text:
# Beamer automatic ordering of overlays

I would like to order automatically some alerts (or other things) in some uncoverenv's. uncoverenv's should be continuously added but alerts should be just on the numbered slide. A minimal example is below. How to get the same result without manual numbering?

\documentclass{beamer}

\begin{document}
\begin{frame}{Frame}
First

\begin{uncoverenv}<4->
Second

\end{uncoverenv}

\begin{uncoverenv}<7->
Third

\end{uncoverenv}

\end{frame}

\end{document}

• Welcome to TeX.SX! What do you mean with order automatically? Something like the + overlay specification (instead of the number)? – TeXnician Oct 12 '17 at 11:56

Like this?

\documentclass{beamer}

\begin{document}
\begin{frame}{Frame}
First

\begin{uncoverenv}<+(1)->
Second

\end{uncoverenv}

\begin{uncoverenv}<+(1)->
Third

• Do you need the (1)? I always thought + would suffice. – TeXnician Oct 12 '17 at 12:05
• I also tried this for nested overlays. But I could not make it. For example \uncover<+(1)>{U1\alert<+(1)>{U1}} did not worked. Any suggestion? – Muhsin Oct 12 '17 at 12:37


text:
# Revision history [back]

I assume you are wondering why Sage is not recognizing that $(x^2 - 6)x^2 - 4x(e^{\frac{2}{5}i\pi} + e^{\frac{-2}{5}i\pi}) - e^{\frac{4}{5}i\pi} - e^{\frac{-4}{5}i\pi} - 1 = (x^2 - 6)x^2 - 8xcos(\frac{2}{5}\pi) - 2*cos(\frac{4}{5}\pi) - 1$, and thereafter doesn't find the four real roots: $x=-2.1755705045849463, -0.618033988749891, 0.17557050458494627, 2.618033988749895$.

Mixing the world of solving algebraic equations - which are exact - with the world of finding roots - which are approximations - is seldom a good idea. If you would split both worlds, it goes fluently.

var('x')
f(x)=(x^2 - 6)*x^2 - 4*x*(e^(2/5*I*pi) + e^(-2/5*I*pi)) - e^(4/5*I*pi) - e^(-4/5*I*pi) - 1
g(x)=real_part(f(x)).simplify()
print g
x |--> x^4 - 6*x^2 - 2*sqrt(5)*x + 2*x + 1/2*sqrt(5) - 1/2

print [find_root(g,-3,-2), find_root(g,-1,0), find_root(g,0,1), find_root(g,2,3)]
[-2.1755705045849463, -0.6180339887498911, 0.17557050458494627, 2.618033988749895]

Stated differently, always simplify your function (= exact) before going into a numerical process such as root finding. Any system - thus also Sage - hangs up because it is impossible to determine the simplification numerically.

I assume you are wondering why Sage is not recognizing that $(x^2 - 6)x^2 - 4x(e^{\frac{2}{5}i\pi} + e^{\frac{-2}{5}i\pi}) - e^{\frac{4}{5}i\pi} - e^{\frac{-4}{5}i\pi} - 1 = (x^2 1=(x^2 - 6)x^2 - 8xcos(\frac{2}{5}\pi) - 2*cos(\frac{4}{5}\pi) - 1$, and thereafter doesn't find the four real roots: $x=-2.1755705045849463, -0.618033988749891, 0.17557050458494627, 2.618033988749895$.

Mixing the world of solving algebraic equations - which are exact - with the world of finding roots - which are approximations - is seldom a good idea. If you would split both worlds, it goes fluently.

var('x')
f(x)=(x^2 - 6)*x^2 - 4*x*(e^(2/5*I*pi) + e^(-2/5*I*pi)) - e^(4/5*I*pi) - e^(-4/5*I*pi) - 1
g(x)=real_part(f(x)).simplify()
print g
x |--> x^4 - 6*x^2 - 2*sqrt(5)*x + 2*x + 1/2*sqrt(5) - 1/2

print [find_root(g,-3,-2), find_root(g,-1,0), find_root(g,0,1), find_root(g,2,3)]
[-2.1755705045849463, -0.6180339887498911, 0.17557050458494627, 2.618033988749895]

Stated differently, always simplify your function (= exact) before going into a numerical process such as root finding. Any system - thus also Sage - hangs up because it is impossible to determine the simplification numerically.

format: plain


text:
aqsalose (maths!)

TIL: 1. @FrontYoungMinds is a wonderful kid-reviewed science journal 2. their maths team are looking for contributors:

blogs.ams.org/matheducation/20

A Mastodon instance for maths people. The kind of people who make $\pi z^2 \times a$ jokes.

Use $ and $ for inline LaTeX, and $ and $ for display mode.


text:
Object

Title: A Good $\lambda$ Estimate for Multilinear Commutator of Singular Integral on Spaces of Homogeneous Type

Abstract:

In this paper, a good $\lambda$ estimate for the multilinear commutator associated to the singular integral operator on the spaces of homogeneous type is obtained. Under this result, we get the$(L^p(X),L^q(X))$-boundedness of the multilinear commutator.

Identifier:

oai:arar.sci.am:13243

May 17, 2021

Feb 12, 2020

1


text: This chapter contains sections titled: Problem And Scope, Evidence About Attention Control, Developing The Skill Of Attention Control, Concluding Remarks, Note, References


