text:
Short guide to the use of laser cutting machines

This is a very short guide that explains how to use of laser cutting machines.

Laser cutting machines allow users to instruct through software the designs that it will follows to cut a material, these includes size, height, shapes, etc.

Introduction
The process start creating a vector graphic, that is a scalable image that follow a defined function, this able the user and system to resize the image holding the form or function if desired. Once the graphic is created it can be opened with the software that controls the laser cutter.

Time: Many works last seconds to be completed, others with more instructions or different settings can last from minutes to hours.

Laser cutting machine
It consist in a bed or grill where the material is placed and a shield to protect users, also a cover. (Max size of material 12x24 inches). It also can include an air filter, this allow to extract any toxic material generated during the cutting process.

The laser cutting machine that we will working with is made by the company: Universal Laser Systems.

Model: VLS 3.5

Software used to control the laser cutting machine: UCP (Universal Laser System Control Panel) V 5.38.58

Material maximum thickness for cutting: 1/4 inches (0.25 inches).

Other tools
Computer connected to the laser cutting machine with a version of its control software installed.

Level peg: Its allow to level the position of the bed in the machine, this allows precise cutting when using the machine.

Other used tools include:

Calipers: Tool used to measure the thickness of the material.

A material to cut: Some laser cutting machines have a limit in the thickness of the material or in the types of materials that can cut. In some cases 1/4 0.125 or less

Auxiliary software
Auxiliary software for vector drawing: Adobe Illustrator, Inkscape and others.

A vector graphics editor software such as Illustrator or Inkscape, they are used to generate scalable image files.

Time
The time required to complete the cutting can range from seconds to hours, depending on the complexity of the project.

Observations:

 * Sometimes the used software can operates only with inches measure and not centimeters, mm, etc.
 * Sometimes the used software can operates only with RGB color model (Red, green and blue) and not with CMYK color mode (cyan, magenta, yellow, and key).
 * Unfinished wood could be preferred, since it is not coated with flammable or odor materials.

1.- Design a vector graphic file
Create the desired cut or design in the vector graphic editor. Some laser cutter machines works only with RGB colors and not with CYMK colors.

Create a new file
Create a new file with distance measured in inches and color in RGB format, for this:

When using Adobe illustrator create a new file, choose a preset (letter 8.5x11 or any other option), in color mode change CMYK to RGB and change the units of measure from points to inches, then click the option create to start the new file.

When using Inkscape the color mode can be changed RGB in the color palette of the files during anytime of the work. To change measure unit in Inkscape select the options file, document properties and change the display units from mm to inches.

Draw an object to be cut
Create an object: If using illustrator choose the 5th icon from the left panel (the option with a square icon). When learning to use the cutter use a small image around 1 inch long or wide... change units to inches if the cutters operates with inches.

This object can be bigger than other object place inside to attain a raster object inside a cut object.

Stroke
The stroke of the object refers to the wide of the line, it is measured in points, lines or objects with a stroke of 0.072 pts (0.001" or 0.254 mm), smaller strokes may not cut the pieces. Strokes can be seen as the thickness of a pen, a line written with a 0.8 mm pen is thicker than a line written with a 0.1 mm pen. If the thickness is to big may show black areas in the material when wood or plywood is used.

Save file to a memory file when creating the file in other computer.

Draw an object to be edged
Create a new object inside the bigger object.

Use color black (number 000000) for this object to edge it but not cut it. Another option is to filled with black color to attain a edge of the whole object and not only its shape.

Use of the ruler
The position of the objects in the design can also be calculated using the ruler, for this press at the same time the keys Ctrl and R. The ruler will appear in the superior and lateral sides of the page.

Changing the color of the lines or shapes
Some cutters works only with RGB colors, RGB color model uses a system of 6 number and letters. To change the color of a line or an object, click on the object, then in the properties window, appearance section, click on the square beside the fill option and in the filling space beside #, type the color number. The three more used colors in laser cutting to indicate what type of task will be done with the line or object are the following:

Black, to raster etching (000000)

Blue, to vector etching (0000FF)

Red, to cut Cutting (ff00000)

Choose the color palette icon and type ff0000, this will create a red color, this will indicate the printer that the line or object will be cut, or 000000 to raster etch, or 0000ff to vector etch.

Cutting, vector etching and raster etching
Once you have designed an object use the color numbers to complete the desired task.

Cutting
To cut objects a stroke with a width of 0.072 must be used and the color must be red (ff0000), the shape of object created will be cut in the wood or material that is being used.

Raster etching
Use black color, 00000, this will vector etch the design.

Vector etching
Use blue color, 0000FF, this will vector etch the design.

Review the file with the vector graphics editor
Insert a USB memory stick in computer that controls the cutter.

Open illustrator, open the file,

Zoom the to see lines they should be marked black and marked red they are marked in gray color, adjust the file to correct color. If color is not rf0000 it will not cut the material.

For this view, material.

Red is cutting lines black is raster lines

Zoom to see all the lines are properly marked or complete if not modify the file.

If everything is fine, then select preview cpu so gets the file ready... if not done may not cut properly the object.

Ctrl p to print (to laser cut)

Remember, if color is not red (ff0000, with 4 0s), and the stroke does not have a width of 0.072 points the object will not be cut.

Printing the object or design with the vector drawing software (Illustrator, Inkscape or other), select for the printer the Universal Laser Systems machine, this will send it to de UCP software that controls the laser cutting machine.

Open UCP, you will see the objects and lines to be raster or edge in black and the lines or objects to be cut in red.

2.- Measure and write the thickness of the material
Measure and write the thickness of the wood with caliper. close it, zero it, and measure, then write while still holding the piece.

3.- Cut the object with the laser cutting machine
The process of using the cutting machine can be summarized in the following steps:

 * 1.- Open the laser cutter machine.
 * 2.- Place the wood in the bed (first measure the thickness of the wood and calibrate the machine)
 * 3.- Use the pointer to see if the object will be cut in the right section of the wood or material.
 * 4.- Close the laser cutting machine,
 * 5.- Choose the type of material and type the thickness of the material,
 * 6.- Turn on the air filter
 * 7.- Press the green (play) to start the cutting.
 * 8.- Turn off the filters a few seconds after the cutting process finish.
 * 9.- Turn off the laser cutting software.
 * 10.- Clean area or continue with the next object to be cut.

