OpenLLM-France/wikimedia huggingface dataset:
# GLSL Programming/Unity/Smooth Specular Highlights

This tutorial covers per-pixel lighting (also known as Phong shading).
It is based on Section “Specular Highlights”. If you haven't read that tutorial yet, you should read it first. The main disadvantage of per-vertex lighting (i.e. of computing the surface lighting for each vertex and then interpolating the vertex colors) is the limited quality, in particular for specular highlights as demonstrated by the figure to the left. The remedy is per-pixel lighting which computes the lighting for each fragment based on an interpolated normal vector. While the resulting image quality is considerably higher, the performance costs are also significant.

### Per-Pixel Lighting (Phong Shading)

Per-pixel lighting is also known as Phong shading (in contrast to per-vertex lighting, which is also known as Gouraud shading). This should not be confused with the Phong reflection model (also called Phong lighting), which computes the surface lighting by an ambient, a diffuse, and a specular term as discussed in Section “Specular Highlights”.
The key idea of per-pixel lighting is easy to understand: normal vectors and positions are interpolated for each fragment and the lighting is computed in the fragment shader.

### Shader Code

Apart from optimizations, implementing per-pixel lighting based on shader code for per-vertex lighting is straightforward: the lighting computation is moved from the vertex shader to the fragment shader and the vertex shader has to write the attributes required for the lighting computation to varyings. The fragment shader then uses these varyings to compute the lighting (instead of the attributes that the vertex shader used). That's about it.
In this tutorial, we adapt the shader code from Section “Specular Highlights” to per-pixel lighting. The result looks like this:
Note that the vertex shader writes a normalized vector to varyingNormalDirection in order to make sure that all directions are weighted equally in the interpolation. The fragment shader normalizes it again because the interpolated directions are no longer normalized.

### Summary

Congratulations, now you know how per-pixel Phong lighting works. We have seen:
* Why the quality provided by per-vertex lighting is sometimes insufficient (in particular because of specular highlights).
* How per-pixel lighting works and how to implement it based on a shader for per-vertex lighting.

### Further Reading

If you still want to know more
* about the shader version for per-vertex lighting, you should read Section “Specular Highlights”.
< GLSL Programming/Unity
# History of video games/Platforms/MACH64
## History

The MACH64 was developed as part of the XgameStation lineup by André LaMothe. The price of the system was $159.95.

## Technology

The kit used a CPLD (Complex programmable logic device), specifically the Lattice Semiconductor ispMACH 4064.

## References

* 1 2 Titus, Jon (November 2008). "Kits for Kids". ECN: Electronic Component News. 52 (12): 19. ISSN 1523-3081.
* ↑ "MACH64™ Programmable Logic Starter Kit". Retrieved 29 August 2022.
* ↑ "ispMACH 4064 Starter Kit". Retrieved 29 August 2022.
# History of video games/Platforms/Logitech G CLOUD gaming handheld
## History
### Development

The hardware of the system was developed by Logitech in partnership with the company Tencent, which handled software.
The system was announced on September 21st, 2022, with a projected launch date of October 17, 2022. The initial price of the system was $300 for preorder, or $349 at launch. The launch of the device was geographically limited to North America, more specifically launching in just the United States and Canada.

## Technology
### Compute

The system was based on the Snapdragon 720G system on a chip, which was considered a mid-range mobile processor at announcement. The system included 4 gigabytes of LPDDR4X RAM.

### Hardware

A dual band Wi-Fi 5 radio is incorporated in the system, sporting a 2x2 MIMO configuration.
The system weighed 463 grams (16.3 oz).

