C is invertible, take X=CA where A is any real matrix having a two-dimensional invariant subspace {\sf span}(v_1,v_2) with Av_1=v_2, Av_2=-v_1 (so that \pm i are eigenvalues of A). Then$$ ...

4

Define the following two vectors \begin{align} \textbf{a}&=(a_1,a_2,...,a_n),\\ \textbf{b}&=(b_1,b_2,...,b_n) \end{align} the dot product is defined such that $|\textbf{a}\cdot \textbf{b}|^2 = |\textbf{a}|^2|\textbf{b}|^2\cos^2\theta$ where $\theta$ is the angle between the two vectors $\textbf{a}$ and $\textbf{b}$. So the desired condition holds if ...

4

Observe that $\frac{1}{n}$ is decreasing $(1)$. $$\int\limits_{1}^{n}{\dfrac{1}{x} \, dx}=\int\limits_{1}^{2}{\dfrac{1}{x}\, dx}+\int\limits_{2}^{3}{\dfrac{1}{x}\, dx}+\cdots +\int\limits_{n-1}^{n}{\dfrac{1}{x}\, dx} \tag{2}$$ For an integrable function $f$, if $m \le f(x)\le M \quad \forall x\in [a,b]$ then $$m(b-a)\le\int\limits_{a}^{b}{f(x) dx} \le ... 4 Hint (for a start):$$t = \frac{x-3}{x+1}$$4 Note that$$ (n!)^2 = \prod_{i=1}^n i(n+1-i) \ge \prod_{i=1}^n n = n^n $$Hence n! \ge n^{n/2}. This gives$$ (2n)! \ge (2n)^n = 2^n n^n $$For n \ge 2 we have 2^n \ge n^2, hence (2n)!\ge n^{n+2}. 4 Hint: Consider f(x)=\frac{\sqrt 2}{2}\sin x- e^x+1. Note that f(0)=0. Now Find f'(x). Then conclude. 3 If (k-1)<\log_2n\le k, i.e. 2^{k-1}< n\le 2^k, then a_{2^{k-1}}\le a_n\le a_{2^k}\le ka_2 (by nondecreasing and your result). We conclude that$$ a_n\le a_2\cdot \lceil \log_2 n\rceil \le a_2(\log_2n+1)\le 2a_2\log_2n$$where the last step uses \log_2 n\ge1 (from n\ge 2) and a_2\ge 0. 3$$\left(\frac{x-3}{x+1}\right)^2-7 \left|\frac{x-3}{x+1}\right|+ 10 \lt 0 \Rightarrow \\ \left(\left|\frac{x-3}{x+1}\right|\right)^2-7 \left|\frac{x-3}{x+1}\right|+ 10 \lt 0 \Delta=\left(-7\right)^2-4 \cdot 10=49-40=9\left|\frac{x-3}{x+1}\right|_{1,2}=\frac{-\left(-7\right) \pm \sqrt{\Delta}}{2}=\frac{7 \pm \sqrt{9}}{2}=\frac{7 \pm 3}{2}$$... 3 Step 1. Prove that$$ x^2+yz+x+1\geq x(x+y+z+1) $$by using the expansion of (x-y-z)^2\geq 0 and x^2+y^2+z^2=2. Step 2. Observe that$$ x+y+z\leq\sqrt{2(x^2+(y+z)^2)}=2\sqrt{1+yz} $$Step 3. By Step 1, we have$$ P\leq\frac{x^2}{x(x+y+z+1)}+\frac{y+z}{x+y+z+1}-\frac{1+yz}{9}=1-Q $$with$$ Q=\frac{1}{x+y+z+1}+\frac{1+yz}{9}. $$By step 2 we have$$ ...

3

The unit circle is parametrized by $\theta\mapsto(\cos\theta,\sin\theta)$: $\hskip 1.5in$ Consider an angle $0\le\theta\le\frac{\pi}{2}$, as depicted above. The red line's length is $\theta$, and $\sin\theta$ is the purple length. Since they both travel the same vertical distance but the red one also travels horizontal distance, the red line is longer, ...

2

http://en.wikipedia.org/wiki/Hoeffding%27s_inequality gives a way to bound the difference between $\frac{1}{\sqrt{3}}$ and the given integral. If we take $X_1,\ldots,X_n$ as indipendent random variables with a uniform distribution over $[0,1]$, then $X_1^2,\ldots,X_n^2$ are bounded indipendent random variables with density function $$... 2 The evaluation of limit is essentially same as here. We have, \displaystyle \lim\limits_{n\to\infty}\int_{0}^{1}\cdots\int_{0}^{1} \left(\dfrac{x_{1}^2+x_{2}^2+\cdots+x_{n}^2}{n}\right)dx_{1}dx_{2}\cdots dx_{n}=\dfrac{1}{3} We can show \displaystyle \lim\limits_{n\to\infty}\int_{0}^{1}\cdots\int_{0}^{1} ... 2 To be 100% vigorous with the proof, you'd need to show that k^3 > 2k +1 for k>4. And since it's an easy one, go ahead and do it with induction again. Otherwise, you're 100% spot on with your induction. Note that you don't need to use strong induction. Weak induction would suffice. It only needs to hold for k into order to prove k+1. But that ... 2 When t \equiv \frac{x-3}{x+1} > 0, the solution to  t^2 - 7t + 10 <0 is  2<t<5. (Factor the quadratic.) When t < 0, the solution to  t^2 + 7t + 10 <0 is  -2<t<-5. On the t < 0 branch, we need to solve -2 < \frac{x-3}{x+1} < 5. We break this up into two possibilities, x < -1 and x > -1, because ... 2 To prove the first inequality it suffices to prove that (x+y)^{p}\le x^{p}+y^{p} for x,y\ge0 and p\in(0,1). Notice that we can use this as follows: \vert x\rvert^{p}\le\lvert x-y\rvert^{p}+\lvert y\rvert^{p} then reversing the roles of x and y. Notice that this Lemma can be proven by reducing to the case when y=1 then looking at ... 2 Hint: 1) From (\frac{a+b}{2})^2\le\frac{a^2+b^2}{2} verify that (k+1)^2 < 2[(i+1)^2+(k-i+1)^2], 2) \sum_{n\ge 1}\frac{1}{n^2} = \frac{\pi^2}{6}. 2 One can forget p(s), r(s) and the rest and simply try to show that, for every a\lt b,$$\|u\|_a\leqslant\|u\|_b.$$To wit, considering v=|u|^a and p=b/a\gt1, note that Hölder inequality yields$$ \int |u|^a=\int v\leqslant\left(\int v^p\right)^{1/p}=\left(\int |u|^b\right)^{a/b}, $$that is,$$ \left(\int |u|^a\right)^{1/a}\leqslant\left(\int ...