ULS (user defined landscape): Change media to user defined landscape.modasue

Level the print bed
The leveling peg is kept in its own box, since only works for that particular laser cutting machine and no other nor similar model, even when where produced by the same maker, or is the same model, or was produced the same year. The piece is made for that machine only.

The box that holds the box was made to open it just from the upper corner, keep the level in when is not being used to prevent losing the peg.

Open the laser cutting machine cover.

Lift the metallic cover or shield of the laser header.

The controls in the left area of the laser cut will work to operate the material bed, to move the bed up or down, it will not move the laser header.

Put the leveling peg beside the laser red box area and the bed and hold it with the left hand.

Press the up to maker until the leveling peg is close or in front of the red box.

Caution: Do not put the leveling peg under the red box, it should be positioned just beside it, in order to avoid that the red box touch press the top of the leveling peg against the bed. It should just touch the side of he leveling peg.

At this point raise one button at the time the leveling peg, until it gets exactly aligned with the beginning of the diagonal line in the middle of the leveling peg.

The leveling peg will be located besides the laser cutting area, nor to the sides, not under, just besides to it, touching it with its borders. From this point one button at the time one movement is the correct level... one movement up is to high, one movement down is to low.

With one hand hold the leveling piece while with other hand control the height of the material bed up and down.

In this position the diagonal area of the leveling peg and the red box will be aligned, this means that the cut of the laser will be precise as required and cut the designs as intended from the top of the layer of the material until the dept of the raster or cut.

Once the machine is leveled, close the metal shield and close the metallic cover.

This step will allow the machine to know at what level is located the surface of the material to be cut, at the same time will allow a precise cut using this information.

Take the leveling peg and put it back inside of its box.

Place the material in the cutting bed
After measuring the thickness of the material, place the material into the bed.

Use of the UCP software
Open the UCP software, it can be open from the menu or form small the icons beside the clock. It may show the last printed design used.

Controls
Controls: zoom (in and out), second, third and forth button

Zoom in or out to move or see the object

click focus view to see if the red light is marked over the material

if not move the object on the software to an area near the material

or focus view in an area with material and then click in point level button it will take the object to the area,

then focus view the whole object points or borders are in the material area... leave some space far from material border.

The laser machine can be turned on or off with the control in the software installed in the computer.

Other options: Material selection, material thickness, laser power, raster power, level the print bed.

Reviewing the file
After printing the file in the Laser cutting machine software, you can see if the color of the object is red (to cut) or it has defined lines. This will allow you to know if your job is viable. You can zoom the object to see more details.

Material selection
Select the material that is being used: Settings, material,s database... In the case of plywood, choose: Natural, wood, medium wood, birch.

Start at zero

apply ok and close the laser cutter.

Change media file... using defined landscape. On illustrator or laser cutter software.

Raster first
Turn on the filter, close the lid.

Note for rastering/etichng: #00000

Use raster color for the objects:: #000000, 0.072 pt stroke.

Select the material: Natural, wood, medium, birch and use the thickness of the material measured: For example: 0.124

Select the option apply, then press ok.

Once the instructions are correct press the green button in order to run your job.

With the menu in the laser cutting machine computer program click the fifth button (beside the control bottom, zoom, view, move, go to, then square)

The raster will start and last for a few seconds, in some cases it can take minutes or hours. Time can be saved with modifications of the file.

Hold the the material and press the cut area down to see if it will not be separated from the material because a complete (deep) cut was not done since it was a raster cut, repeat it with a cutting length

Turn on the air filter
Press red button on the filter to turn filter on. (It is a big gray metallic box located besides the laser cutter).

Cut the material
Repeat the process, but this time the bigger object will be black and will be cut.

Change the lines or objects to color red (FF0000) since this is the color for cutting, and the stroke must be 0.072 pt (not 0.72 nor other width) since this is the stroke width for cutting.

This time repeat, the process but click skip raster and increase vector 2 % vector cort.

Select the material, and us the thickness: For example 0.127 brw

This second process the material will be completely cut with the bigger object shape and the inner object will be just rastered.

Press the green button (play) on software on computer to star the cutting. It will take a few seconds or minutes until is completed.

When laser cut is completed, turn off the filter,

Leave the material to cool a few seconds.

Press the cut section down while pressing the material up to release the cut segment. Hold the the material and press the cut area down, this will separate the cut piece with from the rest of the material.

Other options of UCP software
Zoom: To zoom into the image, also the image can be restored to its complete size.

Pointer: To see in the printer where a selected point is located in the material bed.

Go to, to go to a particular area or move the object to another area, or relocate the object to another area of the canvas or part of the material bed.

Other controls are

 * Laser power
 * Raster power

Cut the material
The material cutting process will be executed from the control software installed in the computer connected to the cutting machine. Initially you will do first a test cut or raster, after it, apply more depth to complete work.

Always run a test cut/raster on the material.

Rastering engraving, vector engraving and cutting objects with laser cutting machines
Add a object or draw a line or object, click the option fill (white box) and choose a color to fill the object with a color.

Raster engraving
Rastering is the translation of a "non vector" image into a workpiece, there for the outcome is not as clear as a vector engraving.

Vector engraving
Vector engraving is is the translation of a "vector image" into a workpiece, there for the outcome is not as clear as a vector engraving.

Cutting objects
When selecting a object, the border of the object can be etched to avoid square angles in the corner of the objects.

Rastering, engraving and cutting texts with laser cutting machines
The stroke refers to the wide of the lines not to the deep of the cut.

Select the option T (Type), type a text and change the stroke and filling colors.

The text or objects will be cut when a red line appears in ULS Control Panel software. Another option for practice is the use of 3d texts and make effects with inkscape adding gradients of the object.

Final steps
Turn off the equipment.

Put the used materials in their correspondent area.

Clean the area.

Safety measures

 * Never stare at the laser light directly nor with binoculars, microscopes, etc. The intense light during laser engraving or cutting can permanently the eye sight, it can cause cataracts and burns (retinal burn). To monitor the engraving can be used cellphones camera along there is not direct eye seeing of the laser beam.