## References

* 1 2 3 4 Amadeo, Ron (21 September 2022). "Logitech builds Android-powered Steam Deck clone for portable cloud gaming" (in en-us). Ars Technica. https://arstechnica.com/gadgets/2022/09/logitech-builds-android-powered-steam-deck-clone-for-portable-cloud-gaming/.
* 1 2 3 4 Faulkner, Cameron (September 22, 2022). "I briefly played with Logitech’s new G Cloud Gaming Handheld". The Verge. https://www.theverge.com/2022/9/22/23367556/logitech-g-cloud-gaming-handheld-console-hands-on-xbox-nvidia-geforce.
* ↑ Bains, Callum (22 September 2022). "Why Logitech's Steam Deck rival is too ahead of its time" (in en). TechRadar. https://www.techradar.com/news/why-logitechs-steam-deck-rival-is-too-ahead-of-its-time.
* 1 2 Pickard, James (22 September 2022). "Logitech G Cloud: where to preorder the gaming handheld and save $50" (in en). TechRadar. https://www.techradar.com/deals/logitech-g-cloud-preorder-where-to-buy.
* ↑ Evenden, Ian (22 September 2022). "Logitech's G Cloud: A $349 Android Powered Game Streaming Handheld" (in en). Tom's Hardware. https://www.tomshardware.com/news/logitech-g-cloud-handheld.
* ↑ Greenwald, Will (September 21, 2022). "Logitech G Cloud Is a Steam Deck-Style Handheld With a Streaming Focus" (in en). PCMAG. https://www.pcmag.com/news/logitech-g-cloud-is-a-steam-deck-style-handheld-with-a-streaming-focus.
# History of video games/Platforms/MARS FPGA
## Technology

The system featured an ARM64 based CPU in conjunction with a FPGA. The system was designed to be compatible with MiSTer cores.
The front controller ports were designed to be modular.

## References

* ↑ "MARS: Multi Arcade & Retro System". RetroRGB. 17 October 2023. https://www.retrorgb.com/mars-multi-arcade-retro-system.html.
* ↑ Funk, Ben (17 October 2023). "A 4K Nintendo 64 Console Is Coming To Relive Your Retro N64 Games In High Resolution" (in en-us). HotHardware. https://hothardware.com/news/analogue-3d-nintendo-64-fpga-4k-retro-gaming-announcement.
* ↑ McFerran, Damien (17 October 2023). "MiSTer Rival MARS FPGA Will Let You Use Your Old Controllers & Peripherals". Time Extension. https://www.timeextension.com/news/2023/10/mister-rival-mars-fpga-will-let-you-use-your-old-controllers-and-peripherals.
# History of video games/Platforms/Let's! TV Play Classic
## History

This series of consoles was only released in Japan.

## References

* ↑ "Let's! TV Play Classic". Wikipedia. 29 March 2021. Retrieved 31 October 2021.
# History of video games/Platforms/Light Games
## History

The Grandstand Light Games system was a projector based console released in 1988. It is one of the few consoles that elected to go with a projector based design, alongside its contemporary the Proscreen, and the much later 2020 console the BL6.

## Technology

The Grandstand Light Games uses a projector to display graphics. The projector shines through a LCD in the cartridge, which produces the graphics in lieu of slides.
The top of the console includes a cartridge slot.

## Games

There are at least nine cartridges for the Light Games console.

## External Resources

* Handheld Museum - Playtime Light Games page.
* Game Medium - Light Games page.
* Video Game Console Library - Gallery of Educational Systems including Light Games.

## References

* 1 2 "Gallery of Educational Systems". Video Game Console Library. Retrieved 16 November 2020.
* ↑ "Grandstand Light Games". Retrieved 16 November 2020.
* ↑ See photo of console and cartridge.
* ↑ Barsanti, Sam; Hughes, William (22 March 2021). "The rise and fall of the Game Boy's weirdest rivals" (in en-us). The A.V. Club. https://www.avclub.com/the-game-com-cometh-the-rise-and-fall-of-the-game-boy-1846501180/slides/3.
* ↑ "Playtime Light Games". www.handheldmuseum.com. Retrieved 16 November 2020.
* ↑ "Grandstand Light Games". Retrieved 20 December 2020.
# History of video games/Platforms/Light Pong
## History

A crowdfunding campaign for Light Pong was launched on Kickstarter in late 2021.

## Technology

Light Pong is designed as a 1 dimensional gaming console.
Despite the name suggesting it only plays a version of Pong, the console plays a number of games.

## References

* ↑ "This One-Dimensional Flexible Pong Game Looks Like a Lot of Fun" (in en-us). Gizmodo. https://gizmodo.com/somehow-this-one-dimensional-flexible-pong-game-still-l-1847777381.
* 1 2 Smith, Emmett (29 September 2021). "Light Pong is an interactive gaming console that doesn't need a screen — Future Blink" (in en). Mashable. https://mashable.com/video/interactive-gaming-console.
# History of video games/Platforms/M17
## History

In October of 2023 the system cost $55.99 with a 64GB capacity or $62.99 for double the storage.