2

First, note that next recurrent relation is true for sequence $(a_n)$: $$a_0=1,\\ a_{n+1} = a_n+\frac{1}{a_n}, \qquad n\ge 0.\tag{1}$$ Yes, $a_0=1$, $a_1 = 1+\frac{1}{1}=2$ for both definitions; if $a_{n+1}$ is defined by $(1)$, then $$a_{n+1} = a_n+\dfrac{1}{a_n} = a_n + \dfrac{1}{a_{n-1}+\frac{1}{a_{n+1}}} = a_n + \dfrac{a_{n-1}}{1+a_{n-1}^2}, \qquad ... 2 A proof just with Cauchy-Schwarz: From Cauchy-Schwarz, one have that$$ (\sum_i \frac{1}{x_i})(\sum_i \frac{x_i}{i^2}) \ge (\sum_i \frac{1}{i})^2. $$But since \sum_i \frac{1}{x_i} \le \sum_i \frac{1}{i}, one have that$$ \sum_i \frac{x_i}{i^2} \ge \frac{(\sum_i \frac{1}{i})^2}{\sum_i \frac{1}{x_i}} \ge \frac{\sum_i \frac{1}{i}}{\sum_i \frac{1}{x_i}} ...

2

There is one step that is not (always) valid. The inequality $$x^2 + (k+1)xy \geqslant \frac{1}{x}(x^2+(k+1)xy)$$ only holds for $x+(k+1)y \geqslant 0$, if $x > 1$. If $x+(k+1)y < 0$ and $x > 1$, you have a strict inequality in the other direction, $$x^2 + (k+1)xy < \frac{1}{x}(x^2+(k+1)xy).$$ However, in that case, the desired inequality ...

2

First of all: you cannot take derivatives (and even if so, your middle one is incorrect) to preserve inequalities. That said, let's go over it: 1) It is enough to show that $\sin x\le x$ when $x\ge 0$ because $\sin x$ is an odd function, so for $x<0$ write $-y=x$ whence the first inequality implies $$-\sin -y \le y\iff \sin(-y)\ge -y\iff \sin x\ge x$$ ...

2

For any $k\geq 1$ we have: $$(2^{k+3}-1)(2^{k+2}-1)=2^{2k+5}-3\cdot 2^{k+2}+1\leq16(2^{2k+1}-1)$$ and for any $k\geq 3$ we have: $$3(2k+1)\geq 16,$$ hence we have to check only the cases $k=1,2$.

2

I think you are doing a mistake here. $\sin(x)+\cos(y)+\tan^2(y)+\cot^2(x)+5 = (\sin(x)+ \csc^2(x)) + (\cos(y)+ \sec^2(y))+ 3$ . Not, what you have written. Considering that to be a typo, Notice that the things in the bracket are independent, so we just find minimum value of each separately. Consider $f(x)=\sin(x)+\csc^2(x) \ge \sin(x)+\csc(x) \ge 2$. ...

2

Taken literally, property (2) does not imply (1). Indeed, let $f(x)=-1$ if $|x|=1$ and $f(x)=0$ otherwise. Then (2) holds but (1) fails for $x=0$ and $r=1$. But generally, one considers locally integrable functions up to equivalence a.e. And property (2) implies that $f$ agrees a.e. with a subharmonic function, for which (1) holds by definition. Here are ...

1

By the Rearrangement Inequality (but we don't need anything that general) the left side is minimized, for fixed $x_i$, if the $x_i$ are increasing. And then the minimum is reached if the $x_i$ are as small as possible, which gives $x_i=i$. Remark: If we don't want to quote the Rearrangement Inequality, it is clear that if $i\lt j$ and $x_i \gt x_j$, then ...

1

first we check $abc=0$,if $a=0 ,\implies 2\sqrt{bc}\le b+c$,it is true.the "=" will hold when $b=c$ in case $abc \not=0$ let $c=Max${$a,b,c$}, we discuss two cases: $a^2+b^2+c^2 \ge 2(ab+bc+ac) \implies c\ge a+b+2\sqrt{ab} \implies ab \le \dfrac{c^2}{16}$ LHS $\le\sqrt{a^2+bc}+\sqrt{b^2+ac}+\sqrt{c^2+\dfrac{c^2}{16}}\iff ... 1 I propose that the question has a typo and that the inequalities in the index of the summation cannot be strictly less than and need to be less than or equal to. Here is why. Consider the case where$n=2$and$r=3$. Clearly, the left hand side is an application of binomial theorem and we have$a_1^3+3a_1^2a_2+3a_1a_2^2+a_2^3\$ The right hand side is (from ...

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text:
Math/CS Home People Faculty and Staff Alumni Prospective Students Request Information Apply Online Now Academics Preparation Majors Mathematics Math/Economics Math/Physics Computer Science Minors Mathematics Applied Mathematics Statistics Computer Science Courses Mathematics Computer Science Schedule Colloquium Series Off-Campus Opportunities Quantitative Skills Center Awards and Activities Transfer Credit Organizations Kappa Mu Epsilon Information News Calendar Facilities Careers Links Mission Giving

## 2018-2019 Academic Year Colloquium Schedule

 Submit Item (Faculty/Staff Only)

### September 13, 2018

 Title: Casino Carnival Games: Past, Present, and Future Speaker: Mark Bollman Professor of Mathematics Mathematics and Computer Science Albion College Albion, MI Abstract: Beyond the "big four" casino table games of baccarat, blackjack, craps, and roulette, over 1000 different games have been designed, proposed for casino use, and approved by the state of Nevada. In this presentation, we shall look at the math behind some of the games that have fallen by the wayside and at the mathematical issues that arise in designing a new game of chance. An opportunity to investigate the mathematics behind a new game proposal will be announced. Location: Palenske 227 Time: 3:30 PM Citation Click for BibTeX citation

### September 20, 2018

 Title: Planning for Graduate Study in Mathematics and Computer Science Speaker: David A. Reimann Professor Mathematics and Computer Science Albion College Albion, Michigan Abstract: A degree in mathematics or computer science is excellent preparation for graduate school in areas such as mathematics, statistics, computer science, engineering, finance, and law. Come learn about graduate school and options you will have to further your education after graduation. Location: Palenske 227 Time: 3:30 Citation Click for BibTeX citation

