OpenLLM-France/wikimedia huggingface dataset:
# Physics and Astronomy Labs/Graphical integration of uniform acceleration

In this lab we will use vector to graphically find the motion associated with uniform acceleration. For students who develop this lab, it is also a lesson on creating and understanding the svg files preferred by Wikiversity and its sisters.
Open up Inkscape and create an initial velocity vector, called ${\vec {v}}_{0}$ and an "acceleration" vector called ${\vec {a}}\Delta t$ (note that the latter is actually acceleration time a short time, $\Delta t$.
* Let ${\vec {r}}_{0}$ represent the location of the particle at $t=0$, which is at the tail of ${\vec {v}}_{0}$.
* Let ${\vec {r}}_{1}$ = ${\vec {v}}_{0}\Delta t$.
# Physics and Astronomy Labs/Heisenberg's uncertainty and Beethoven's fugue/gallery

Each of the three images shown above have good summaries that you can read if you click the links and scroll down a bit.

### References and footnotes

* ↑ Someday somebody should place and image like this oneon commons, with the dots spread out enough so that they resemble individual "measurements".
# Physics and Astronomy Labs/Force table

force table, angles and weight example
angle 1 is 0 degrees 550 grams
angle 2 152 degrees 400 grams
angle 3 220 degrees 250 grams
# Physics and Astronomy Labs/Optics: Human eye model (Pasco)
## overall impressions

good lab, with lots of "pluses" and a few "minuses"

#### Plusses

* Students are impressed
* More than two hours of activities are possible
* Most of the images are not clear

#### Minuses

* Lots of small parts
* One of the devices leaks
* You need a really bright light (not provided) to illuminate the source
* Not all of the images are good: We found that object distances of more than one meter created barely discernible images. Also, the option of an adjustable focal length lens does not seem worth the bother (and it makes a poor image).

## Notes on manual
### Purpose of these notes

The intent of these notes is to guide the students and instructor through Instruction Manual 012-13032A available at ftp://ftp.pasco.com/support/Documents/English/OS/OS-8503/Human%20Eye%20Model%20Manual%28OS-8503%29.pdf
# Physics and Astronomy Labs/Optics: Human eye model (Pasco)/C

we went to this page
# Tunnel

A tunnel is an underground passage. Some tunnels are used for cars, and others are used for trains. Sometimes, a tunnel is used for movement of ships. Some tunnels are built for communication cables and some are built for electricity cables. Other tunnels are built for animals.
The Channel Tunnel between France and England is one of the longest tunnels in the world. It is 50 kilometers long. The longest tunnel in the world, the Gotthard Base Tunnel, is being dug in Switzerland.

## Some reasons to build a tunnel

* A subway is based on a network of tunnels that are dug underground so the trains will not disturb and will not be disturbed by the local transport.
* On the path of a railroad track or a road, a tunnel is dug when the lane encounters an obstacle such as a mountain to avoid bypassing the obstacle.
* A tunnel is built sometimes to overcome a water obstacle as a replacement for building a bridge structure above it.
* A tunnel is built to connect between military posts so the movement between them will not be visible for the enemy.
* A tunnel is built for infrastructure like electricity cables, water, communication and sewerage to avoid damage and disruption above ground.
# Turbo 2000 for Atari

This short article by Dan Polansky briefly covers Turbo 2000 system for Atari 8-bit computers. The system allowed the magnetic tape recorder/datasette (used with compact cassettes) to read and write in 2270 bits per second instead of the original 600. As a consequence, a 90 minute cassette could contain approximately 1.5 MB; assuming a game has no more than 48 KB, this yields at least 30 games per 90 minute cassette. The system was of Czechoslovak origin, made by Jiří Richer in 1987 in Prague. It required a hardware modification of the XC12 datasette and accompanying software, usually available on a cartridge. The software had to turn ANTIC chip off; the only display available during loading were black and white moving strips.
A key motivation for this modication seems to be that, in the late 1980ies in Czechoslovakia, Atari disk drives were very expensive, unlike the XC12 datasettes. And XC12 datasettes were needlessly slow with their 600 bits/s, where the effective rate was even lower since the original Atari format split files into data blocks/packets separated by gaps (a packet storing 128 bytes), whereas Turbo 2000 had only one gap separating the file header from the body. If we reckon with the gaps, the effective rate may perhaps be 500 bits/s for multi-block files, resulting in a speed-up of over 4 times.
There were multiple systems labeled as Turbo in Czechoslovakia. The technical differences and compatibility are unclear. One variant was called Super Turbo, which allowed flexible bit rate in the range of 2700 to 5000 bit/s. Super Turbo seems to have been compatible with Turbo 2000 in some sense.
A tentative speculation about turning off ANTIC: the loading and saving code would have used busy wait to do timing to track the length of one bit. It would need a fixed number of CPU cycles burned by the given 6502 code. However, ANTIC's direct memory access (DMA) would make the timing too variable; when ANTIC reads RAM to access a display list, player/missile graphics data or video memory ("playfield"), 6502 cannot access RAM and has to wait. Moreover, it is possible that ANTIC is less busy during vertical blank (the beam is off screen); if so, the same 6502 code is faster during vertical blank. See also Wikipedia: ANTIC.
A variant of XC12 labeled XC13 was allegedly sold, ready for Turbo 2000 (and thus requiring no more hardware modification). Absent images of XC13 and the scarcity of sources, it is not clear how reliable that information is.
# Tuned Mass Damper