## Technology

The system used an RK3126 as a processor. The system included 256MB of RAM and 4GB of eMMC storage.
The system ran Linux as an operating system.

## References

* 1 2 Alderson, Alex (25 October 2023). "M17: New cheap gaming handheld powerful enough to emulate PS1 and SNES titles now available for US$55.99" (in en). Notebookcheck. https://www.notebookcheck.net/M17-New-cheap-gaming-handheld-powerful-enough-to-emulate-PS1-and-SNES-titles-now-available-for-US-55-99.762291.0.html.
* ↑ Retro Game Corps (October 23, 2023). "M17 Review: Surprisingly Good $55 Retro Handheld". Retrieved 25 November 2023.
* ↑ Taki Udon (September 29, 2023). "A $35 Hidden Gem? // M17 Retro Handheld Review". Retrieved 25 November 2023.
# History of video games/Platforms/Lenovo Legion Play
## History

Evidence suggested the device was planned for demonstration at MWC (Mobile World Congress) 2021, but was pulled.
The Lenovo Legion Play came to light in October of 2021 as the result of a leak. There was widespread doubt over the value of the handheld based around game streaming following the leak.
The console was often seen as a potential rival to the Steam Deck and the Nintendo Switch.

## Technology
### Controls

The system would have twin analog sticks, one on the upper left and one on the bottom right.
Four face buttons would be housed on the upper right. Clockwise a yellow Y button would be at the top of the diamond pattern, a red B button would be at the right of the diamond, a green A would be at the bottom of the diamond, and finally a blue X button would be housed at the left of the diamond.
The bottom left side of the device would have housed the D-Pad.
Dual shoulder buttons would have been available.
There are potentially 2-4 other auxiliary buttons visible on the face of the device, though it is unclear if they are really buttons or ornamentation.

### Hardware

The system would sport a full HD, 16:9 aspect ratio, HDR 10, 7 inch display. There is conflicting information regarding the bezels on the device.
The console would have been powered a 7,000 mAh capacity battery. A USB type C port would have been used.
Either twin speakers or a headphone jack would provide for audio.
The console would support haptic feedback from two motors.

### Software

The console would have ran a customized version of Android.
Nvidia GeForce Now would have been supported.
A Google Play icon was visible on the launcher.

## References

* 1 2 3 4 5 "Lenovo Legion Play leaked: An Android-based rival to Steam Deck, Switch". Android Authority. 4 October 2021. https://www.androidauthority.com/lenovo-legion-play-3033467/.
* ↑ "You told us: You aren't super keen on the Lenovo Legion Play handheld". Android Authority. 7 October 2021. https://www.androidauthority.com/lenovo-legion-play-poll-results-3036481/.
* 1 2 "Lenovo's Leaked Cloud Gaming Console is a Flawed Concept" (in en). Digital Trends. 5 October 2021. https://www.digitaltrends.com/gaming/lenovo-legion-play-leak/.
* ↑ Lopez, Ule (10 November 2021). "Steam Deck Shipping Delayed Until February 2022". Wccftech. https://wccftech.com/steam-deck-shipping-delayed-until-february-2022/.
* 1 2 3 4 5 6 "Lenovo Legion Play is an upcoming Android handled console". GSMArena.com. https://www.gsmarena.com/lenovo_legion_play_is_an_upcoming_android_handled_console-news-51254.php.
* 1 2 3 4 Schoon, Ben (4 October 2021). "Lenovo 'Legion Play' leak shows off an Android-powered 'cloud gaming console'". 9to5Google. https://9to5google.com/2021/10/04/lenovo-legion-play-android-cloud-gaming-console/.
* 1 2 3 "Lenovo Legion Play handheld Android game console leaks". SlashGear. 4 October 2021. https://www.slashgear.com/lenovo-legion-play-handheld-android-game-console-leaks-04693718/.
# High School Calculus/Implicit Differentiation
### Implicit Differentiation