### September 27, 2018

 Title: Reducibility and Balanced Intransitive Dice Speaker: Michael Ivanitskiy1 and Michael A. Jones2 1University of Michigan; 2Mathematical Reviews Ann Arbor, MI Abstract: We will review some results about balanced intransitive $n$-sided dice and what it means for a set of dice to be reducible based on a concatenation operation. Using data from the Online Encyclopedia of Integer Sequences, the lexicographical ordering of dice, and permutations, we are able to construct new integer sequences representing the number of $n$-sided reducible and irreducible dice. We define a notion of margin and explain how margins are effected by concatenation. We introduce a new splicing operation that generalizes concatenation and give conditions for when the resulting dice are balanced and irreducible. Finally, we construct new integer sequences for the number of fair, balanced dice and the largest margins for $n$-sided, balanced intransitive dice. Bonus: You will either get to make or will be given a set of balanced, intransitive dice. Location: Palenske 227 Time: 3:30 PM Citation Click for BibTeX citation

### October 4, 2018

 Title: Multi-Lens Analysis of Office Dynamics and Space Usage Speaker: Angela Morrison, '17 Graduate Student Mathematics Michigan State University East Lansing, Michigan Abstract: Workplace optimization is critical for organizations to make the most of their real estate as well as help employees stay more productive at work. Steelcase Space Analytics equips organizations with tools and data needed to measure and improve the effectiveness of the workplace by applying their proprietary sensing capability. This project aims to analyze office space dynamics and usage by investigating correlations between and within sensing and survey datasets sourced from Steelcase's 2 West (2W) facility. The data consists of sensor output that describes how often spaces are in use, as well as survey data that reports how the 2W employees feel about using certain spaces. Clustering analysis was developed to study the hidden trends of the sensor data and generalized linear mixed model (GLLM) was constructed to investigate the correlations between the sensor data and space traits data. The results showed that the significant space traits indicated by the GLMM were also the popular ones from survey data analysis. Location: Palenske 227 Time: 3:30 PM Citation Click for BibTeX citation

### October 11, 2018

 Title: Spherical Panoramic Photographic Polyhedra Speaker: David A. Reimann Professor Mathematics and Computer Science Albion College Albion, Michigan Abstract: Conventional cameras view a small solid angle, limiting the both the field of view and projective distortion. However, multiple individual pictures are need to have full spherical coverage. Cameras that can directly take spherical panoramic photos, such as the Ricoh Theta~S, have become available as relatively inexpensive consumer products. Unlike a traditional camera, this camera has two hemispherical lenses, allowing it to see simultaneously in every direction around the camera. These cameras produce an equirectangular projection, where each latitude row has the same number of pixels, which has severe distortion at the poles. One approach to hardcopy display is to map the image onto the surface of a small polyhedron, such as a Platonic or Archimedean solid, which reduces the distortion. Using such polyhedra resembles the process artist Dick Termes uses for painting on a sphere, which he calls a Termesphere. These techniques force the viewer to see the world inside-out. This work maps the spherical photo to the inside of a large polyhedra to create a miniature pavilion which can be entered for a personal panoramic experience. Other interesting applications and issues will be discussed. Location: Palenske 227 Time: 3:30 PM Citation Click for BibTeX citation

### November 15, 2018

 Title: The Geometry of Polynomials Speaker: Matt Boelkins Professor of Mathematics, Grand Valley State University Mathematics Grand Valley State University Allendale, MI Abstract: In the geometry of polynomials, we seek to understand relationships among certain sets connected to polynomial functions. For example, Marden's Theorem reveals stunning connections between the critical numbers of a cubic polynomial with complex zeros and the inscribed in-ellipse of the triangle whose vertices are the polynomial's zeros. In this talk, we'll discuss several important historical results from the geometry of polynomials and survey developments in the past 25 years that are centered on polynomial root-dragging, the study of how continuously changing one or more roots of a polynomial function affects various properties of the function. We will encounter some surprising structural results about polynomial functions that deserve to be more well-known and also see beautiful interplay between calculus and Euclidean geometry. Location: Palenske 227 Time: 3:30 PM Citation Click for BibTeX citation