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Generate leads, increase sales and drive traffic to your blog or website. Question 1 What is the measure in degrees of the angle A = 7π/6? a) 150° b) 210° c) 100° d) 120° Question 2 What is the measure in radians of the angle A = 330°? a) 11π/3 b) 7π/4 c) 7π/6 d) 11π/6. What is the measure (in radians) of a central angle, θ,that intercepts an arc of length 12 mm on a circle with radius 4 cm? Trig/Alg 3 Name _____ U5D1 HOMEWORK Date _____ period _____ In a circle with radius 10 centimeters, an arc is intercepted by a central angle with measure. What is the measure, in radians, of the smaller angle formed between the hour and minute hands? Round your answer to one decimal place. For example, look at the sine function for very small values:. 40 ∘ ´ 20 = 401 3 ∘ = π 180 × 121 3 = 121π 180 radian. Radians - Revision Quiz 1. Welcome to your Radians and special angles Quiz. Previewing Radians - Revision Quiz 1. SIN(RADIANS(45)) = 0. About this Quiz This is an online quiz called UNIT CIRCLE Practice RADIANS There is a printable worksheet available for download here so you can take the quiz with pen and paper. Convert to either DMS or decimal form 1)117. Express in degree measure an angle of 2π/5 radians (With explanation, !) - Let's Answer The World! Posted on. Radian angles & quadrants. Trigonometric Functions I. For example, to convert 120 degrees you would have 120 x π/180 = 120π/180. Only registered, enrolled users can take graded quizzes Related Items. This set of task cards is designed for students to practice converting between degrees and radians and is great practice for the Unit Circle. They measure an angle in relation to a section of the unit circle's circumference. Secondly they show you how adeptly they can convert a bunch of radian measures to degree measures by multiplying radians by 180. Radian Measure Quiz. 2 Harvest Quiz and Mike's Quiz 2. Radians and Degrees Quiz DRAFT. Multiple choice questions on Relation between Radians and Degree quiz answers PDF to practice grade 10 math test for online classes. Radians to degrees. Radian Measure and the Unit Circle Approach - Wiley: Home. Games, activities and quizzes to help you learn and practice trigonometry, We have games for SOHCAHTOA, Right Triangles, Trig Ratios, Unit Circle, Trig Identities, Trig Formulas, Law of Sines, Law of Cosines, Trigonometric Graphs, Inverse Trigonometry and Quizzes, examples with step by step solutions, worksheets. You can take a New Quizzes assessment on the Quizzes page in Canvas. Click for details. Quiz 2: Trigonometric Functions of Special Angles. This trigonometry video tutorial provides a basic introduction into radians and degrees. The following radian measures come up frequently, and the student should know their degree equivalents: (Topic 4 and Topic 5. Name (2 pts) (2 pts) (4 pts) (2 pts) 1. Repeat the process as many times as you'd like. In a circle of radius 1, the radian measure of a given central angle can be thought of as the length of the arc associated with the angle. Radians - Revision Quiz 1. Trigonometric Functions I. 90°/180° = ½. Definition of radian. Question 1 What is the measure in degrees of the angle A = 7π/6? a) 150° b) 210° c) 100° d) 120° Question 2 What is the measure in radians of the angle A = 330°? a) 11π/3 b) 7π/4 c) 7π/6 d) 11π/6. Therefore: arc length = angle in radians x radius. Play this game to review Algebra II. Some of the worksheets below are Radian and Degree Measure Worksheet with Answers, Radians is the standard unit of angle measure. Note: The radian is the standard unit of angular measure, used in many areas of mathematics. theradianproject. Pi radians are equal to 180 degrees: π rad = 180° One degree is equal 0. Radian Measure and the Unit Circle Approach - Wiley: Home. com is a free online quiz making tool. Because a full rotation equals 2*pi radians, one degree is equivalent to pi/180 radians. "Relation between Radians and Degree" quiz questions and answers PDF: π radians are equal to with answers for distance learning classes. Stanley SYRFM Reusable Face Mask. You can calculate this by converting both numbers into fractions. Equation Of A Straight Line Quiz. Compared to other units, radian is preferred because of its natural nature. v is the linear velocity measured in metres per second (ms-1). For full credit show your work. Go to Trigonometric Functions I 10 Questions. Degrees & Radians Conversion Practice Date_____ Convert each degree measure into radians. In a phasor diagram, the frequency of each of the waves shown by the phasors is: a) The same for all waves, and shown by the point of origin of the phasors. You can use it to explain all possible measures of angles from 0-degrees to 360-degrees. Tip: See also math. 400 mil 4000 mil 7. Math 121-01 (Quiz 2) September 8, 2017 This quiz is worth 20 points. In order to transform from degrees in radians we only need to know how much 180° or 360° is in radians. Skincare Concerns: Dark Spots, Dryness, and Dullness. Nudity or sexual content Hateful, harmful, violent, or abusive content Harassment Child abuse Promotes terrorism. Multiple choice questions on Relation between Radians and Degree quiz answers PDF to practice grade 10 math test for online classes. to travel around a circle. Note: If r is in "cm", v will be in "cm/s". 2 r Definition of Radian One radian is the measure of a central angle that intercepts an arc equal in length to the radius of the circle. OutBack Power GS8048A-01 Radian Series Inverter/Charger 8kW 48VDC, Grid-Interactive/Off-Grid, Listed to UL1741-SA. Note: π/4 rad can be expressed as real number or as a decimal as 0. To leave the "Quiz Me" feature, click RESET (or press "r" on the keyboard). Express $$\dfrac{{7\pi }}{6}$$ radians in degrees. Multiple choice questions on converting angles from degrees to radians and from radians to degrees with answers at the bottom of the page. Select Source. Stanley SYRFM Reusable Face Mask. Trig Functions II Test. Choose a Herald: a. "Quiz Me" feature: Click the "Quiz Me" button in the toolbar (or press "q" on the keyboard) and a point will randomly be chosen on the unit circle. Quiz of the Day #quiz #QuizTime #reasoning #reasoningquiz #questionoftheday #radianbookcompany #education #question #learning #reasoningquestions. HTML Quiz CSS Quiz JavaScript Quiz SQL Quiz MySQL Quiz PHP Quiz Python Quiz NumPy Quiz Pandas Quiz SciPy Quiz jQuery Quiz Java Quiz Bootstrap Quiz Bootstrap 4 Quiz C++ Quiz C# Quiz R Quiz XML Quiz Cyber Security The RADIANS() function converts a degree value into radians. Radians SV22GL-2 Glow-In-The-Dark Economy Vest. One radian is equal 57. Convert 225 degrees to Radians in Terms of pi - With Work › See more all of the best education on www. 233 will return 32. The degree value to be converted into radians. The solved questions answers in this Test: Degree & Radian Measure quiz give you a good mix of easy questions and tough questions. This quiz and worksheet will help you get a good grasp of the principle of conversion between radians and degrees and why it is important in. Relationship between Degrees and Radians: In a circle, the arc measure of the entire circle is 360º and the arc length of the entire circle is represented by the formula for circumference of the circle:. Practice: Radians & degrees. For example, -32. Radians to degrees. Start studying Radians & Reference Angles. Note: 5π/4 rad can be expressed as real number or as a decimal as 1. Change answer; Math. Level 1 45 seconds each Level 2 one minute each. If secθ > 0 and tanθ < 0, the angle θ is in: A. You can use it to explain all possible measures of angles from 0-degrees to 360-degrees. The Pythagorean identity. 78539816339745 radian. 1π radian = degrees. Solution: By the formula, we know; Angle in radians = Angle in degree × π/180. Convert 150 degrees to Radians in Terms of pi - With Work › See more all of the best education on www. Age Under 20 years old 20 years old level 30 years old level 40 years old. This quiz and worksheet will help you get a good grasp of the principle of conversion between radians and degrees and why it is important in. Precalculus| RADIAN TO DEGREE | COMPLEMENTARY |SUPPLEMENTARY Quiz 2nd Sem Due May 20 at 11:59pm Points 16; Questions 1; Available May 18 at 12am - May 20 at 11:59pm 3 days; Time Limit 90 Minutes Instructions. Start studying Sine of Degrees and Radians. The unit circle is a great way to remember your trig values. Learn vocabulary, terms, and more with flashcards, games, and other study tools. One radian is the measure of a central angle of a circle that is subtended by an arc whose length is equal to the radius of the circle. It describes all the negatives and positive angles in the circle. Unit Circle to Sine and Cosine Functions. Started by TPG, June 11, 2020. 25° Sketch each angle in standard position and state the reference angle (in the same measure as the. In the parentheses, write the coordinates of each point; on the solid line write the angle measure in degrees, and on the dotted line write the angle. Radian angles & quadrants. Free student math practice. It could appear as a derived unit, the quizmaster just didn't feel like it. Create a Review Quiz. Highlighted Ingredients:. 