When a functional relation between x and y cannot be readily solved for y, the preceding rules may be applied directly to the implicit function.
The derivative will usually contain both x and y. Thus the derivative of an algebraic function, defined by setting the polynomial of x and y to zero.
Given the function y of x
$x^{5}+y^{5}-5xy+1=0$
Find ${\operatorname {d} y \over \operatorname {d} x}$
Since
${\operatorname {d} \over \operatorname {d} x}(x^{5}+y^{5}-5xy+1)=0$
$=5x^{4}+5y^{4}{\operatorname {d} y \over \operatorname {d} x}-5y-5x{\operatorname {d} y \over \operatorname {d} x}=0$
In solving for ${\operatorname {d} y \over \operatorname {d} x}$ we must first factor the differentiation problem
In doing this we get
${\operatorname {d} y \over \operatorname {d} x}(5y^{4}-5x)+(5x^{4}-5y)=0$
From here we subtract the ${\operatorname {d} y \over \operatorname {d} x}$ to one side
Thus giving us
$5x^{4}-5y=-{\operatorname {d} y \over \operatorname {d} x}(-5x+5y^{4})$
Here I am going to skip a step in solving this implicit differentiation problem. I am going to skip the step where I divide the -1 over to the other side.
From here we divide the polynomial from the $\operatorname {d} y \over \operatorname {d} x$ over to the other side. Giving us
$\left({\frac {-5x^{4}+5y}{-5x+5y^{4}}}\right)={\operatorname {d} y \over \operatorname {d} x}$
Now we simplify and get
${\operatorname {d} y \over \operatorname {d} x}=\left({\frac {x^{4}-y}{x-y^{4}}}\right)$
Find ${\operatorname {d} y \over \operatorname {d} x}$ given the function
$xy^{2}+x^{2}y=1$
Find ${\operatorname {d} y \over \operatorname {d} x}$ given the function
$x+y+(x-y)^{2}+(2x-3y)^{3}=0$
# High School Calculus/Authors
## Raja Almukkahal

My educational background includes a PhD in physics and a Master of Science in physics and mathematics. I have been teaching physics, mathematics and astronomy for over 20 years at several colleges and private schools in different states. I currently live with my wife and boy (3.5 years) in Alexandria, VA.

## Victor Cifarelli

Victor Cifarelli (Ph.D., Mathematics Education, Purdue University) is an Associate Professor of Mathematics and the Coordinator of the Mathematics Education Program in the Department of Mathematics at the University of North Carolina at Charlotte. His doctoral research focused on the role of reflective abstraction as a learning process in mathematical problem solving. His current research examines how solvers reflect on and test the viability of their evolving intuitions, and transform their initial hypotheses and conjectures into actual solution activity. Dr. Cifarelli has presented his research at AERA, PME, and PME-NA. His articles have appeared in the Journal of Mathematical Behavior, Focus on Learning Problems in Mathematics and the Proceedings of PME and PME-NA. Over the past several years, he has been an active contributor to SIG/RME as a reviewer and presenter of research papers. In addition to his research interests, Dr. Cifarelli has demonstrated an on-going commitment to the professional development of mathematics teachers. He has taught a variety of undergraduate and graduate mathematics and mathematics education courses including mathematics for elementary education majors, mathematics education for elementary and middle school education majors, and graduate mathematics courses for secondary mathematics teachers. He has co-directed a pair of projects for elementary, middle, and secondary grades mathematics teachers under the Eisenhower Professional Development Program and also has conducted numerous in-service workshops for middle grades and secondary mathematics teachers.

## Louise Jarvis

Louise Jarvis graduated from Mary Washington College (now University of Mary Washington) in 1987 with a double major of Mathematics and Sociology. She earned her MS in mathematics from the University of Rhode Island in 1989. She taught college-level math classes for 10 years and has worked with all levels of mathematics. She has been a writer for the math educational industry for several years. She also home educates her children in all subjects.
# High School Calculus/Definite Integrals

A definite integral can also be defined as

### The Area Under the Curve

The area under the curve is found by finding [a,b]
where [a,b] are points on the x axis
[a,b] are the points on which you want to find the area
This can be denoted by $a\leq Area\leq b$
This is denoted by $\int _{a}^{b}f(x)$
# High School Calculus/Derivatives