text:
To display formula inside a box or frame, we must use \boxed function of amsmath package: \usepackage{amsmath} For exemple: \parbox[pos][height][contentpos]{width}{text}, width defines the width of the paragraph box. A visible element can be a letter, image, geometric shape, etc. See my code snippets section under figures for code examples. Creative Commons Attribution-ShareAlike License. LaTeX’s defaults are 0.4pt and 3pt, respectively. You can add a simple frame to an image or to text by using the \frame{...}, \framebox{...}, or \fbox{...} commands. Abstract. enatibus Aliquam tesque mauris. TeX builds pages by gluing boxes together according to the default TeX rules, default LaTeX rules, or document commands. Often, figures have a white background which makes the figure border invisible on white paper. To make the table more readable, following are the ways to color it: Welcome to a teeny tiny corner of the vast interwebs. mbox is the shorthand no-option version of Makebox. This is only useful if the content contains manual line breaks and you wish to fit the resulting material. To add a line the command \draw[gray, thick] defines a graphic element whose colour is gray and with a thick stroke. To add a border to a figure, we simply use the frame option. Often, figures have a white background which makes the figure border invisible on white paper. From Wikibooks, open books for an open world, Scientific Reports (Bachelor Report, Master Thesis, Dissertation), http://www.personal.ceu.hu/tex/spacebox.htm, https://en.wikibooks.org/w/index.php?title=LaTeX/Boxes&oldid=3693573. Such extensions are configured using a block within the tex configuration of your MathJax configuration object. The solution that I have right now is along the line \begin{center} \makebox[\textwidth]{ %am putting it inside a makebox for the ... colorbox around whatever, you jut … Configuring TeX Extensions¶. An example is shown below: Note that the width does not have be wider than the contents: for instance, setting width to 0 typesets the content without changing the current position. (E.g., this would allow for an overstrike.) The following commands placed at the beginning of an article document will set the header of all pages (one-sided) t… A visible element can be a letter, image, geometric shape, etc. Now that we control the horizontal, the obvious next step is to go for the vertical. TeX builds pages by gluing boxes together according to the default TeX rule… Similarly, we can add a border to subfigures. The two optional parameters set for the height and depth of the raisebox. LaTeX Project Public License 1.3c. However, this would give a simple box with thin black lines and a certain distance to the content. enatibus This prints a thick and more distant frame: The framed package is available that adds the framed environment which provides an an easy way to frame a paragraph within a document: A savebox is a non-rendered box that is saved for later repeated rendering via the usebox command. Some extensions have options that control their behavior. There are often workarounds for these limitations. As we are drawing a line that ends up in the same place we started, it is better to finish the statement with the key… Use dollar symbols around the text, for example, use '$\int_1^{20} x^2 dx$' for inline mode or '$$\int_1^{20} x^2 dx$$' for display mode. Note that contentpos has no effect if the box is not larger than the text it contains. In this example two lines and one point are drawn. The graphicx package features additional boxes. One of the simplest and most commonly used commands in TikZ is the \drawcommand. Sorry, your blog cannot share posts by email. Example. No problem for LaTeX. Great day! The colour of a second … (adsbygoogle = window.adsbygoogle || []).push({}); Need help with your thesis or book project? A more complete description of boxes and glue can be found in chapters 11 and 12 of Donald E. Knuth's, 'The TeXbook'. We then finish the statement by closing it with a semicolon. \begin{minipage}[pos][height][contentpos]{width} text \end{minipage}. Both packages provide a common set of commands for colour manipulation, but the latter is more flexible and supports a larger number of colour models so is the recommended approach. Appearance is controlled through CSS so it can be restyled. The size of a box is typically related to the size and position of its contents, but it doesn't have to be. For example, the color extension allows you to set the padding and border-width used for the \colorbox and \fcolorbox macros. In paragraph mode, text is broken into lines and lines are broken into pages. The pos parameter takes a one letter value: center, flushleft, flushright, or spread the text to fill the box. A box is the TeX term for an invisible container that can hold a visible element, nothing, or other boxes. The idea behind the minipage command is that within an existing page "built in" an additional page. The symbol % tells the LaTeX when to ignore the rest of the line. amsmath Latex \boxed. Hope this eases the TikZ-ing! A \pbox has the same parameters as a \parbox, but if the user provided width parameter is larger than the actual contents of the pbox the pbox shrinks to fit the content. The \fcolorbox commands use the same parameters as \fbox (see \fbox & \framebox ), \fboxrule and \fboxsep, to set the thickness of the rule and the boundary between the box interior and the surrounding rule. It can be top, bottom, or center. The main motivation for this blog post is to highlight what customizations I did to generate pdf and epub versions for self-publishing my ebooks. Can be extended with callbacks & event-hooks without altering the source files. \boxed. The image is copied to your pictures folder and automatically added to your website gallery. A table of contents will automatically be created, complete with Multi-column and multi-row cells in LaTeX tables, Control the width of table columns (tabular) in LaTeX. command lets you define the vertical properties of a box. You can add color to a row in a table by inserting a package command in the table. See Colors. Besides fixed lengths, you can also provide user defined length macros or TeX/LaTeX defined length macros and primitives such as \width, \height, \depth and \totalheight. latex documentation: Coloring Table. I tried changing the border settings in the css file, but it didn't help. 2 4.22 wisi. Both packages provide a common set of commands for colour manipulation, but the latter is more flexible and supports a larger number of colour models so is the recommended approach. The simplest manner to use colours in your LaTeX document is by importing the package color or xcolor. Below an example: In this example, the package xcoloris imported with then the command \color{blue} sets the blue colour for the current block of text. This page was last edited on 28 May 2020, at 01:27. the command \savebox stores the specified content in the placeholder without rendering it in the document; and \usebox renders the content of the placeholder into the document. It can be one of center, top, bottom or spread. In this case for the itemizeenvironment. 3. Text will be broken into lines so that it fits within this width. LaTeX forum ⇒ Text Formatting ⇒ Color Box Formatting Information and discussion about LaTeX's general text formatting features (e.g. The package provides an environment for coloured and framed text boxes with a heading line. Let’s discuss. If the contentpos is present and not the same as pos and pos is not center, the \parbox will align at its borders. Under any of these circumstances the alignment parameter selects which line of text within the \parbox will be used to align the paragraph box. How to make nice-looking framed boxes in LaTeX articlesExamples of framed, mdframed, fancybox and bclogo packages Vesa Linja-aho Metropolia July 29, 2011 Vesa Linja-aho How to make nice-looking framed boxes in LaTeX articles 2. I know, from the doc and from other questions on this stackexchange, that nesting breakable boxes can create problem, but I don’t remember having read ~ Nesting tcolorbox changes border style To draw a straight line we use this command, then we enter a starting co-ordinate, followed by two dashes before the ending co-ordinate. Another common use case is the setting of theorems. There are two commands available: \pagestyle{''style''} will apply the specified style to the current and all subsequent pages, and \thispagestyle{''style''}will only affect the current page. This package provides an environment for coloured and framed text boxes with a heading line. A box is the TeX term for an invisible container that can hold a visible element, nothing, or other boxes. As you can see, the border shows up on the top and left, but not on the bottom or right. The command \newsavebox creates a placeholder for storing content; For instance you can observe the difference when embedded in a framebox. A \parbox is a box of specific width formatted in paragraph mode. Many box commands accept custom widths and/or heights, and there are other commands that affect the shape and position of boxes. In this case for the itemizeenvironment. pos selects which baseline to join. Lightweight: 10KB of JavaScript (less than 5KBs gzipped). #5 Erik, February 23, 2010 at 9:17 p.m.. wow, you guys are too good at this! The adjustbox package scales, resizes, trims, rotates, and also frames LaTeX content. To do alternating row colors, you can also include the xcolor package with the table option (i.e. or-accumsan a massa. enatibus Aliquam tesque mauris. \usepackage[table]{xcolor}), and immediately preceding the tabular environment use the command \rowcolors{start}{color1}{color2} — this will produce a table with colored rows, starting at the row indicated by