1415 radians. The bare bones definition: Radian is a measure of an angle (just as degree is a measure of angle). From the quiz author Locate the angles of the unit circle - in radians. radians(x) Parameter Values. All of the above. 2) Convert 52° to radians. Round your answers to the nearest tenth, where necessary. Practice: Radians & degrees. The unit was formerly an SI supplementary unit (before that category was abolished in 1995) and the radian is now an SI derived unit. Convert each radian measure into degrees and fill in your answer. ca Trigonometry One Practice Exam 95π 6. Name_____ Trigonometry, Quiz 2 Consider a radian angle. SHOW WORK FOR EACH PROBLEM!! 1) 165° 2) 100° 3) 1020° 4) 665° 5) -215° 6) -70° 7) 110° 8) 555° Convert each radian measure into degrees. ½ · ∏ = ∏/2 radians. Safe + Steel anti-rebound bar. What does Radian mean? Information and translations of Radian in the most comprehensive dictionary definitions resource on the web. , , , , 24) How many solutions are there to the equation: x° = x radians One: ° = radians. Select Number of questions. There are a little more than 6 radians in a circle. 295779513 degrees: 1 rad = 180°/π = 57. Degrees & Radians quiz to test math skills. When you start the game you receive a question and have to choose the correct answer from different choices. BIG Trig Quiz Review Sheet Find the length of each arc. Example #5. An angle of 1 radian. Interactive game on all parts of the unit circle, angles, radians, degrees. In a phasor diagram, the frequency of each of the waves shown by the phasors is: a) The same for all waves, and shown by the point of origin of the phasors. Nudity or sexual content Hateful, harmful, violent, or abusive content Harassment Child abuse Promotes terrorism. Safe + anti-slip harness pads. This means that 60° is equivalent with 1. On this page you can read or download 3 13 quiz radian measure in PDF format. Charts, Worksheets, and 35+ Examples! The Unit Circle is probably one of the most important topics in all of Trigonometry and is foundational to understanding future concepts in Math Analysis, Calculus and beyond. cuts off an arc equal to. Find the length of a circular arc subtended by an angle of radians if the radius ofthe circle is 36 cm. 85 is the SIN of 45 radians which means by default, excel takes all the angles in radians and not degree. Tim Brzezinski. Meaning of Radian. Radians SV22GL-2 Glow-In-The-Dark Economy Vest. The solved questions answers in this Test: Degree & Radian Measure quiz give you a good mix of easy questions and tough questions. 25° Sketch each angle in standard position and state the reference angle (in the same measure as the. "Quiz Me" feature: Click the "Quiz Me" button in the toolbar (or press "q" on the keyboard) and a point will randomly be chosen on the unit circle. One radian is the measure of a central angle of a circle that is subtended by an arc whose length is equal to the radius of the circle. Say: Half a circle is a little more than three radians. This radian arts and crafts activity is designed to help students conceptually understand what a radian is. Convert 510 o to Radians Preview this quiz on Quizizz. TPG Darkeyes Members Darkeyes 1 post;. Find the exact value of cos (-7 π/6) and the reciprocal of this trigonometric ratio. 400 mil 4000 mil 7. View Elsabet_-_Radians_and_Arc_Length_Quiz. It is measured in radians/second. If the clockwise direction is used, the angle is simply assigned a negative value. To convert any given angle from the measure of degrees to radians, the value has to be multiplied by π/180. Only registered, enrolled users can take graded quizzes Related Items. radians() method converts a degree value into radians. 90°/180° = ½. If you need the radian measurement in decimal format, remember the value of pi is approximately 3. Reported content will be reviewed by Screencast-O-Matic to determine whether they violate guidelines. 1950 10 mi 51 r 12 18 in Find the area of each sector. REPORT CONTENT. It is reflects Algebra 2 (algebra ii) …. The radian measure of a complete circle (360°) is exactly 2π radians, because the circumference of a circle of radius 1 is exactly 2π. Example 3. I became a trigonometry teacher for the school year 2006. What does radians mean? Information and translations of radians in the most comprehensive dictionary definitions resource on the web. There are two types of sectors, minor and major sector. 4 Vundo's Quiz 3 Missions 3. How many radians can fit in a half-circle? Use worksheet 1 and let the students work to figure out that there are approximately six radians in a circle and three radians in a half-circle. (2π to be exact. It describes all the negatives and positive angles in the circle. rotate_x — rotates a vector around the x-axis by the angle in degrees. Change answer; Math. If you don't see any interesting for you, use our search form on bottom ↓. Found a mistake? Let us know about it through the REPORT button at the bottom of the page. 15) 240° 16) 315° 17) 125° 18) -340° Convert each radian measure into degrees. 1 Rand's Quiz 2. In short, it shows all the possible angles which exist. The time to complete one full cycle, or one oscillation, is called the period, T. An angle's measurement in radians is numerically equal to the length of a corresponding arc of a unit circle; one radian is just under 57. Quiz 9 1 Inverse Trigonometric Functions Find The Value Chapter 7 4 Precalculus 2 Youtube from i. (The speed of the gears are the same as they are connected. Name_____ Trigonometry, Quiz 2 Consider a radian angle. Radians per second are the angular velocity. Found a mistake? Let us know about it through the REPORT button at the bottom …. Select Source. They measure an angle in relation to a section of the unit circle's circumference. Nudity or sexual content Hateful, harmful, violent, or abusive content Harassment Child abuse Promotes terrorism. Num high ratings:-Login to rate: When angle is measured in Radians, the relationship between arc length, radius and angle is: To convert angle between degrees and radians use: Example 1. Quiz of the Day #quiz #QuizTime #maths #mathsquiz #mathematics #questionoftheday #MathsQuestions #radianbookcompany #competitiveexams #mathschallenge #education #learning. 003 (Fall 2011) Quiz #3 November 16, 2011 Name: Kerberos Username: Please circle your section number: Section. Convert each degree measure into radians. If we look at the unitary circle below we can see that 180° = π and 360° = 2π. With Radians MyViz Custom Apparel Design program, you can design and customize your high visbility safety apparel. To leave the "Quiz Me" feature, click RESET (or press "r" on the keyboard). Who thinks girls can't fight better than boys play Valorant as Jett! She is quick as light and more dangerous than you can imagine. Note: The radian is the standard unit of angular measure, used in many areas of mathematics. Start studying Radians & Reference Angles. Question 4 of 5. x — Chapter 8 summary and quiz. Topics on the quiz include converting radians to degrees and the main …. The graph below shows radian measure in all 4 Quadrants with their corresponding angles. Show Class. rotate_x_rad — rotates a vector around the x-axis by the angle in radians. To show the answer click the chosen point (or press ENTER on the keyboard). Next lesson. com is a free online quiz making tool. Unit Circle with Everything. Good luck — the …. If secθ > 0 and tanθ < 0, the angle θ is in: A. Safe + Steel anti-rebound bar. Trigonometric Ratios Quiz. Trig Test II Review Assignment. You can use this fact to convert from degree measure to radian measure. Quiz of the Day #quiz #QuizTime #maths #mathsquiz #mathematics #questionoftheday #MathsQuestions #radianbookcompany #competitiveexams #mathschallenge #education #learning. 005555556π = 0. Math algebra free online quizzes. Simple Math Minefield (1-100) 785. In a circle of radius 1, the radian measure of a given central angle can be thought of as the length of the arc associated with the angle. Using the formula v = ωr, the linear speed of a point on the surface of the drill bit is, v = ωr. 2π radians. Trigonometry Rules for Radians. This is a gap-fill quiz. 003 (Fall 2011) Quiz #3 November 16, 2011 Name: Kerberos Username: Please circle your section number: Section. You can navigate to next or previous quiz questions, or go to a specific numbered question and answer. Converting angles to decimal format, converting angles to degrees, minutes and seconds, converting radians to degrees, simplifying trigonometrical identities. The definition of radians and how to convert to degrees. Convert 510 o to Radians Preview this quiz on Quizizz. For example, a pizza slice is an example of a sector representing a fraction of the pizza. Learn vocabulary, terms, and more with flashcards, games, and other study tools. We at Radian Book Company are dedicated to carrying the legacy of our mentor Dr. It is measured in radians/second. radians() method converts a degree value into radians. This radian arts and crafts activity is designed to help students conceptually understand what a radian is. Liquidity Quiz - Answers Q: Calculate the Acid Ratio. ECSE-1010 Quiz 4 Fall 2020 2 M. Determine the value What is the measure of the …. Meaning of Radian. 