Some other safety measures can be implemented such as the follow:

 * An air filter will be used (BOFA AD-500 iQ Laser Fume & Dust extraction system): It will be turned on before start the cutting. It will extract all the gas and particles produced during the cutting process.

 * Illumination and emergency illumination controls to properly see the environment.

 * Motion detection to detect movement in the laser cutting room.

 * Supervision of the cutting during the cutting process.

 * Installation of alarm buttons to use in case of accidents, that can be connected with emergency response services.

 * Instructions about what to do in case if an accident occurs, such as contact personal.

 * Some installations include a kill switch that turn off all the equipment, including the laser cutting machine, the computers and monitors connected to the laser cutting machine, this avoid to turn off each component, but should be used just in emergencies.


text:
Sylheti/Slang

The origins and history of Sylheti slang
The slang likely emerged organically within the community, influenced by the local Pakrit linguistic roots, conservative cultural values, and an ethnocentric perspective, reflecting the expressions of the Sylheti people in informal and social settings.

Situations where slang may not be suitable
Sylheti slang is best suited for casual and informal settings, like when you're hanging out with close friends or family. Situations where Sylheti slang may not be suitable:

How slang evolves over time and the influence of social media and technology
The catchy phrase "ꠍꠦꠟꠚꠤ ꠝꠣꠞꠅ," which translates to "kill a selfie" in English, reflects the evolving slang in Sylheti culture, showcasing how local languages adapt to contemporary trends influenced by social media and technology, demonstrating how expressions born from global trends can seamlessly integrate into local languages.

Contribute to the Wikibook with new slang expressions you may encounter

 * [ Add a new slang!]

Links to online resources, dictionaries, or courses for those interested in learning more about Sylheti slang

 * Sylheti Swear Words

license: Creative Commons - Attribution Share-Alike - https://creativecommons.org/licenses/by-sa/4.0/

title: Sylheti/Slang


text:
Chess Opening Theory/1. d4/1...Nf6/2. Bf4/2...e6/3. e3/3...b6

= London System Indian Setup with 2. Bf4 e6 =

The Indian Setup with ...e6 in the London System represents a flexible and adaptive approach for Black against the London. When White opts for the London System by playing 1.d4 and 2.Bf4, the setup with ...Nf6 and ...e6 allows Black to keep multiple options open for further development.

 * 1) Pawn Structure & Central Control:
 * 2) * White's d4 pawn, supported by the Bf4 bishop, grants a slight central space advantage.
 * 3) * Black's ...e6 provides the option for a central break with ...d5, directly challenging White's central structure.
 * 4) Piece Activity:
 * 5) * White's Bf4 is actively placed and targets the d6 square.
 * 6) * Black's Nf6 challenges the e4 square, discouraging immediate pawn advances by White.
 * 7) Plans and Strategies:
 * 8) * White often proceeds with Nf3, e3, and Bd3 to complete development and ensure central control.
 * 9) * Black has several plans, including playing ...d5 for a symmetrical structure or opting for a double fianchetto with ...b6 and ...g6.
 * 10) Key Imbalances:
 * 11) * If Black chooses ...d5 and exchanges occur on d5, the resulting pawn structure becomes symmetrical, shifting the game's dynamics towards piece activity and coordination.

Theory table
. '''1. d4 Nf6 2. Bf4 e6'''


text:
User:Adolfo Martin Fuentes

Welcome to my personal page at Wikibooks!

title: User:Adolfo Martin Fuentes


text:
Chess Opening Theory/1. d4/1...Nf6/2. Bf4/2...e6/3. e3

= London System Indian Setup with 2. Bf4 e6 =

After 3. e3, White aims for a solid, unbreakable center and potential queenside expansion, while Black seeks to challenge the center and develop harmoniously, keeping multiple pawn breaks and piece maneuvers in mind. After the moves 1. d4 Nf6 2. Bf4 e6 3. e3, both sides have committed to certain pawn structures and plans:

White's Position and Plans:

 * 1) Pawn Structure & Central Control:
 * 2) * White's pawn chain (d4-e3) is solid and tough to break. This setup supports the dark-squared bishop on f4 and restricts Black's pawn breaks.
 * 3) Piece Activity:
 * 4) * The Bf4 targets the d6 square and is also out of the pawn chain, ensuring its active participation in the game.
 * 5) Plans:
 * 6) * Development and King Safety: Nf3 and Bd3 are natural moves, followed by O-O.
 * 7) * Queenside Play: With the center secure, White can consider a queenside expansion with c4 (often after Nbd2), possibly followed by Qb3, Rc1, and a3-b4.
 * 8) * Center Control: Maintaining the pawn on d4 and preventing ...e5 or ...c5 breaks.
 * 9) * King's Side Attack: If Black fianchettoes the king's side, h2-h3 followed by g2-g4 can be a pawn storm plan.

Black's Position and Plans:

 * 1) Pawn Structure & Central Control:
 * 2) * Black's ...e6 provides support for a potential ...d5 pawn break, directly challenging White's center.
 * 3) Piece Activity:
 * 4) * The Nf6 is well placed, pressurizing the e4 square.
 * 5) Plans:
 * 6) * Central Breaks: ...d5 is the most straightforward plan to challenge White's central structure.
 * 7) * Bishop Development: The light-squared bishop can be developed to d6, challenging White's Bf4, or to e7. An alternative plan involves a fianchetto setup with ...b6 and ...Bb7.
 * 8) * Queenside Play: ...c5 can be an effective pawn break to challenge the center and open lines for the rooks and queen.
 * 9) * King's Side Play: If White overextends on the kingside, counterplay with ...Nh5 can challenge the Bf4 or ...f5 can be considered in some setups.
 * 10) * Knight Maneuvers: The knight on b8 can be developed to d7 or c6 based on the requirements of the position.

Theory table
. '''1. d4 Nf6 2. Bf4 e6 3. e3'''


text:
User talk:2601:400:C200:9760:686E:164F:494A:DA65

Warning
—Atcovi (Talk - Contribs) 16:07, 7 October 2023 (UTC)


text:
Chess Opening Theory/1. d4/1...Nf6/2. Bf4/2...e6

= London System Indian Setup with early Bf4 and Black ...e6 = A modernized approach is to delay the development of the Knight to f3 until after the development of the Dark Square Bishop (DSB) to f4 in the London System lies in a few key areas. The Indian Setup with ...e6 in the London System represents a flexible and adaptive approach for Black against the London. When White opts for the London System by playing 1.d4 and 2.Bf4, the setup with ...Nf6 and ...e6 allows Black to keep multiple options open for further development.