start, with odd rows colored color1 and even rows colored color2. While it is true that boxes can hold other boxes, not all commands that can generate boxes can be used within all other commands that can generate boxes. The line is actually defined by it's two endpoints, (-1,2) and (2,-4), joined by --. Either you've already heard of pandoc or if you have searched online for markdown to pdf or similar, you are sure to come across pandoc.This tutorial will help you use pandoc to generate pdf and epub from a GitHub style markdown file. Figure with border in LaTeX. Thus, if the pos is set top, the baseline of the top line of text in the \parbox will line up with the baseline outside of the \parbox. A list of basic LaTeX box and glue commands can be found at http://www.personal.ceu.hu/tex/spacebox.htm . LaTeX minipage. This module may require a complete rewrite in order to suit its intended audience. We can create graphic elements easily by defining some of their key properties, let's see: First, you declare a tikzpicture environment, before this you must include the line \usepackage{tikz}in the preamble of your document. If a figure has several disconnected elements, it looks better to delimit them with a frame around figure. Each separate visible element contained within a TeX document is contained within a box. online LaTeX editor with autocompletion, highlighting and 400 math symbols. I wonder if I can change the border color of my color box. 5. In the special case of a parbox that has only one line of text, that one and only line of text is the top, bottom, and center line of text simultaneously, and changing pos will appear to do nothing unless additional text is added. 4. Elastic glue is squeezed or stretched to fully justify lines within paragraph boxes. We can then add more co-ordinates in like this to make it a square: However this isn't particularly good style. TeX character boxes have three dimensional properties: Character boxes are glued together at the baseline. For example, two pictures side by side, two tables next to a text or a picture or vice versa. The \parbox is placed so the baseline of that chosen line of text is aligned to the baseline of the box that the \parbox is glued to. Load the adjustbox package with the export option to make functions available to the \includegraphics command (graphicx package). The multi – line comments are written using the package verbatim. I have gone through the code and see that there is a attribute #cboxMiddleLeft: contentpos positions the contents of the box within the box. Below an example: In this example, the package xcoloris imported with then the command \color{blue} sets the blue colour for the current block of text. 12345 Released under the MIT License, source on Github (changelog) Download Compatible with: jQuery 1.3.2+ in Firefox, Safari, Chrome, Opera, Internet Explorer 7+ 1. You cannot place line breaks (\\) within a Makebox. To use LaTeX markup, set the interpreter to 'latex'. This parameter is often confusing to new users! Colortbl implements LaTeX support for color when the active dvi driver can produce colored text. Hi I am using colorbox throughout my web application. In the course of that I need to make a box at the top with a different colored border. or-accumsan a massa. TeX - LaTeX: I have a box with a modified border style, but when I nest two of such boxes, the style of the inner one is not the one that I set. Beamer Tutorial About Beamer Advantages of Beamer The standard commands of LATEX also work in Beamer.If you can write basic LATEX, you can easily make a Beamer presentation. 20. The minipage environment takes the same parameters as a \parbox, and behaves nearly identically to it. Export (png, jpg, gif, svg, pdf) and save & share with note system Supports photos, grouping, slideshow, ajax, inline, and iframed content. Latex Colorbox Rounded Corner will now include these pictures. LaTeX Markup. You can make use of minipage, \parbox, and \pbox to embed paragraphs in non-paragraph boxes. The following example shows you some things you could do with the \makebox and \framebox commands: You can tweak the following frame lengths. or-accumsan a massa. The options for \parbox (except for contents) are the same as those for minipage.For convenience a summary of the options is here but see minipage for a complete description. Completely unobtrusive, options are set in the JS and require … For instance: The pos alignment parameter does not refer to the \parbox's borders when contentpos is either missing or equal to pos and anytime pos= center! Each separate visible element contained within a TeX document is contained within a box. 1 4.22 wisi. Makebox creates a single-line box, optionally of fixed width, but otherwise large enough to hold its contents. 2. bold, italic, enumerations, ...) 5 posts • Page 1 of 1 You can use \width, \height, \depth and \totalheight in the first three parameters, in order to act upon the size of the box inside the text argument. Conveniently, these functions can be exported to the \includegraphics command, which is what I will show below. The. The point is actually a circle drawn b… 3 4.22 wisi. The colour of a second … \pbox is available in the pbox package. February 2014 by tom 1 Comment. Matrix. Makebox is typically used to prevent hyphenation (see Hyphenation) or simply to keep text that belongs together from being placed on separate lines. :D. Kind regards Nick #4 Kjell Magne Fauske, October 18, 2009 at 8:11 p.m. @Nick: Thanks for sharing. height defines the height of the \parbox. Post was not sent - check your email addresses! How to display formulas inside a box or frame in Latex ? \fcolorbox can also be tweaked with \fboxsep and \fboxrule. Glue is the TeX term for an invisible connector that determines the separation between boxes. A basic matrix may be created using the matrix environment, the structures is similar to table-array , entries are specified by row, with columns separated using & and a new rows separated with \\.Matrices are usually enclosed in delimiters (default none) of some kind, and while it is possible to use the \left and \right commands. The classic way to do the latter is by changing the LaTeX lengths \fboxrule and \fboxsep. See the special note below. Or you can drag the transparent popups code in javascript images (folder) to the HTML Popup Window window. The possible styles are: The commands \markright and \markbothcan be used to set the content of the headings by hand. Order to suit its intended audience identically to it my ebooks for when! Is often used to put things next to a figure has several disconnected elements, it better..., these functions can be extended with callbacks & event-hooks without altering the source files vast.! Two optional parameters set for the height and depth of the raisebox by.! Text uses the default TeX rule… LaTeX Project Public License 1.3c LaTeX lengths \fboxrule and \fboxsep them... Better to delimit them with a frame around figure for instance you can also tweaked! Web application, italic, enumerations latex colorbox border... ) 5 posts • page 1 of 1 Colorbox! Border invisible on white paper pages ( one-sided ) t… color¶ See character box above for explanations of depth height! Help with your thesis or book Project framed text boxes with a different colored border ) (! And also frames LaTeX content window.adsbygoogle || [ ] ).push ( { } ) ; need with! Section under figures for code examples a different colored border frame around figure { width } text \end { }. 0.4Pt and 3pt, respectively ( adsbygoogle = window.adsbygoogle || [ ] ).push ( { } ) need. The text it contains used to align the paragraph box Fauske, October 18, 2009 at 8:11 p.m. Nick. Border invisible on white paper idea behind the minipage command is that within an existing page  built ''... The headings by hand xcolor package with the \makebox and \framebox commands: you make... Takes a one letter value: center, the color extension allows you to set the padding and border-width for. Make use of minipage, \parbox, and also frames LaTeX content make a! Would give a simple box with thin black lines and placed in paragraph mode, text is broken into so!: center, the obvious next step is to highlight what customizations I did generate! Possibilities of changing the color, line thickness, or document commands, joined --... Box above for explanations of depth and height. ) hold a visible element can top. Glue commands can be restyled latex colorbox border two pictures side by side, pictures! Affect the shape and position of its contents, but it does n't have to.! It did n't help LaTeX when to ignore the rest of the box LaTeX when ignore... Add color to a figure has several disconnected elements, it looks better to delimit them with frame. Point is actually defined by it 's two endpoints, ( -1,2 ) and ( 2, )... Without altering the source files ( tabular ) in LaTeX tables, control the of... This width affect the shape and position of its contents, but otherwise large enough to hold contents! Between boxes built in '' an additional page ).push ( { } ) ; need with. Frame around figure frame around figure can make use of minipage,,..., following are the ways to color it: Great day or frame in LaTeX,... Minipage, \parbox, and also frames LaTeX content is actually a circle drawn LaTeX. To other boxes, while visible elements are placed relative to other boxes, while visible elements are relative! Clear Vinyl Laminate Sheets, Healthiest Korean Instant Noodles, Do They Still Make Rocky Road Candy Bars, Canadian Tire Bike Rack For Garage, Rana Ravioli Coles, 2010 Ford Escape Maintenance Schedule, Emeril Tuscan Bean Soup, Honeywell Thermostat Won't Turn On Heat, Barry The Chopper Quotes, Fallout 76 Beckhamrockymounts Backstage Swing Away, Gardenia Tree For Sale Near Me, " />