1 Rand's Quiz 2. To recall, a sector is a portion of a circle enclosed between its two radii and the arc adjoining them. Worked Solution You must have an active subscription to access course content. 25π rad = 0. February 17, 2020. BIG Trig Quiz Review Sheet Find the length of each arc. Stanley® SYE21-10D Over the Glass. Only at Sephora. mathcentre. Radians and the Trigonometric Ratios. Movie Downvote GIFs. 9998476951563913 Note that all of the trig functions convert between an angle and the ratio of two sides of a triangle. 2 Explain how the unit circle in the coordinate plane enables the extension of trigonometric functions to all real numbers, interpreted as radian measures of angles traversed counterclockwise around the unit circle. 1) Convert 90° to radians. Heres a quiz on some of the basics of Trig. 83% average accuracy. We at Radian Book Company are dedicated to carrying the legacy of our mentor Dr. To calculate area of a sector, use the following formula: Undefined control sequence \measuredangle. One radian is just under 57. What are the x-values at the maxima and minima of this function? 90° and 270° or. Python offers inbuilt methods to handle this functionality. Quiz – Finding Trig Ratios F P PreTest Review F/A P Test – Trig in Radians 1 Radian is defined as the size of an angle that is subtended by an arc with a length. Math test activities for students and teachers of all grade levels. pdf from MATH MISC at Bellevue College. Algebra 2 Course - Unit 19 The Unit Circle, Degrees and Radians, Inverse Trig Functions, Trig Equations. An angle's measurement in radians is numerically equal to the length of a corresponding arc of a unit circle; one radian is just under 57. Radian works well in any graphic design project and purpose, both as a display typeface and in smaller sizes. Skincare Concerns: Dark Spots, Dryness, and Dullness. This plethora of printable worksheets specifically deals with the conversion of degrees to radians and vice-versa. These relations allow conversion from degrees to radians and vice versa. divide and conquer. Question 5 of 5. 2 Explain how the unit circle in the coordinate …. 10th - 12th grade. Example 2: 7/4π radians = 7π/4 x 180/π = 1260π/4π ÷ 4π/4π = 315°. An angle's measurement in radians is numerically equal to the length of a corresponding arc of a unit circle; one radian is just under 57. Convert angle measures given in degrees to radians and vice versa. Calculate Properties--Change Arc to Match--Links. atan2 Arc tangent of two variables -- pass in two values like (x, y), and you'll. 0472 radians. Improve your math knowledge with free questions in "Convert between radians and degrees" and thousands of other math skills. To leave the "Quiz Me" feature, click RESET (or press "r" on the keyboard). Aggarwal (renowned author and mathematician). 1 Description 2 Events 2. Degrees Radians Degrees, denoted by °, are a measurement of angle size that is determined by dividing a circle into 360 equal pieces. The Official Knights Radiant Order Quiz. Find the length of a circular arc subtended by an angle of radians if the radius ofthe circle is 36 cm. Radiant Quiz. Learn More. Types Of Triangles Quiz. TPG Darkeyes Members Darkeyes 1 post;. 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Other articles where Radian is discussed: steradian: …solid and the English word radian, a steradian is, in effect, a solid radian; the radian is an SI unit of plane-angle measurement defined as the angle of a circle subtended by an arc equal in length to the circle's radius. c) Different for each wave, and shown by the change in angle. & Intro to Trigonometry Name: _____ Period: ____ Date: _____ You MUST SHOW YOUR WORK in a legible fashion using mathematically correct notation. clickcalculators. 292 #79 – 94 , #95 – 100, 106, 107 Thursday 10/3. Converting special angles between degrees and exact radians. 49) - 4p 3 50) 11p 4 51) - p 6 52) 125p 36 Find the length of each arc. Python includes two functions in the math package; radians converts degrees to radians, and degrees converts radians to degrees. 20 Questions Show answers. It explains the definition of the radian and how to calculate the a. Algebra 2: Converting Degrees and Radians. Radians and Arc Length Quiz FORMULAS: Arc Length Radians/Degrees % Degrees = × &'( = Radians = × &'( % = 1. Title: degrees to radians with key Author: boydl Created Date: 4/8/2015 9:48:54 AM Keywords (). Since all circles are similar, one radian is the same value for all circles. Degrees and radians are the two types of units to measure angles and are frequently used in high school math. Safety comes in many colors, styles, and standards. Solution: By the formula, we know; Angle in radians = Angle in degree × π/180. Trigonometry Rules for Radians. If you don't see any interesting for you, use our search form on bottom ↓. If we look at the unitary circle below we can see that 180° = π and 360° = 2π. The good thing is that it's fun and easy to learn!. Math algebra free online quizzes. Unit 1, Unit 2, Unit 3, Unit 4, Unit 5. Normally it is best to leave the answer with ∏ because that is exact. Radians will only account for a small portion (around 5%) of SAT math questions, but you still want to get those questions right!Radians are one of the trickier concepts. Trigonometric Equations And Inequations Quiz. Change each mil measurement to radian measure. One radian is just under 57. 25π rad = 0. Radians - Revision Quiz 1. Take the Quiz: Trigonometry. com In this unit, we extend these ideas into functions that are defined for all real numbers! However, what if we measured the circle according to how many units we went. We typically will draw angles in the coordinate plane with the initial side along the. Exercises and Quizzes. Quiz – Finding Trig Ratios F P PreTest Review F/A P Test – Trig in Radians 1 Radian is defined as the size of an angle that is subtended by an arc with a length. As it turns out, one radian is equal to approximately 57. The hands of a clock show 7:10. Followers 0. 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Plugging the angle value, in degrees, in the previous formula, we get: α rad = π × 45 /180 =. Math algebra free online quizzes. The smaller gear has a radius of. 1-20 Square Roots 375. This article explains an easy way to memorize points on the unit circle. So our answer is ∏/2 radians. An angle's measurement in radians is numerically equal to the length of a corresponding arc of a unit circle; one radian is just under 57. Except in practical geometry, in calculus. Identifying Trig Ratios: Quick Formative Assessment. To match the output of your calculator you need: >>> math. 1 Rand's Quiz 2. This quiz previously ran as. degrees = radians × 180° / π. Definition of radian: Radians are an angular measurement. What is the measure, in radians, of the smaller angle formed between the hour and minute hands? Round your answer to one decimal place. Sinusoidal Application Problems Worksheet. Convert each degree measure into radians. Free student math practice. Converting special angles between degrees and exact radians. There are two types of sectors, minor and major sector. › Posted at 3 days ago. 3 mil! 12! 8 3! 2! 2. Name 600 s 8 mi 77t 15 cm 1500 12 km 37t 10 cm 75Tt cm- Date mi 1057t cm 17 cm 57t 2897t cnv k mg 13 km Convert each degree measure into radians and each radian measure into degrees. It is measured in radians/second. Free student math practice. System Of Linear Equations Using Matrices Quiz. Therefore =. Nudity or sexual content Hateful, harmful, violent, or abusive content Harassment Child abuse Promotes terrorism. This quiz previously ran as. Even easier, this calculator can solve it for you. Her real name is Joon-Hee and belongs to South Korea. Below steps show the …. rotate_x — rotates a vector around the x-axis by the angle in degrees. 01745329252 rad. Topics on the quiz include converting radians to degrees and the main ways of. degress () and radians () are methods specified in math module in Python 3 and Python 2. Because radian measure is the ratio of two lengths, it is a unitless measure. Express $$\dfrac{{7\pi }}{6}$$ radians in degrees. For example, if you want to create a large. All of the above. Please click "Next". Good luck — the stickman is counting on you! Learn with flashcards, games and more — for free. Get Free Access See Review. rotates the vector by a given angle in radians in place. This is a copy of the video http://www. Below steps show the …. Tip: See also math. Honors Algebra 2/ Trigonometry. Radians - Revision Quiz 1. You can think of a radian as a partial circumference of a circle. org are unblocked. Aggarwal (renowned author and mathematician). The fate of Roshar hangs in the balance, and once again radiant spren seek to bond with humankind. Find the exact value of cos (-7 π/6) and the reciprocal of this trigonometric ratio. 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text:
# Homework Help: Vector proof