Benefits

 * Flexibility: By developing the DSB to f4 first, the player maintains flexibility in knight placement. This can be particularly useful in responses to unexpected opening moves by the opponent. For instance, the knight may be better placed on e2 or d2 depending on the opponent's setup.
 * Pawn Structure & Central Control:
 * White's d4 pawn, supported by the Bf4 bishop, grants a slight central space advantage.
 * Black's ...e6 provides the option for a central break with ...d5, directly challenging White's central structure.
 * Piece Activity:
 * White's Bf4 is actively placed and targets the d6 square.
 * Black's Nf6 challenges the e4 square, discouraging immediate pawn advances by White.
 * Plans and Strategies:
 * White often proceeds with Nf3, e3, and Bd3 to complete development and ensure central control.
 * Black has several plans, including playing ...d5 for a symmetrical structure or opting for a double fianchetto with ...b6 and ...g6.
 * Key Imbalances:
 * If Black chooses ...d5 and exchanges occur on d5, the resulting pawn structure becomes symmetrical, shifting the game's dynamics towards piece activity and coordination

 * Control Over Key Squares: The DSB placed on f4 controls the e5 square, a critical central square. This can prevent the opponent from easily establishing a strong central pawn duo or knight outpost. Meanwhile, delaying the knight's development means that the e5 square is not blocked and can be contested by pawns if necessary.
 * Defensive Potential: The DSB on f4 can contribute to the defense of the king, especially if the player decides to castle kingside. This can be essential in fending off early attacking attempts by the opponen

Drawbacks

 * Delayed Knight Development: A potential drawback of this strategy is that it delays the development of the Knight to f3, which can slow down overall piece development and the ability to castle. This could potentially lead to a disadvantage in the opening, especially if the opponent is fast in their development.
 * Potential Weakness: Delaying the knight development could also potentially leave the d4 pawn weak if the opponent attacks it early. The knight on f3 often helps in defending this pawn in the early stages of the game.

Conclusion
Like any strategic decision in chess, the decision to delay the development of the Knight to f3 until after the DSB to f4 in the London System depends on the specific position, the player's understanding of the position, and their overall game strategy. It's a decision that offers both potential benefits and drawbacks, and understanding these can help a player make the best decision for their specific situation.

Theory table
. '''1. d4 Nf6 2. Bf4 e6'''


text:
Chess Opening Theory/1. d4/1...Nf6/2. Bf4/2...e6/3. e3/3...d5/4. Nd2

= London System Main Line with Black ...e6 and ...c5 =

In the London System, following the moves '''1. d4 Nf6 2. Bf4 e6 3. e3 d5 4. Nd2''', White's strategy emphasizes proactive queenside development for defensive purposes and capitalizes on the activity of the dark-squared bishop to press for an advantage. White's strategy is based on the following core principles:

 * 1) Queenside Development for Defense: By proactively developing pieces on the queenside, White ensures a robust defense of the b2 pawn. This pawn often becomes vulnerable to attacks, especially when Black aims for ...Qb6, putting direct pressure on it.
 * 2) Leveraging the Active Bishop: The placement of the dark-squared bishop on f4 grants White a dynamic piece that can exert influence across the board. Its active positioning enhances White's prospects in both the middlegame and the endgame.
 * 3) Counteracting the Queen’s Gambit Declined Approach: While Black can attempt to adopt the structure and plans of the Queen's Gambit Declined, this often turns favorable for White. With the dark-squared bishop already actively placed outside the pawn chain, White generally retains a minor advantage, especially as the game transitions into endgame scenarios.

Theory table
. '''1. d4 d5 2. Bf4 Nf6 3. e3 e6 4. Nd2'''


text:
Algebra/Chapter 1/Units

1.8: Units

In mathematics, we are primarily concerned with measuring things. We can represent these measurements of physical qualities, such as length, mass, temperature, current, area, volume, intensity, etc. using what are called units of measurement.

title: Algebra/Chapter 1/Units


text:
Chess Opening Theory/1. d4/1...Nf6/2. Bf4/2...e6/3. e3/3...d5/4. Nd2/4...c5

= London System Main Line with Black ...e6 and ...c5 =

After '''1. d4 Nf6 2. Bf4 e6 3. e3 d5 4. Nd2 c5''', Black opts for a setup reminiscent of the Queen's Gambit Declined (QGD). This approach aims for a solid yet flexible structure, central and queenside counterplay, and harmonious development of pieces:

 * 1) Solid Central Pawn Structure: With ...e6 and ...d5, Black sets up a strong pawn chain in the center, often making it difficult for White to easily break through.
 * 2) Challenging White's Center: The move ...c5 directly targets White's central d4 pawn. This pawn break aims to destabilize White's pawn center and create counterplay on the queenside.
 * 3) Development and King Safety: Black can continue with natural developing moves such as ...Nc6 and ...Bd6, exchanging off White's active dark-squared bishop if possible. Following up with ...O-O ensures the king's safety.
 * 4) Activating the Light-Squared Bishop: One of Black's challenges in the QGD setup is the passive light-squared bishop on c8. Black can consider plans such as ...b6 and ...Ba6, or even a timely ...e5 pawn break, to free this bishop.
 * 5) Queenside Counterplay: Using the semi-open c-file, Black can look to increase pressure on the queenside. Rooks can be quickly deployed to the c-file, and pieces like the knight on b8 can be developed to c6, supporting the ...c5 break and increasing pressure on d4.
 * 6) Central Breaks: Depending on White's setup, Black can consider the ...e5 break in the center, especially if the opportunity arises where the d4 pawn can be targeted.

Theory table
. '''1. d4 d5 2. Bf4 Nf6 3. e3 e6 4. Nd2 c5'''


text:
Algebra/Chapter 1/Exercises

A set of exercises related to concepts from Chapter 1.