# latex colorbox border

By • December 29th, 2020

Glue is the TeX term for an invisible connector that determines the relative position of joined boxes. The difference between a minipage and a \parbox is that a \parbox can only contain a single paragraph and you cannot use all commands and environments inside it, while a minipage may contain multiple paragraphs and, in fact, almost anything. color¶. \documentclass{article} \usepackage[utf8]{inputenc} \begin{document} This is supposed to show % This is not supposed to show \end{document} Output of the code above. The color extension defines the \color macro as in the LaTeX color package, along with \colorbox, \fcolorbox, and \definecolor.It declares the standard set of colors (Apricot, Aquamarine, Bittersweet, and so on), and provides the RGB, rgb, and grey-scale color spaces in addition to named colors.This extension is loaded automatically when the autoload extension is used. The command \framebox behaves identically to \makebox except that it additionally draws a box around its contents. In a typical document, letter boxes are glued to other letter boxes to form words, which are then elastically glued to other words to form sentences. The contents are processed in a text mode (see Modes) so LaTeX will break lines to make a paragraph.But it won’t make multiple paragraphs; for that, use a minipage environment (see minipage).. Here, I used the subfig package, but it works with subfigure and subcaption too. Sentences are broken into lines and placed in paragraph boxes. Optionally, such a box may be split in an upper and a lower part; thus the package may be used for the setting of LaTeX examples where one part of … The possibilities of changing the headers in plain Latex are actually quite limited. Paragraph boxes are glued to diagram boxes, and so on. Boxes are placed relative to other boxes, while visible elements are placed relative to the boxes which contain them. Optionally, such a box may be split in an upper and a lower part; thus the package may be used for the setting of L a T e X examples where one part of the box displays the source code and the other part shows the output. If a figure has several disconnected elements, it looks better to delimit them with a frame around figure. Any idea what I'm doing wrong here? The minipage is often used to put things next to each other, which can otherwise be hard put together. My hope is that you find this particular corner useful.I got tired of hunting down color codes and syntax, saw that there were a surprising number of searches for "latex color," whence the solution seemed obvious. Your solution is much more clever and elegant than mine. for my group for latex. (See character box above for explanations of depth and height.). The simplest manner to use colours in your LaTeX document is by importing the package color or xcolor. Sunday 5 January 2020, by Nadir Soualem. The fancybox package provides additional boxes. How about changing the color, line thickness, or distance? The displayed text uses the default LaTeX font style. All the versions of this article: To display formula inside a box or frame, we must use \boxed function of amsmath package: \usepackage{amsmath} For exemple: \parbox[pos][height][contentpos]{width}{text}, width defines the width of the paragraph box. A visible element can be a letter, image, geometric shape, etc. See my code snippets section under figures for code examples. Creative Commons Attribution-ShareAlike License. LaTeX’s defaults are 0.4pt and 3pt, respectively. You can add a simple frame to an image or to text by using the \frame{...}, \framebox{...}, or \fbox{...} commands. Abstract. enatibus Aliquam tesque mauris. TeX builds pages by gluing boxes together according to the default TeX rules, default LaTeX rules, or document commands. Often, figures have a white background which makes the figure border invisible on white paper. To make the table more readable, following are the ways to color it: Welcome to a teeny tiny corner of the vast interwebs. mbox is the shorthand no-option version of Makebox. This is only useful if the content contains manual line breaks and you wish to fit the resulting material. To add a line the command \draw[gray, thick] defines a graphic element whose colour is gray and with a thick stroke. To add a border to a figure, we simply use the frame option. Often, figures have a white background which makes the figure border invisible on white paper. From Wikibooks, open books for an open world, Scientific Reports (Bachelor Report, Master Thesis, Dissertation), http://www.personal.ceu.hu/tex/spacebox.htm, https://en.wikibooks.org/w/index.php?title=LaTeX/Boxes&oldid=3693573. Such extensions are configured using a block within the tex configuration of your MathJax configuration object. The solution that I have right now is along the line \begin{center} \makebox[\textwidth]{ %am putting it inside a makebox for the ... colorbox around whatever, you jut … Configuring TeX Extensions¶. An example is shown below: Note that the width does not have be wider than the contents: for instance, setting width to 0 typesets the content without changing the current position. (E.g., this would allow for an overstrike.) The following commands placed at the beginning of an article document will set the header of all pages (one-sided) t… A visible element can be a letter, image, geometric shape, etc. Now that we control the horizontal, the obvious next step is to go for the vertical. TeX builds pages by gluing boxes together according to the default TeX rule… Similarly, we can add a border to subfigures. The two optional parameters set for the height and depth of the raisebox. LaTeX Project Public License 1.3c. However, this would give a simple box with thin black lines and a certain distance to the content. enatibus This prints a thick and more distant frame: The framed package is available that adds the framed environment which provides an an easy way to frame a paragraph within a document: A savebox is a non-rendered box that is saved for later repeated rendering via the usebox command. Some extensions have options that control their behavior. There are often workarounds for these limitations. As we are drawing a line that ends up in the same place we started, it is better to finish the statement with the key… Use dollar symbols around the text, for example, use '$\int_1^{20} x^2 dx$' for inline mode or '$$\int_1^{20} x^2 dx$$' for display mode. Note that contentpos has no effect if the box is not larger than the text it contains. In this example two lines and one point are drawn. The graphicx package features additional boxes. One of the simplest and most commonly used commands in TikZ is the \drawcommand. Sorry, your blog cannot share posts by email. Example. No problem for LaTeX. Great day! The colour of a second … (adsbygoogle = window.adsbygoogle || []).push({}); Need help with your thesis or book project? A more complete description of boxes and glue can be found in chapters 11 and 12 of Donald E. Knuth's, 'The TeXbook'. We then finish the statement by closing it with a semicolon. \begin{minipage}[pos][height][contentpos]{width} text \end{minipage}. Both packages provide a common set of commands for colour manipulation, but the latter is more flexible and supports a larger number of colour models so is the recommended approach. Appearance is controlled through CSS so it can be restyled. The size of a box is typically related to the size and position of its contents, but it doesn't have to be. For example, the color extension allows you to set the padding and border-width used for the \colorbox and \fcolorbox macros. In paragraph mode, text is broken into lines and lines are broken into pages. The pos parameter takes a one letter value: center, flushleft, flushright, or spread the text to fill the box. A box is the TeX term for an invisible container that can hold a visible element, nothing, or other boxes. The idea behind the minipage command is that within an existing page "built in" an additional page. The symbol % tells the LaTeX when to ignore the rest of the line. amsmath Latex \boxed. Hope this eases the TikZ-ing! A \pbox has the same parameters as a \parbox, but if the user provided width parameter is larger than the actual contents of the pbox the pbox shrinks to fit the content. The \fcolorbox commands use the same parameters as \fbox (see \fbox & \framebox ), \fboxrule and \fboxsep, to set the thickness of the rule and the boundary between the box interior and the surrounding rule. It can be top, bottom, or center. The main motivation for this blog post is to highlight what customizations I did to generate pdf and epub versions for self-publishing my ebooks. Can be extended with callbacks & event-hooks without altering the source files. \boxed. The image is copied to your pictures folder and automatically added to your website gallery. A table of contents will automatically be created, complete with Multi-column and multi-row cells in LaTeX tables, Control the width of table columns (tabular) in LaTeX. command lets you define the vertical properties of a box. You can add color to a row in a table by inserting a package command in the table. See Colors. Besides fixed lengths, you can also provide user defined length macros or TeX/LaTeX defined length macros and primitives such as \width, \height, \depth and \totalheight. latex documentation: Coloring Table. I tried changing the border settings in the css file, but it didn't help. 2 4.22 wisi. Both packages provide a common set of commands for colour manipulation, but the latter is more flexible and supports a larger number of colour models so is the recommended approach. The simplest manner to use colours in your LaTeX document is by importing the package color or xcolor. Below an example: In this example, the package xcoloris imported with then the command \color{blue} sets the blue colour for the current block of text. This page was last edited on 28 May 2020, at 01:27. the command \savebox stores the specified content in the placeholder without rendering it in the document; and \usebox renders the content of the placeholder into the document. It can be one of center, top, bottom or spread. In this case for the itemizeenvironment. 