1. Oct 29, 2006

### thenewbosco

Prove that $$\frac{|B|A+|A|B}{|A|+|B|}$$ is the bisector of the angle formed by A and B. where i have used normal text for vector and abs value bars to represent magnitude of vector.

i have no clue how to get started on this. i have tried many approaches such as constructing a triangle with a, b, and b-a, but i cannot seem to make any progress. a couple of hints on getting started would be appreciated

2. Oct 29, 2006

Write two equations:

$$ax+by+c = 0$$
$$cx+dy+e = 0$$

3. Oct 29, 2006

### thenewbosco

and what do these equations represent?

4. Oct 29, 2006

### Office_Shredder

Staff Emeritus
I don't know off the top of my head (i'm not a vector geometry expert), but if you call the bisector vector C, taking $$A \cdot C$$ and $$B \cdot C$$ and knowing the cosine half angle formula should be a decent way to start

5. Oct 29, 2006

### Hurkyl

Staff Emeritus
You want to know that the vector you constructed (I'll call it C) is the angle bisector of A and B. Therefore, you want to know:

(1) The angle between A and B
(2) The angle between A and C
(3) The angle between B and C

don't you?

6. Oct 29, 2006


text:
The BBC floppy disk image is a test setup intended to demonstrate Cowgol and provide me something to test. It’s not really intended for use for daily development, because it’s really slow.