This set contains 55 exercises (including the Conceptual Questions)

Conceptual Questions
 Q1.1 (Alien Society) Imagine you came across an alien from a distant planet, where all of its civilians have a solid grasp of English and had three fingers on each hand. Though this civilization is intelligent, they had never learned about what "counting" is or how to do it. In addition to that, they had never learned about what a "number" is, what they're called, or what they looked like. Think about how you might teach this civilian about counting and numbers so that they can go back to their planet to teach their people of this knowledge. What tools might you use to explain the idea? What are some of the concepts you'd want to get across? What are some of the difficulties that might arise from this task?

 Q1.2 (What is a Number?) Define what a "number" is in your own words. Define what a "numeral" is in your own words.

 Q1.3 (Sign of Zero) Is the number zero positive, negative, or neither? Explain your reasoning.

 Q1.4 (Difference of Decimals) What is the difference between "ten" and "one-tenth"?

 Q1.5 (Picture Perfect) Suppose the number line actually existed physically. Would you be able to take a photo of the entire number line if you backed away far enough?

 Q1.6 (Explaining the Writing of Numbers) Explain in your own words how you write numbers, both in word form and with numerical symbols.

 Q1.7 (Largest Number Possible) What is the largest and smallest three-digit number you can write using the digits 0, 8, and 4? Use each digit only once, and explain how you obtained your results. If you wrote these numbers to the right of a decimal point, what is the largest number you can make.

 Q1.8 (A Million) A million is one thousand thousands. Explain how this is so.

 Q1.9 (Reading it Wrong) Explain what is wrong with reading "50,002" as "fifty-thousand and two". Explain what is wrong with reading "2.203" as "two and two hundred and three thousanths".

 Q1.11 (Number Associations) What whole numbers are associated with each word?

a. zilch b. duo c. decade d. a pair e. naught f. trio g. four score h. century

 Q1.12 (Problem with Fractions) Why can't we say that 3/5 of the figure below have been shaded in?

 Q1.13 (Large Numbers) Determine if the following is true: "The more digits a number has, the larger it is".

 Q1.14 (Signs) A fast-food menu has the cost of a hamburger listed as .99¢. Explain what is wrong with this.

 Q1.15 (Operations on the Number Line) Determine the performed operation that is being represented in each diagram.

 Q1.16 (Inverse Operations) What is the inverse operation of “I put my shoes on today, and I walk out of my house”?

 Q1.17 (Powers of 1) Find $$1^2$$, $$1^3$$, and $$1^4$$. What can you assume about any power of 1?

 Q1.18 (Viral Math Expression) The seemingly simple expression below has stumped many people across the Internet. Some will argue the answer is 9, while others will argue it is 1. However, there is a fundamental issue with the way that the expression is written, leading to these two different answers, can you figure out what it is? $$6 / 2(1+2)$$

Section 1.1
 1.1 (Locating Numbers) Draw a number line, and then figure out where the following values might be located on it.

$$\frac{3}{11}, 0, 0.0001, 5, \frac{1}{4}, -2.3$$

 1.2 (Comparing Numbers) For each given pair of numbers, determine which of the two is larger.

a. 4, 100 b. 9, 9.0001 c. -7, -2 d. -5, 0 e. 100, 100

 1.3 (Weighing Bull Sharks) A biologist is studying bull shark populations. She records the weights of four sharks, in pounds, that she has caught. Order the bull sharks from lightest to heaviest.

 1.4 (Place Values) Find the place value of the number 5 in each of the following numbers.

a. 5,000,000 b. 0.5 c. 105 d. 3572896 e. 123,456,789 f. 0.000005 g. 8051 h. 85,931 i. 800,026

 1.5 (Writing Numbers) Translate to mathematical symbols

 1.6 (Writing Numbers in Words) Write the following numbers in words

a. 9 b. 10 c. 274 d. 8,322 e. 1,000,000,009 f. 1,343,234,985 g. 0.01

 1.7 (Numbers in Expanded Form) In the number 7,893, there are "7 thousands", "8 hundreds", "9 tens", and "3 ones". We therefore say that a number is in expanded form when it is written as follows:

7 thousands + 8 hundreds + 9 tens + 3 ones or 7000 + 800 + 9 + 3

Write the following numbers in expanded form:

a. 473 b. 6852 c. 73,016 d. 570,003 e. 3,519,803 f. 48,000,061 g. 37.89 h. 124.575 i. 7496.5467 j. 6.40941

 1.8 (Fraction Diagrams) Write a fraction to describe what part of the diagrams below are shaded. Write a fraction to describe what part of the diagrams aren't shaded in.

 1.9 (Fruit Basket) A basket of fruit holds 5 mangoes, 7 apples, 12 oranges, and 20 pomegranates. a. What fraction of the fruits in the basket are apples? b. What fraction of the fruits in the basket are not oranges? c. What fraction of the fruits in the basket are oranges or pomegranates?

Section 1.2
 1.10 (Make 1000 out of 8) Eight digits “8” are written together, like below, and plus signs “+” are inserted in between to get the sum of 1000. Where were the plus signs added?

$$8 \ \ \ 8 \ \ \ 8 \ \ \ 8 \ \ \ 8 \ \ \ 8 \ \ \ 8 \ \ \ 8$$

 1.11 (Unknown Sum) In the addition problem below, A, B, and C each represent three different digits. What are the digits?

$$\begin{array}{r}AAA\\ + \ BBB \\ \hline AAAC\end{array}$$

 1.12 (Unknown Product) A six-digit number with 1 as its left-most digit is three times bigger when we put the one at the end of the number instead. What number is this?

 1.13 (Fractions and Decimals) Use long division to find the decimal expansion of each fraction.

 1.14 (Terminating and Repeating Decimals) You may notice from Problem 1.7 that when you convert a fraction to a decimal, you will sometimes get what is called a repeating decimal. Take for example the fraction $$\frac{3}{11}$$.

$$\frac{3}{11} = 0.272727272727...$$

The decimal form of $$\frac{3}{11}$$ consists of the two digits 2 and 7 in an infinitely repeating sequence. To simplify things, instead of writing the above, we denote it as 0.27.

a. Use this bar notation to write each of the repeating decimals from Problem 1.13. b. We see that in the fraction above, the fractional part repeats after two digits. We say that this number has a period of 2. Likewise, we say that the number $$\frac{1}{7}$$ has a period of 6, because the number repeats after 6 digits. From the numbers below, which of them has the largest period?