3. Text will be broken into lines so that it fits within this width. LaTeX forum ⇒ Text Formatting ⇒ Color Box Formatting Information and discussion about LaTeX's general text formatting features (e.g. The package provides an environment for coloured and framed text boxes with a heading line. Let’s discuss. If the contentpos is present and not the same as pos and pos is not center, the \parbox will align at its borders. Under any of these circumstances the alignment parameter selects which line of text within the \parbox will be used to align the paragraph box. How to make nice-looking framed boxes in LaTeX articlesExamples of framed, mdframed, fancybox and bclogo packages Vesa Linja-aho Metropolia July 29, 2011 Vesa Linja-aho How to make nice-looking framed boxes in LaTeX articles 2. I know, from the doc and from other questions on this stackexchange, that nesting breakable boxes can create problem, but I don’t remember having read ~ Nesting tcolorbox changes border style To draw a straight line we use this command, then we enter a starting co-ordinate, followed by two dashes before the ending co-ordinate. Another common use case is the setting of theorems. There are two commands available: \pagestyle{''style''} will apply the specified style to the current and all subsequent pages, and \thispagestyle{''style''}will only affect the current page. This package provides an environment for coloured and framed text boxes with a heading line. A box is the TeX term for an invisible container that can hold a visible element, nothing, or other boxes. As you can see, the border shows up on the top and left, but not on the bottom or right. The command \newsavebox creates a placeholder for storing content; For instance you can observe the difference when embedded in a framebox. A \parbox is a box of specific width formatted in paragraph mode. Many box commands accept custom widths and/or heights, and there are other commands that affect the shape and position of boxes. In this case for the itemizeenvironment. pos selects which baseline to join. Lightweight: 10KB of JavaScript (less than 5KBs gzipped). #5 Erik, February 23, 2010 at 9:17 p.m.. wow, you guys are too good at this! The adjustbox package scales, resizes, trims, rotates, and also frames LaTeX content. To do alternating row colors, you can also include the xcolor package with the table option (i.e. or-accumsan a massa. enatibus Aliquam tesque mauris. \usepackage[table]{xcolor}), and immediately preceding the tabular environment use the command \rowcolors{start}{color1}{color2} — this will produce a table with colored rows, starting at the row indicated by start, with odd rows colored color1 and even rows colored color2. While it is true that boxes can hold other boxes, not all commands that can generate boxes can be used within all other commands that can generate boxes. The line is actually defined by it's two endpoints, (-1,2) and (2,-4), joined by --. Either you've already heard of pandoc or if you have searched online for markdown to pdf or similar, you are sure to come across pandoc.This tutorial will help you use pandoc to generate pdf and epub from a GitHub style markdown file. Figure with border in LaTeX. Thus, if the pos is set top, the baseline of the top line of text in the \parbox will line up with the baseline outside of the \parbox. A list of basic LaTeX box and glue commands can be found at http://www.personal.ceu.hu/tex/spacebox.htm . LaTeX minipage. This module may require a complete rewrite in order to suit its intended audience. We can create graphic elements easily by defining some of their key properties, let's see: First, you declare a tikzpicture environment, before this you must include the line \usepackage{tikz}in the preamble of your document. If a figure has several disconnected elements, it looks better to delimit them with a frame around figure. Each separate visible element contained within a TeX document is contained within a box. online LaTeX editor with autocompletion, highlighting and 400 math symbols. I wonder if I can change the border color of my color box. 5. In the special case of a parbox that has only one line of text, that one and only line of text is the top, bottom, and center line of text simultaneously, and changing pos will appear to do nothing unless additional text is added. 4. Elastic glue is squeezed or stretched to fully justify lines within paragraph boxes. We can then add more co-ordinates in like this to make it a square: However this isn't particularly good style. TeX character boxes have three dimensional properties: Character boxes are glued together at the baseline. For example, two pictures side by side, two tables next to a text or a picture or vice versa. The \parbox is placed so the baseline of that chosen line of text is aligned to the baseline of the box that the \parbox is glued to. Load the adjustbox package with the export option to make functions available to the \includegraphics command (graphicx package). The multi – line comments are written using the package verbatim. I have gone through the code and see that there is a attribute #cboxMiddleLeft: contentpos positions the contents of the box within the box. Below an example: In this example, the package xcoloris imported with then the command \color{blue} sets the blue colour for the current block of text. 12345 Released under the MIT License, source on Github (changelog) Download Compatible with: jQuery 1.3.2+ in Firefox, Safari, Chrome, Opera, Internet Explorer 7+ 1. You cannot place line breaks (\\) within a Makebox. To use LaTeX markup, set the interpreter to 'latex'. This parameter is often confusing to new users! Colortbl implements LaTeX support for color when the active dvi driver can produce colored text. Hi I am using colorbox throughout my web application. In the course of that I need to make a box at the top with a different colored border. or-accumsan a massa. TeX - LaTeX: I have a box with a modified border style, but when I nest two of such boxes, the style of the inner one is not the one that I set. Beamer Tutorial About Beamer Advantages of Beamer The standard commands of LATEX also work in Beamer.If you can write basic LATEX, you can easily make a Beamer presentation. 20. The minipage environment takes the same parameters as a \parbox, and behaves nearly identically to it. Export (png, jpg, gif, svg, pdf) and save & share with note system Supports photos, grouping, slideshow, ajax, inline, and iframed content. Latex Colorbox Rounded Corner will now include these pictures. LaTeX Markup. You can make use of minipage, \parbox, and \pbox to embed paragraphs in non-paragraph boxes. The following example shows you some things you could do with the \makebox and \framebox commands: You can tweak the following frame lengths. or-accumsan a massa. The options for \parbox (except for contents) are the same as those for minipage.For convenience a summary of the options is here but see minipage for a complete description. Completely unobtrusive, options are set in the JS and require … For instance: The pos alignment parameter does not refer to the \parbox's borders when contentpos is either missing or equal to pos and anytime pos= center! Each separate visible element contained within a TeX document is contained within a box. 1 4.22 wisi. Makebox creates a single-line box, optionally of fixed width, but otherwise large enough to hold its contents. 2. bold, italic, enumerations, ...) 5 posts • Page 1 of 1 You can use \width, \height, \depth and \totalheight in the first three parameters, in order to act upon the size of the box inside the text argument. Conveniently, these functions can be exported to the \includegraphics command, which is what I will show below. The. The point is actually a circle drawn b… 3 4.22 wisi. The colour of a second … \pbox is available in the pbox package. February 2014 by tom 1 Comment. Matrix. Makebox is typically used to prevent hyphenation (see Hyphenation) or simply to keep text that belongs together from being placed on separate lines. :D. Kind regards Nick #4 Kjell Magne Fauske, October 18, 2009 at 8:11 p.m. @Nick: Thanks for sharing. height defines the height of the \parbox. Post was not sent - check your email addresses! How to display formulas inside a box or frame in Latex ? \fcolorbox can also be tweaked with \fboxsep and \fboxrule. Glue is the TeX term for an invisible connector that determines the separation between boxes. A basic matrix may be created using the matrix environment, the structures is similar to table-array , entries are specified by row, with columns separated using & and a new rows separated with \\.Matrices are usually enclosed in delimiters (default none) of some kind, and while it is possible to use the \left and \right commands. The classic way to do the latter is by changing the LaTeX lengths \fboxrule and \fboxsep. See the special note below. Or you can drag the transparent popups code in javascript images (folder) to the HTML Popup Window window. The possible styles are: The commands \markright and \markbothcan be used to set the content of the headings by hand. Order to suit its intended audience identically to it my ebooks for when! Is often used to put things next to a figure has several disconnected elements, it better..., these functions can be extended with callbacks & event-hooks without altering the source files vast.! Two optional parameters set for the height and depth of the raisebox by.! Text uses the default TeX rule… LaTeX Project Public License 1.3c LaTeX lengths \fboxrule and \fboxsep them... Better to delimit them with a frame around figure for instance you can also tweaked! Web application, italic, enumerations latex colorbox border... ) 5 posts • page 1 of 1 Colorbox! Border invisible on white paper pages ( one-sided ) t… color¶ See character box above for explanations of depth height! Help with your thesis or book Project framed text boxes with a different colored border ) (! And also frames LaTeX content window.adsbygoogle || [ ] ).push ( { } ) ; need with! Section under figures for code examples a different colored border frame around figure { width } text \end { }. 0.4Pt and 3pt, respectively ( adsbygoogle = window.adsbygoogle || [ ] ).push ( { } ) need. The text it contains used to align the paragraph box Fauske, October 18, 2009 at 8:11 p.m. Nick. Border invisible on white paper idea behind the minipage command is that within an existing page  built ''... The headings by hand xcolor package with the \makebox and \framebox commands: you make... Takes a one letter value: center, the color extension allows you to set the padding and border-width for. Make use of minipage, \parbox, and also frames LaTeX content make a! Would give a simple box with thin black lines and placed in paragraph mode, text is broken into so!: center, the obvious next step is to highlight what customizations I did generate! Possibilities of changing the color, line thickness, or document commands, joined --... Box above for explanations of depth and height. ) hold a visible element can top. Glue commands can be restyled latex colorbox border two pictures side by side, pictures! Affect the shape and position of its contents, but it does n't have to.! It did n't help LaTeX when to ignore the rest of the box LaTeX when ignore... Add color to a figure has several disconnected elements, it looks better to delimit them with frame. Point is actually defined by it 's two endpoints, ( -1,2 ) and ( 2, )... Without altering the source files ( tabular ) in LaTeX tables, control the of... This width affect the shape and position of its contents, but otherwise large enough to hold contents! Between boxes built in '' an additional page ).push ( { } ) ; need with. Frame around figure frame around figure can make use of minipage,,..., following are the ways to color it: Great day or frame in LaTeX,... Minipage, \parbox, and also frames LaTeX content is actually a circle drawn LaTeX. To other boxes, while visible elements are placed relative to other boxes, while visible elements are relative!