## Instructions

You need:

• A BBC Micro with a 6502 Tube second processor. (Or BBC Master Turbo.)

• A single floppy disk drive.

• An ADFS file system ROM.

To use, simply boot the disk with SHIFT+BREAK and it’ll run the compiler, turning a source file called $.TestProg into a binary called $.cow/out. (The first time you run it it will precompile the standard library, which saves time on subsequent runs.)

If you don’t have one of these, here’s a screencast.

## Big warnings

• The compiler is really slow. Really, really slow. There are some design flaws which mean that the standard library is way more expensive to compile than it should be, but the end result means it takes about eight minutes to compile anything. I’m working on this.

• The compiler is really buggy. Really, really buggy. This is a really early release, and it’s about in a state where it’ll compile “Hello, world” — mostly. Caveat emptor and your mileage may vary. See anything wrong? File a bug! No matter how trivial. Remember, if you don’t report it, I can’t fix it…

• The driver script has no error checking. If your program has compilation errors, the script (which is a just a crude *EXEC script) will push on anyway. Be ready with CTRL+SHIFT to see the messages if it looks like anything’s going wrong. Then press CTRL+BREAK to interrupt things.

• BREAK doesn’t work properly. The mini Tube OS tries to reenter the last executed program when you press BREAK, which doesn’t really work here; I’m looking for a fix for this. But for now, if you just press BREAK, it’ll rerun random bits of compiler pipeline and bad stuff will happen. Use CTRL+BREAK instead.

• Cowgol binaries hate Basic. Cowgol stomps all over Basic’s private workspace, and they don’t clean up properly afterwards. (Because reasons.) Basic can get upset, including crashlooping with Bad program errors. To be safe, only run Cowgol programs from the Supervisor. Use this to enter it:

*GO F800

• The compiler does lots and lots of file access. In fact, it’s mostly I/O bound. The faster your disk system, the better. (If you try Cowgol on a real hard drive, please let me know!) It also needs a file system which has decent support for writing to multiple files simultaneously; DFS doesn’t work so well, even aside from the 200kB disk size limit.

• The compiler doesn’t set the execution address of the output binary yet. Sorry. Set it yourself, or do:

*LOAD cow/out 800
*GO 800


text:
# Utility method to view submatrices

I implemented an utility method that is able to view an Array[n, m] in another smaller dimension [k, l], where n%k = 0 and m%l = 0.

Example:

              -- --     -- --
---   ---     |1 2|     |3 4|
|1 2 3 4|     |5 6|     |7 8|
|5 6 7 8|  => -- --(a0) -- --(a1)
|4 3 2 1|     -- --     -- --
|8 7 6 5|     |4 3|     |2 1|
---   ---     |8 7|     |6 5|
-- --(a2) -- --(a3)

public static IEnumerable<T[,]> ViewAsNByM<T>(this T[,] values, int n, int m)
{
var count = values.GetLength(0)*values.GetLength(1);
for (int i = 0; i < count/(n*m); ++i)
{
var matrix = new T[n, m];
for (int j = 0; j < n; ++j)
{
for (int k = 0; k < m; ++k)
{
matrix[j, k] = values[j + (i / m * n), (k + i*m)% values.GetLength(0)];
}
}
yield return matrix;
}
}

Nunit test:

[Test]
public void TestViewAsNbyM()
{
var numbers = new[,]
{
{1, 2, 3, 4},
{5, 6, 7, 8},
{4, 3, 2, 1},
{8, 7, 6, 5}
};

var aux = numbers.ViewAsNByM(2, 2).ToList();
Assert.AreEqual(4, aux.Count);

var a0 = new[,] {{1, 2}, {5, 6}};
var a1 = new[,] {{3, 4}, {7, 8}};
var a2 = new[,] { { 4, 3 }, { 8, 7 } };
var a3 = new[,] { { 2, 1 }, { 6, 5 } };

Assert.That(aux, Is.EquivalentTo(new[] {a0,a1,a2,a3}));
}

• I don't have any suggestions (right now) but I'm curious what is it for? ;-P – t3chb0t Aug 20 '16 at 9:55
• @t3chb0t I think I will be using it for a sudoku game. To view the whole board as 3,3 groups – Bruno Costa Aug 20 '16 at 9:56
• there is no validation in method you mentioned before n%k = 0 and m%l = 0 – Disappointed Aug 20 '16 at 11:34

• Your solution seems to work fine fine for square matrix(where n = m). However, when presented with non-square matrix, the result becomes purely sporadic. This may or may not be problematic, depending on which kind of matrix you have to deal with.
• Modulo % is quite expensive.
• You are copying the array item by item. It is not the best way to it, especially when you are copying a continuous section within an array (where m > 1)
• You should cache the result of values.GetLength(0), and more importantly values[0].GetLength(0), as they are expensive.

public static IEnumerable<T[,]> ViewAsNByM2<T>(this T[,] values, int n, int m)
{
int height = values.GetLength(0), width = values.GetLength(1);
int rows = height / n, columns = width / m;

for (int row = 0; row < rows; row++)
{
for (int column = 0; column < columns; column++)
{
var matrix = new T[n, m];
for (int i = 0; i < n; i++)
{
Array.ConstrainedCopy(
values, (row * n + i) * width + column * m,
matrix, i * m,
m);
}
yield return matrix;
}
}
}

• Array.ConstrainedCopy is a nice tip. It was also nice that you could avoid the modulo. – Bruno Costa Aug 24 '16 at 20:14

(k + i*m)% values.GetLength(0)

This should have been (k + i*m)% values[0].GetLength(0)

It seems my implementation is a bit stricter than stated. In matter of fact it only allows matrices where k=sqrt(n) and l=sqrt(m).