 1.15 (Mixed Fractions) Write the following improper fractions as mixed fractions.

 1.16 (Sharing Pizza) Billy's family ordered a large pizza. His father had $$\frac{1}{6}$$ of it, and his mother had $$\frac{1}{5}$$ of what remained. Later on, Billy's sister ate some pizza, and then Billy had the remaining pizza when there was exactly a half of what they started with (Billy is a large kid). What fraction of what their parents had left for her did the sister have?

 1.17 (Stamp Collection) The picture to the right shows stamps, arranged in four groups of four. How many stamps are in that image? While you can count them individually, there is a much faster way of getting the total.

 1.18 (Decimal Operations) Explain how addition with decimals is comparable to addition with whole numbers, how are they different? Do the same thing with multiplication with decimals.

 1.19 (A Sum and a Difference) The sum of two numbers is 104 and their difference is 32. What is the value of the larger number?

 1.20 (On Allison's Street) Allison's house is on the same street as the library, post office, and supermarket, as shown in the diagram below. The distance from Allison's house to each of the three buildings is different. Based on this information, at which point is Allison's house located?

Section 1.4
 1.21 (Bank Account) Nick deposits $2 into a bank account on the first day, $4 on the second day, and $8 on the third day. He will continue to double the deposit each day. How much will he deposit on the tenth day?

Section 1.6
 1.22 (Using Divisibility Rules) Use divisibility tests to find the remainder of the following quotients:

Reason and Apply
 1.23 (Count the 24ths) Without performing division, how many $$\frac{1}{24}$$'s are in $$\frac{2}{3}?$$

 1.24 (Negative Negative Negative Negative...)

a. What is $$-(-(-2))$$? b. What is $$-(-(-(-2)))$$? c. What if there were 20 minus signs in front of the 2? d. What if there were 75 minus signs in front of the 2?

 1.25 (Using Bar Graphs) Look at the diagram below, and use it to answer the following questions.

 1.26 (Using Multibar Graphs) Look at the diagram below, and use it to answer the following questions.

 1.27 (Using Line Graphs) Look at the diagram below, and use it to answer the following questions.

 1.28 (Creating a Bar Graph) Look at the table below, and use it to create a bar graph.

 1.29 (Reading Meters) The amount of electricity in a household is measured in kilowatt-hours. Determine the reading on the meter shown below. (When a pointer is between two numbers, use the smaller number).

 1.30 (Sky High) The table below shows the altitude each of the cloud types are found at. Graph the numbers on the vertical number line below.

 1.31 (Rulers) Look at the diagram of a ruler below.

a. How many tick marks are between 0 and 1? b. What number is the arrow pointing to?

 1.32 (Page Numbers) How many numerals are required to number all of the pages of a book containing 450 pages?

 1.33 (Operations with Repeating Decimals) Calculate:

a. 0.55555... + 0.66666... b. 0.99999... + 0.11111... c. 1.11111... - 0.22222... d. 0.33333... * 0.66666... e. 1.22222... * 0.81818...

Challenge Problems
 1.34 (One to Ten) To get yourself thinking about this, try this simple mathematical game:

Take the numbers 1 through 10 on the left side of an equation, and pick a number for the right side.

Example: 1 2 3 4 5 6 7 8 9 10 = 1

Now put operators between those numbers. Only use parentheses when necessary.

Example: 1 + 2 - 3 + 4 - 5 + 6 + 7 + 8 - 9 - 10 = 1

Change the number on the right-hand side. Can you generate an expression for this number? If not, can you prove why not?

Does this change if you change the order of the numbers?

 1.35 (Diffy Squares) Draw a square. One each of the corners of that square, write the numbers 7, 5, 9, and 2. Now, draw a second square around the first one so that it it goes through each of the four corners. At each corner of the second square, write the difference of the numbers at the closest corners of the smaller square: 7-5 = 2, 9-5 = 4, 9-2 = 7, and 7-2 = 5.

Repeat this process until you come to a pattern of four numbers that do not change.

a. What is the pattern? b. Try this same procedure with another set of four starting numbers. Do you end up with the same pattern? c. Explains what happened.

 1.36 (The Binary Number System)

 1.37 (The Hexadecimal Number System)

title: Algebra/Chapter 1/Exercises


text:
A Guide to Discord/Bots

Bots are automated Discord users utilizing the Discord API. They can be identified in a server by the "BOT" tag next to their name.

MEE6
Named after Mr. Meeseeks, a character from the Adult Swim series Rick and Morty, MEE6 is one of the most popular bots on Discord, utilized in 15,300,000 servers. MEE6 has many functions, including:
 * sending a welcome message to new members who join a server
 * rewarding a user with XP points if they stay consistently active in a server
 * playing music
 * announcement functions for Twitch, YouTube, Twitter, and Reddit

Commands

Carl-bot
Carl-bot is another popular Discord bot, utilized in 3,950,000 servers. Carl-bot offers many features, including adding reaction roles, moderation, and logging.

Commands

Dyno
Dyno is an all-purpose Discord bot that offers moderation, custom commands, and other features.

Commands

title: A Guide to Discord/Bots


text:
BASIC Programming/Introduction

= Introduction =

title: BASIC Programming/Introduction


text:
BASIC Programming/Normative BASIC

= Normative BASIC =

The BASIC Programming Language has been standardized, firstly in the United States of America (USA) by the American National Standards Institute (ANSI), and later in Europe by the European Computer Manufacturers Association (ECMA), giving rise to the American National Standard (ANS) X3.60-1978 for Minimal BASIC and X3.113-1987 for Full BASIC by the former, and to the European Computer Manufacturers Association Standard 55 for Minimal BASIC in 1978 and Standard 116 for Full BASIC in 1986 by the latter.

The aim of the standards is to promote the interchangeability of BASIC programs among a variety of systems and through strict co-operation between both organizations it was possible to maintain full compatibility between the respective ANSI and ECMA standards.

The standards establish, among others:

 * the syntax of a program written in BASIC, and
 * the semantic rules for interpreting the meaning of a program written in BASIC.