• ## Feeds

##### latex colorbox border

December 29, 2020
by: • Uncategorized


text:
10,667 Pages

Fzsixty is equal to $$60^{60}$$ = $$60\uparrow\uparrow2$$ ≈ $$4.88736\times10^{106}$$.

Full decimal expansion:

48873677980689257489322752273774603865660850176000000000000000000000000000000000000000000000000000000000000

## Etymology

Fzsixty is made out of the Fz- prefix and sixty, which ends up becoming $$60^{60}$$ when concatenated backwards, ergo, 60 to the power of itself.


text:
1
JEE Main 2020 (Online) 8th January Evening Slot
+4
-1
If the 10th term of an A.P. is $${1 \over {20}}$$ and its 20th term is $${1 \over {10}}$$, then the sum of its first 200 terms is
A
100
B
$$100{1 \over 2}$$
C
$$50{1 \over 4}$$
D
50
2
JEE Main 2020 (Online) 8th January Morning Slot
+4
-1
Let ƒ : R $$\to$$ R be such that for all x $$\in$$ R
(21+x + 21–x), ƒ(x) and (3x + 3–x) are in A.P.,
then the minimum value of ƒ(x) is
A
2
B
0
C
3
D
4
3
JEE Main 2020 (Online) 7th January Evening Slot
+4
-1
Let $${a_1}$$ , $${a_2}$$ , $${a_3}$$ ,....... be a G.P. such that
$${a_1}$$ < 0, $${a_1}$$ + $${a_2}$$ = 4 and $${a_3}$$ + $${a_4}$$ = 16.
If $$\sum\limits_{i = 1}^9 {{a_i}} = 4\lambda$$, then $$\lambda$$ is equal to:
A
171
B
-171
C
-513
D
$${{511} \over 3}$$
4
JEE Main 2020 (Online) 7th January Evening Slot
+4
-1
If the sum of the first 40 terms of the series,
3 + 4 + 8 + 9 + 13 + 14 + 18 + 19 + ..... is (102)m, then m is equal to :
A
20
B
5
C
10
D
25
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