While my previous implementation was what I strictly needed to view an array of 9 by 9 as 3 by 3, the algorithm can be adjusted in order to support any divisor of (n, m), including 1. Meanwhile I also decided that I prefer using jagged arrays.

public static IEnumerable<T[][]> ViewAsNByM<T>(this T[][] values, int m, int n)
{
var count = values.GetLength(0)*values[0].GetLength(0);
for (int i = 0; i < count/(n*m); ++i)
{
var matrix = new T[m][];
for (int j = 0; j < m; ++j)
{
matrix[j] = new T[n];
for (int k = 0; k < n; ++k)
{
int idxRow = j + (i/(values[0].GetLength(0)/n))*m;
int idxCol = (k + i*n)%values[0].GetLength(0);
matrix[j][k] = values[idxRow][idxCol];
}
}
yield return matrix;
}
}

And a test

[Test]
public void TestViewAsNbyM6By6()
{
var numbers = new[]
{
new[] { 1, 2, 3, 4, 5, 6},
new[] { 5, 6, 7, 8, 9, 1},
new[] { 4, 3, 2, 1, 0, 9},
new[] { 8, 7, 6, 5, 4, 3},
new[] { 2, 1, 0, 9, 8, 7},
new[] { 6, 5, 4, 3, 2, 1}
};

var aux = numbers.ViewAsNByM(3, 3).ToList();
Assert.AreEqual(4, aux.Count);

var a0 = new[] { new[] { 1, 2, 3 }, new[] { 5, 6, 7 }, new [] {4, 3, 2} };
var a1 = new[] { new[] { 4, 5, 6 }, new[] { 8, 9, 1 }, new [] {1, 0, 9} };
var a2 = new[] { new[] { 8, 7, 6 }, new[] { 2, 1, 0 }, new[] { 6, 5, 4 } };
var a3 = new[] { new[] { 5, 4, 3 }, new[] { 9, 8, 7 }, new[] { 3, 2, 1 } };

Assert.That(aux, Is.EquivalentTo(new[] { a0, a1, a2, a3 }));
}

• do we need to review your question or answer ? – Disappointed Aug 24 '16 at 11:19
• @Disappointed Due to community rules you should review my question. The code is not that different anyway. If you have other issues that you detected please give a new answer. – Bruno Costa Aug 24 '16 at 11:44


text:
## Blender Node API, what do we want?

Discussion related to the 'LuxBlend' Blender 2.4+ python exporter script.

Moderators: Ratow, SATtva, coordinators

### Blender Node API, what do we want?

So, I was contacted by Lukas Tönne, a Blender dev, who started working on a Node API for Blender back in December.

I'll quote what he said:
Code: Select all
<lukas_t> hey :)<lukas_t> DingTo pointed me at the BA luxrender/cycles/render API/custom nodes discussion yesterday ;)<lukas_t> i had put the custom node project on ice a few weeks back, but seeing the demand growing makes me want to pick it up again<lukas_t> part of the problem with the code was that it was simply too broad and unfocused<lukas_t> but i think i have a better idea of what can be done with reasonable effort and without breaking too much glass<lukas_t> i need to set some tangible goals (which will also make funding from blender dev fund possible :D)<lukas_t> and luxrender devs and users are probably a good source of suggestions and feedback :)<lukas_t> also the vfx guys (big topic atm of course)

The discussion he refers to is here, and spans a few pages.

I've also been talking with the Yafaray developers, who also would like to be able to create custom nodes in Blender for their exporter.

So, I was thinking if we can figure out what we "need" from a Node API, and then coordinate with the Yafaray guys to find some common feature set which is essential for us both, then we have a much greater chance of getting this implemented.

Now, I've not used the node stuff in Blender much yet, so I'd like some feedback from you blender pros in terms of workflow. I think initially it's best if we aim for workflow and highlevel features to present to Lukas, and take it from there.
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Lord Crc

Posts: 4517
Joined: Sat Nov 17, 2007 2:10 pm

### Re: Blender Node API, what do we want?

I'd suggest something similar to the current workflow for the cycles material nodes. Input nodes would set up the shader type (glass / diffuse / metal / etc) which would go to the output node on a per object basis. On the input nodes you would enter in parameters like color/specularity and whatnot. In between the input and output nodes would be space to modify those parameters like texture inputs to affect the material's parameters. I'm a little busy, but I'll try and whip up a picture with the current nodes to get the just of what I'm saying.
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A-man

Posts: 691
Joined: Sat Apr 24, 2010 4:24 pm

### Re: Blender Node API, what do we want?

For those who haven't worked with Cycles before, here's a really simple node setup for a matte red surface:

The material output node represents the final result of that Blender mat, and the diffuse bsdf node gives the surface its properties. It has sockets on it for textures.

In Lux, a mesh has several different shaders, surface, interior, exterior, and emission. The way this maps out in Blender is that each Blender material acts as a group of all 4 shaders, so I figure the material output node would represent that. Cycles adds two types of material nodes, "shaders" and "textures". What I would propose doing would be to add 4 for Lux: "surface shader", "volume shader", "emission shader", and "texture". For surface, those would be the normal mat types, matte, glossy, metal2, etc. Volume shaders would be a "clear" and a "homogeneous" node (with exponential/cloud/whatever nodes as we need them ). Emission nodes would just have one node called "emission". Kinda awkward, but I can't think of a better way of doing it with the way Blender's node editor is set up. Then there would be a texture node type for all of our texture types.

So given that, I made some quick mockups in Illustrator so you can visualize how the node graph would flow. Here's the Lux version of that red matte material:
node-mockup-matte-01.png (11.3 KiB) Viewed 1508 times

And here's some glass2 beer with measured absorption from the file delicious_beer.dat:

EDIT: Forgot cycles screenshot
Last edited by J the Ninja on Mon Feb 27, 2012 9:32 pm, edited 1 time in total.
-Jason

J the Ninja

Posts: 2249
Joined: Wed May 19, 2010 9:54 pm
Location: Portland, USA

### Re: Blender Node API, what do we want?

So for what we need to accomplish that:

-The need to define our own nodes (duh) and which groups they are part of in the "add node" menu. These should only appear when Lux is the active render engine. For reference, see how the "shader" and "texture" groups are added to material nodes when Cycles is selected
-The ability to define custom input/output types (we would need: color texture, float texture, fresnel texture, surface shader, volume shader, and emission shader)
-Jason

J the Ninja

Posts: 2249
Joined: Wed May 19, 2010 9:54 pm
Location: Portland, USA

### Re: Blender Node API, what do we want?

Btw. I think it would be cool if the "old" system could still remain besides of the nodes (like it is in Cycles atm). When you are really working some things are very faster to accomplish with nodes, but in some other cases the "old" system is faster (like when you just need a glossy material quick - add a material, switch it to glossy).
Nodes are mainly an advantage when building very complex materials (like the ones that were submitted to the Materials & Textures Competition), the "old" system is faster when you just need a simple material.

B.Y.O.B.