Nowadays, only the ECMA standards are publicly available.

Character Set
The set of allowable character is given by:

 * the set of capital letters from A to Z,
 * the set of digits from 0 to 9,
 * the set of symbols !, #, $, %, &,, +, -, *, /, ^, ., ,, ;, :, <, =, >, _, ?, ', "
 * the space character

List of Reserved Keywords
Reserved keywords in Minimal BASIC are (26 in total):

 * 1) BASE
 * 2) DATA
 * 3) DEF
 * 4) DIM
 * 5) END
 * 6) FOR
 * GO
 * 1) GOSUB
 * 2) GOTO
 * IF
 * 1) INPUT
 * 2) LET
 * 3) NEXT
 * ON
 * 1) OPTION
 * 2) PRINT
 * 3) RANDOMIZE
 * 4) READ
 * 5) REM
 * 6) RESTORE
 * 7) RETURN
 * 8) STEP
 * 9) STOP
 * 10) SUB
 * 11) THEN
 * TO

Its meaning will be explained within the next sections.

Convention for the Name of Variables
Variables are used in BASIC to hold either character strings or numeric values, the latter being either of scalar or vectorial nature.

In the case of variables for character strings, each variable name is composed of a single letter between A - Z and the dollar sign $. So, A$, B$, ..., Z$ are all valid variable names for character strings, while A# or Z% are not.

In the case of variables for numeric scalar values, each variable name is composed of a single letter between A - Z and an optional digit. So, A, B, C1, D2, etc., are valid variable names for scalar values, while A11, B22, etc., are not.

In the case of variables for numeric vectorial values, each variable name is composed of a single letter between A - Z and either a number or two, separated by a comma, enclosed within parentheses for a one or a two dimensional array. So, A(1), B(2), C(1,1), D(2,2), etc., are valid variable names for vectorial values.

This convention makes the explicit declaration of variables not necessary in BASIC, since a dollar sign serves to distinguish a character string from a numeric value, and the presence of subscripts distinguishes a vectorial from a scalar variable.

Character Strings and Numeric Constants
Character strings are defined by any combination of characters from the allowable character set written within double quotation marks, the length of any character string being limited to 18 characters (with the exception of character strings in a print or remark-statement, to be seen later, which can be as long as line numbers and the line length limit permit). So, "", " ", "1 2 3 4 5 6 7 8 9", "A B C D E F G H I", "! # $ % & ... ' ", etc., are allowable character strings, while "1 2 3 4 5 6 7 8 9 0", "A B C D E F G H I J", "! # $ % & + - * / ^ ., ; : < = > _ ? ' ", etc., are not, since they exceed the 18-character limit.

Numeric constants denote scalar numeric values in a decimal representation in positional notation of a number. There are four general syntactic forms of optionally signed numeric constants:

 * implicit point representation (sd...d), like in the case of 1, 2, +1, -2, etc.,
 * explicit point unscaled representation (sd...drd...d), like in the case of 1.0, 2.0, +1.0, -2.0, etc.,
 * explicit point scaled representation (sd...drd...dEsd...d), like in the case of 1.0E1, 2.0E-1, +1.0E+1.0, -2.0E-2.0, etc.,
 * implicit point scaled representation (sd...dEsd...d), like in the case of 1.0E1, 2.0E-1, +1.0E+1, -2.0E-2, etc.,

where:

 * s is an optional sign (+ or -),
 * d is a decimal digit (0 - 9),
 * r is a period (.), and
 * E means 10 to the power.

Numeric constants can have any number of digits, although internally not less than six significant decimal digits and a range between 1E-38 and 1E+38.

Numeric constants whose magnitude is less than machine infinitesimal are replaced by zero, while constants whose magnitude are larger than machine infinity are replaced by machine infinity with the appropriate sign.

General Program Structure
BASIC is a line-oriented language, in the sense that a BASIC program can be considered as a sequence of lines, the last of which is an end-line, and each of which contains a keyword. Moreover, each line begins with a unique line number, which serves as a label for the statement contained in that line.

So, in BASIC every program can be represented with the following Backus-Naur form (BNF):

 * program = block end-line
 * block = line / for-block
 * line = line-number statement
 * line-number = digit digit? digit? digit?
 * end-line = line-number end-statement
 * end-statement = END
 * statement = data-statement / def-statement / dimension-statement / gosub-statement / goto-statement / if-then-statement / input-statement / let-statement / on-goto-statement / option-statement / print-statement / randomize-statement / read-statement / remark-statement / restore-statement / return-statement / stop-statement

So, the following simple examples are valid examples of a program in BASIC:

 * a two-line program (just a remark-statement, which serves to document the program and produces no output, and an end-statement, which terminates the program):

 * a three-line program (just a remark-statement, a print-statement, which prints a character string, and an end-statement):

Programs lines are executed in sequential order, starting with the first one, until:

 * some other action is dictated by a control statement, or
 * an exception condition occurs, which results in abnormal termination of the program, or
 * a stop-statement or end-statement is executed.

So, in the first example, the first line,, is composed of a non-control statement which produces no output or internal activity, passing then to the second line,  , which is composed of a control statement, the end-statement, which ends the program.

In the second example, there exists an additional line between the remark and the end-statement lines, being composed of a print-statement, also a non-control statement, which prints a character string.

The value of the line-numbers are positive integers, with leading zeroes having no effect. So, 1, 01, 10, 010, etc., are all valid line-numbers. Normally, line-numbers are given as multiples of 5 or 10, e.g., 10, 20, 30, 40, etc., which allows for room in case an additional line must be inserted in between existing lines.

Additionally, lines can be up to 72-characters long, so leaving 4 characters for the line-number, and a blank space as a separator between the line-number and the keyword, leaves 67 printable characters left for the statement in a line.

Spaces may occur anywhere in a BASIC program without affecting the execution of that program and may be used to improve the readability of the program.

All keywords in a program can be preceded by at least one space and, if not at the end of a line, can also be followed by at least one space.

Spaces shall not appear:

 * 1) at the beginning of a line
 * 2) within line numbers
 * 3) within keywords
 * 4) within numeric constants
 * 5) within function or variable names
 * 6) within two-character relation symbols

Program Variables
Variables in BASIC are associated with either numeric or string values and, in the case of numeric values, may be either simple variables or references to elements of one or two-dimensional arrays, which are then called subscripted or compound variables.