* Tangent Lines and Rates of Change
* The Derivative
* Techniques of Differentiation
* Derivatives of Trigonometric Functions
* The Chain Rule
* Implicit Differentiation
* Linearization and Newton's Method
# High School Calculus/Evaluating Limits
### Evaluating Limits

What is a limit? A limit is a place on the graph that the function either does not touch or go past.
When evaluating a limit we may have to factor sometimes in order to get L. L is the point in which the function does not touch or go past.
$\lim _{x\to c}f(x)=L$
Let's start off with a rather simple limit.
$\lim _{x\to 3}x^{2}+x+3$
$3^{2}+3+3=15$
$L=15$
As you can see what we did was just plug 3 into the function to get L
This doesn't always work. This is easily shown in fractions.
I will show you two different ways to evaluate the limits. The first is by factoring and the second is by using L'Hopital's rule.

### Evaluating Limits by Factoring

This is a fairly simply concept, not something easily done. It is especially hard if you have a hard time identifying how polynomials can be rewritten.
Ex.1
$\lim _{x\to -2}{\frac {(x+2)^{2}}{x+2}}$
This gives us $L={\frac {0}{0}}$
This is an indeterminate form. This means we have to find some other way to evaluate the limit so we can get the correct L
Let's look at how $(x+2)^{2}$ is factored
By factoring we now get $\lim _{x\to -2}{\frac {(x+2)(x+2)}{x+2}}$
$\lim _{x\to -2}{\frac {1*(x+2)}{1}}$
$-2+2=0$
$L=0$
Ex.2
$\lim _{x\to 2}{\frac {x^{2}+2x-8}{x-2}}$
${\frac {2^{2}+2*2-8}{2-2}}$
$={\frac {0}{0}}$
Once again this is an indeterminate form. Let's see if we can use factoring to get and answer.
Factoring the polynomial $x^{2}+2x-8$ we find that it equals $(x-2)(x+4)$
Let's use the factored in the limit equation.
$\lim _{x\to 2}{\frac {(x-2)(x+4)}{x-2}}$
As you can see the (x-2) will cancel each other out. Leaving us with
$\lim _{x\to 2}x+4$
$2+4=6$
$L=6$
This type evaluating limits will take some time, but with practice can be done quickly.

### L'Hopital's Rule

This rule is my favorite way to solve limits with indeterminate form.
This way is a bit more advanced so I will cover it briefly, but I will show some examples and the idea behind it. This is probably something you will learn in Calculus II
When you have a limit that you have confirmed that is in indeterminate form you can use L'Hopital's Rule.
This is the rule
When $\lim _{x\to c}f(x)={\frac {0}{0}}$, ${\frac {\infty }{\infty }}$, ${\frac {\infty }{0}}$, ${\frac {-\infty }{\infty }}$, ${\frac {\infty }{-\infty }}$, or ${\frac {-\infty }{-\infty }}$ use L'Hopital's rule. Which is $\lim _{x\to c}{\frac {f^{\prime }(x)}{g^{\prime }(x)}}$
Ex. 1
$\lim _{x\to 5}{\frac {x^{2}-3x-10}{x-5}}$
${\frac {5^{2}-3*5-10}{5-5}}={\frac {0}{0}}$
Now that we have identified that it is in an indeterminate form we use L'Hopital's rule
$\lim _{x\to 5}{\frac {2x-3}{1}}$
$2*5-3=7$
$L=7$
This is an extremely simplified form of how this rule is used. It is a really nice way to solve limit problems that give you indeterminate forms.
# High School Calculus/Evaluating Definite Integrals
### Evaluating a Definite Integral