Posts: 1911
Joined: Wed Nov 10, 2010 4:10 pm
Location: Germany

### Re: Blender Node API, what do we want?

B.Y.O.B. wrote:Btw. I think it would be cool if the "old" system could still remain besides of the nodes (like it is in Cycles atm). When you are really working some things are very faster to accomplish with nodes, but in some other cases the "old" system is faster (like when you just need a glossy material quick - add a material, switch it to glossy).
Nodes are mainly an advantage when building very complex materials (like the ones that were submitted to the Materials & Textures Competition), the "old" system is faster when you just need a simple material.

Honestly, having a "use nodes" button that switches between the current panel UI and node materials using a UI almost identical to the way Cycles does is probably the way things will wind up. Because it's both the best solution and will probably be the simplest to do anyway.
-Jason

J the Ninja

Posts: 2249
Joined: Wed May 19, 2010 9:54 pm
Location: Portland, USA

### Re: Blender Node API, what do we want?

J the Ninja wrote:Honestly, having a "use nodes" button that switches between the current panel UI and node materials using a UI almost identical to the way Cycles does is probably the way things will wind up.

Will this button only switch the "use nodes"-state for a single material or for every material globally? What do you think would be better?

B.Y.O.B.

Posts: 1911
Joined: Wed Nov 10, 2010 4:10 pm
Location: Germany

### Re: Blender Node API, what do we want?

Hi,

Nice!
To sum up:
- a node is a container of internal properties, inputs and outputs
- each property has a type, a name and eventually a value
- types will include floats, filenames, colors, string, bools, user defined types (with no explicit value)
- inputs can be connected to outputs if and only if the types matches
- it'd be nice to have 2 views for the graph: a node view and a hierarchical list view (that one would provide the current GUI)
- the graph needs to be saved within the blend file

Am I missing something?

Jeanphi
jeanphi

Posts: 6624
Joined: Mon Jan 14, 2008 7:21 am

### Re: Blender Node API, what do we want?

J the Ninja wrote:
Screen Shot 2012-02-27 at 6.19.44 PM.png

Compare also with my original prototype diagram

dougal2

Posts: 3075
Joined: Mon Jan 14, 2008 7:21 am

### Re: Blender Node API, what do we want?

I think a node editor is a great idea. Nodes make things more complex but nodes seem to have emerged as a meme so I think we should switch to them because it makes things more consistent and comfortable for users. Looking at dougal's screen shot, on the left we see a clean compressed display of all the options, on the right we see a psudo flowchart which takes up a lot more space with nice lines connecting them.

I think there is a video which really captures this idea, something I am sure LordCrc will remember: http://www.theonion.com/video/breaking- ... ati,14204/

www.carbonflux.org - photographing the imagination.

Carbonflux

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Next


text:
# Refresh dynamic variable when used with Get

I came across this issue with a more complicated program I was working on.

Suppose we have a volatile variable data:

In[1]:= data = RandomReal[{0,1},{10}];

As this cell is evaluated,

In[2]:= Dynamic@data

refreshes as expected.

However, if we want to save a certain instance of data and later load it in:

In[3]:= DumpSave["filepath.mx",data]

(change value of data to something else)

In[4]:= <<"filepath.mx"

the dynamic cell (In[2]) isn't updated (unless you evaluate it again). It can be forced to update on the loading of the .mx file by using a Refresh[...,UpdateInterval->time], but it seems odd that re-evaluating In[1] instantly changes the dynamic cell while redefining data with the .mx file doesn't.

Any explanation for this? And is using the Refresh method a good solution here?

-
I always figured that Update was intended to be used exactly in situations like this, however it doesn't seem to work. – jVincent May 6 '13 at 14:58

I have no insight into the internals but have found several situations where for whatever reasons the automatic determination of the necissity to update fails. I would wish there would be a programmatic possibility to tell Mathematica that a ceratin symbol has changed, but don't know about that. Of course you could do something stupid like this to inforce an update:

 Module[{datax = data}, data =.; data = datax]

Another workaround would be to use Export and Import instead of DumpSave and Get:

 Export["filepath.mx", data];

and then do:

 data = Import["filepath.mx"]

Here the explicit Set for data will trigger the update of the Dynamic.

-

Often I do something kludgy like

Dynamic[foo; data]

<<"filepath.mx"; foo++

It's somewhat similar to Albert Retey's first solution. However, foo is a global variable and data can be an arbitrary piece of code.

Here's a way to dress it up. It does the same thing, but it reads better.

ClearAll[dependsOn, update];
SetAttributes[dependsOn, HoldAll];
SetAttributes[update, HoldAll];
dependsOn[sym_Symbol] := (
dependsOn[sym] = 0;
update[sym] := (dependsOn[sym] = 1 - dependsOn[sym];))

data = RandomReal[{0, 1}, {10}];
DumpSave["filepath.mx",data]

Dynamic[dependsOn[data]; data]

data = RandomReal[{0, 1}, {10}];

<< "filepath.mx"; update[data]

-


text:
# Issues

Issue #96 resolved

# Documentation: Bug in Euclid's proof

Sebastian Korten
created an issue

There is a problem with euclids proof in the tutorial at the beginning of the beamerguide --- it is wrong.\

By the stated proof (13! + 1) should be prime, which it is not (it's 83 * 75024347).\ [Furthermore: (17!+1) = 538105034941 * 661 and (19! +1) = 1713311273363831 * 71)]\

It it true that (19!+1) is not divisible by any integer <= 19, but that is definitely not enough to prove that it is prime.\

You will find euclids proof explained here:\ http://aleph0.clarku.edu/~djoyce/java/elements/bookIX/propIX20.html\

The reason why I report this as a bug is that I read the beamer documentation some years ago and up until two days ago I thought the proof was valid ;o)

I hope you understand that this 'bugs' me ;o)

Btw, I love beamer. Thank you so much for your effort!

1. reporter

This would be a possible fix:

\begin{proof}
\begin{enumerate}
\item<1-> Suppose $P$ is a set containing all known prime numbers
\item<2-> $q = (\prod\limits_{x\in P}{x}) + 1$
\item<3-> $q$ is not divisible by any number in $P$
\item<4-> \alert{Either} $q$ is prime and $q \not\in P$
\item<5-> \alert{or} $q$ is not prime, but has at least two prime factors $a, b \not\in P$
\item<6-> $\Rightarrow$ there are more prime numbers than those in $P$\qedhere
\end{enumerate}
\end{proof}

2. reporter
• removed assignee

Fix to my fix ;o) There are not necessarily "two" prime factors \not\in N if $q$ is not prime, just one