As stated before, simple numeric variables are named by a single capital letter followed by an optional single digit, while subscripted variables are named by a single capital letter followed by one or two numbers, separated in this last case by a comma, enclosed within parentheses.

String variables are also to be named by a single capital letter followed by a dollar sign.

At any instant in the execution of a program, a numeric variable is associated with a single numeric value and a string variable is associated with a single string value, the value associated with the variable possibly being changed by program statements in the course of program execution.

The length of a character string associated with a string variable can change during execution of the program from a length varying between 0 for the empty string to 18 characters.

Simple numeric variables and string variables are declared implicitly through their appearance in the program (also no type definitions are necessary, due to the given naming convention), although it is good programming practice to initialize or set them to meaningful values at the beginning of the program before their use in any statement.

A subscripted variable, on the other hand, refers to the element in the one or two-dimensional array selected by the value or values of the subscripts, being the subscripts integer values.

Unless explicitly declared in a dimension statement (to be seen later), subscripted variables are implicitly declared by their first appearance in a program, in which case the range of each subscript is to be understood from zero to ten, both inclusive, unless the presence of an option-statement indicates that the range is defined from one to ten, both also inclusive.

Caution must be paid, so that the same single letter is not used both for the name of a simple variable and a composed variable, nor for the name of both a one-dimensional and a two-dimensional array.

On the contrary, this restriction does not apply between a simple variable and a string variable, whose names may agree except for the dollar sign.

So, the following simple examples are valid examples of a program in BASIC:

 * the previous three-line program, with a somewhat different comment line and a new character string, which indicates the value of pi, being printed:

 * a modified four-line program which makes use of a let-statement to assign the numeric constant 3.14159265 to the numeric variable P in the second line, and a print-statement with a string constant and a numeric variable as a comma-separated list of arguments in the third line:

 * a modified five-line program which, still making use of a let-statement to assign the numeric constant 3.14159265 to the numeric variable P in the second line, now also makes use of a let-statement to assign the character constant "PI = " to the string variable P$ in a third line -- the print-statement in the fourth line is now composed of the comma-separated list of arguments formed by the string variable and the numeric variable:

Statements
Up to now we have seen how to declare/initialize simple numeric variables and string variables in the course of a program by means of the let-statement and how to print them with the help of the print-statement.

It is sometimes desirable not only to print the value of a variable, let it be a numeric or a character one, but to introduce the value as input to the program in order to compute a numerical value or to print a message depending on the value of a condition. For those cases, one needs to make use of expressions, mathematical functions, and control statements, as we shall see in this section.

Input/Output, Mathematical Operators, Expressions
Expressions are normally classified as numeric expressions or string expressions.

In the case of numeric expressions, these are constructed from variables, constants, mathematical functions, and the mathematical operations of addition, subtraction, multiplication, division, and involution.

The formation and evaluation of numeric expressions follow the normal algebraic rules, and the circumflex accent, the asterisk, the solidus, the plus sign, and the minus sign symbols are used to represent the operations of involution, multiplication, division, addition, and subtraction, respectively.

Unless parentheses dictate otherwise, exponentiation is performed first, then multiplications and divisions, and finally additions and subtractions, where operations of the same precedence are associated from left to right. So, A - B - C is interpreted as (A - B) - C, A / B / C as (A / B) / C, and A - B / C as A - (B / C), since in the first two all the mathematical operators have the same precedence, and hence evaluate from left to right, while in the last one there exists different precedence between operators, and hence the division is evaluated before the subtraction.

The following examples illustrate in a simple way the concepts seen so far:

 * a program that prints the value of the exponentiation of the numeric constant 1.4142 by 2 (also calculates the square of 1.4142), together with some text:

 * a program that defines a numeric variable S with a value of 1.4142, and prints the value of the exponentiation of the numeric variable by 2 (also calculates the square of 1.4142), together with some text:

 * a program that defines a numeric variable S with a value of 1.4142, calculates the product of S by S (also calculates the square of 1.4142), assigns this value to a numeric variable S2, and prints the value of both S and S2 together with some text as string constants:

 * a program that defines a numeric variable S with a value of 1.4142 and another one S2 with 2.0000, and prints the value of the operation of dividing S2 by S, together with some text as string constants:

 * a program similar to the previous one, in that it defines a numeric variable S with a value of 1.4142 and another one S2 with 2.0000, but prints the value of the operation of subtraction of S by the result of dividing S2 by S (giving then a measure of accuracy for the approximation -- this is the nucleus of a numerical method that we will see later to calculate the square root of a number), together with some text as string constants:

 * a program a little bit different to the previous ones, in that it asks the user for a number, whose square is to be calculated:

Mathematical Functions
Up to here we have seen how numeric and character variables are to be defined, the rules for writing lines, basic input and output, and the rules for simple arithmetic.

But what happens, if one needs to calculate the square root of a number? For this purpose, basic mathematical functions are by default provided. These are:

 * the absolute value of a number, ABS(X)
 * the arctangent of a number, ATN(X)
 * the cosine of a number expressed in radians, COS(X)
 * the exponential of a number, EXP(X)
 * the integer part of a number, INT(X)
 * the natural logarithm of a number, LOG(X)
 * the sign of a number, SGN(X)
 * the sine of a number expressed in radians, SIN(X)
 * the square root of a positive number, SQR(X)
 * a uniformly distributed pseudo-random number in the interval (0,1), RND
 * the tangent of a number expressed in radians, TAN(X)

Let us see some examples:

 * a program that calculates the square root of 2 with the help of the SQR mathematical function provided:

 * a program that asks the user for a number, for which its cosine is to be calculated:

 * a program that asks the user for a number, for which its sine is to be calculated:

 * a program that asks the user for a number, for which its tangent is to be calculated:

 * a program that asks the user for a number, for which its exponential is to be calculated:

 * a program that asks the user for a number, for which its natural logarithm is to be calculated:

 * a program to print a pseudo-random number uniformly distributed in the interval (0,1):

Sample Programs
Minimal BASIC sample programs can be found in the corresponding page.

title: BASIC Programming/Normative BASIC