Let's say you have the parabola $x^{2}$ and you want to find the area from x=2 to x=4
$2\leq A\leq 4$
$\int _{2}^{4}x^{2}\,dx$
In order to take the integral of the function you have to do the opposite that of the derivative
The power of the variable x will have a number added to it. So, $x^{(a+1)}$
then the number gets inverted and brought out front.
${\frac {1}{a+1}}*x^{(a+1)}$
$\int _{2}^{4}x^{2}\,dx$
From here we integrate and plug (b) into the indefinite integral and subtract the integral from (a) plugged into the indefinite integral.
$[{\frac {1}{3}}*4^{3}]-[{\frac {1}{3}}*2^{3}]$
Now we evaluate the integral
$[{\frac {1}{3}}*64]-[{\frac {1}{3}}*8]$
$[{\frac {64}{3}}]-[{\frac {8}{3}}]$
${\frac {56}{3}}$
${\frac {56}{3}}$
is the area underneath the curve from 2 to 4. In other words $2\leq A\leq 4$
# High School Calculus/Derivatives of Trigonometric Functions
### Formulas for Differentiation of Trigonometric Functions

In the following formulas the angle u is supposed to be expressed in circular measure.
${\operatorname {d} \over \operatorname {d} x}\sin u=\cos u$
${\operatorname {d} \over \operatorname {d} x}\cos u=-\sin u$
${\operatorname {d} \over \operatorname {d} x}\tan u=\sec ^{2}u$
${\operatorname {d} \over \operatorname {d} x}\cot u=-\csc ^{2}u$
${\operatorname {d} \over \operatorname {d} x}\sec u=\sec u\tan u$
${\operatorname {d} \over \operatorname {d} x}\csc u=-\csc u\cot u$

### Proofs

Proof for the derivative of $\sin u$
Let $y=\sin u$,
then
$y\prime =\sin(u+\Delta u)$;
therefore
$\Delta y=\sin(u+\Delta u)-\sin u$;
In Trigonometry,
$\sin A-\sin B=2\sin {1 \over 2}(A-B)\cos {1 \over 2}(A+B)$
If we substitute $A=u+\Delta u$ and $B=u$,
we have
$\Delta y=2\cos \left(u+{\Delta u \over 2}\right)\ sin{\Delta u \over 2}$
Hence
${\Delta y \over \Delta x}=\cos \left(u+{\Delta u \over 2}\right){\sin {\Delta u \over 2} \over {\Delta u \over 2}}$
When $\Delta x$ approaches zero, $\Delta u$ likewise approaches zero, and as $\Delta u$ is in circular measure, the limit of
${\sin {\Delta u \over 2} \over {\Delta u \over 2}}$
Hence
${\operatorname {d} y \over \operatorname {d} x}=\cos u$
Proof for ${\operatorname {d} \over \operatorname {d} x}\cos u$
${\operatorname {d} \over \operatorname {d} x}\cos u=\sin u\left(-{\operatorname {d} u \over \operatorname {d} x}\right)=-\sin u{\operatorname {d} u \over \operatorname {d} x}$
Proof for ${\operatorname {d} \over \operatorname {d} x}\tan u$
Since $\tan u={\sin u \over \cos u}$
${\operatorname {d} \over \operatorname {d} x}\tan u={\cos u{\operatorname {d} \over \operatorname {d} x}\sin u-\sin u{\operatorname {d} \over \operatorname {d} x}\cos u \over \cos ^{2}u}$
$={\cos ^{2}u{\operatorname {d} u \over \operatorname {d} x}+\sin ^{2}u{\operatorname {d} u \over \operatorname {d} x} \over \cos ^{2}u}={\operatorname {d} u \over \cos ^{2}u}$
$=\sec ^{2}u{\operatorname {d} u \over \operatorname {d} x}$
Proof for ${\operatorname {d} \over \operatorname {d} x}\sec u$
${\operatorname {d} \over \operatorname {d} x}\tan u={\cos u{\operatorname {d} \over {d}x}\sin u-\sin u{\operatorname {d} \over \operatorname {d} x}\cos u \over \cos ^{2}u}$
$={\cos ^{2}{\operatorname {d} u \over \operatorname {d} x}+\sin ^{2}u{\operatorname {d} u \over \operatorname {d} x} \over \cos ^{2}u}={{\operatorname {d} u \over \operatorname {d} x} \over \cos ^{2}u}$
$=\sec ^{2}u{\operatorname {d} u \over \operatorname {d} x}$
# High School Calculus/Functions, Limits, and Continuity

* Equations and Graphs
* Relations and Functions
* Models and Data
* The Calculus
* Finding Limits
* Evaluating Limits
* Continuity
* Infinite Limits
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