Typically, the tuned mass dampers, a kind of seismic vibration control technology, are huge concrete blocks mounted in skyscrapers or other structures and moved in opposition to the resonance frequency oscillations of the structures by means of some sort of spring mechanism.
Taipei 101 skyscraper depicted on the left needs to withstand typhoon winds and earthquake tremors common in its area of the Asia-Pacific. For this purpose, a steel pendulum weighing 660 metric tons that serves as a tuned mass damper was designed and installed atop the structure. Suspended from the 92nd to the 88th floor, the pendulum sways to decrease resonant amplifications of lateral displacements in the building caused by earthquakes and strong gusts.
# Turing

    Navigation: Engineering and Technology » Computer Science » Computer Programming » Turing
Turing is a programming language used in some schools to teach programming to beginners. It is a good example of the RAD design philosophy, which emphasizes ease and speed of software development. C is a better language for writing low-level code, and for professionals in general. Turing can be used to teach logic, algebra, geometry, physics, chemistry, and music theory.

## Prerequisites

* Possession of a copy of Turing (free download, development is stopped)
** You can get a copy of Turing (4.1.1) here
* Understanding of basic computing concepts in DOS and/or Windows.
* Completion of or concurrent enrollment in
** Introduction to Programming
** Introduction to Programming Logic
** Introduction to Computer Science
** College Algebra, Math for computer programming, or equivalent.
* Intentions to succeed and a commitment to learning.
This course is an introductory course in the field of computer programming. It does not require any prior knowledge of practicing computer programming.

## Course Description

This course is intended to teach you all notable aspects of computer programming with the Turing programming language.
Note: Since this course is still under construction, so, you may find one of these tutorials more handy right now.

### Pros and Cons of Turing

Pros
* Simple syntax and built-in Math, Timing, and Input/Output functions
* Easy to learn. Logical operator names for the most part
* Is potentially a lot more powerful than the average C or C++ programmer may think. It depends on the coder's ability and knowledge.
* Runs on every copy of WinXP ever released, by default.
* Runs almost as fast as C, C++, etc. for simple programs
* Can be used to develop 3d games, and can display 512 filled triangles at 20 frames per second on a Pentium 4
* Isn't yet all the way towards becoming completely dead
Cons
* Is not as powerful as a language like C, C++, or Assembly in that it cannot easily access low-level functions such as are needed for device driver programming (Beginners probably won't care)
* Runs significantly slower than C, C++, etc. in some situations
* Developer releases latest buggy version for free, version 4.05 is better in some situations. Developer is out of business.

## Lessons
### Introductory lectures

* Introduction - Design a simple application
* Hello World - Sample application
* Variables and Types - store and manipulate values
* Control Structures and Logical Expressions - If statements and do loops
* Functions and Subroutines - Segment your programs
* Basic Graphical User Interfaces - Intro to built-in GUI functions, and custom GUI routines.
* Event-Driven Design - Event handling.
* Answers To Programming Language Exercises - Answers

### Intermediate lectures

* Group Study at U of G Library, contact user pages of other students for details.

### Advanced lectures

* Introductory Game Design
# Tulip

Tulips are erect flowers with long, broad, parallel-veined leaves and a cup-shaped, single or double flower at the tip of the stem. Colors of the flowers can range anywhere from red to yellow to white. Some tulips are varicolored as a result of a viral disease carried and transferred to the plants by aphids. The tulip is a member of the lily family which flowers in the spring and is a bulbous herb. About eighty species of tulips exist. The tulip gained popularity quickly after it was introduced in western Europe in the Sixteenth century. Tulip bulbs are still a major export of the Netherlands.
# Unit circle/Diagonal/Intersection point/Q and R/Exercise

We consider the rational unit circle
    $E={\left\{(x,y)\in \mathbb {Q} ^{2}\mid x^{2}+y^{2}=1\right\}}\,$
and the line
    $G={\left\{(x,y)\in \mathbb {Q} ^{2}\mid x+y=0\right\}}\,.$
* Determine the intersection points $E\cap G$.
* What is the answer when we consider the situation not over $\mathbb {Q}$, but over the real numbers $\mathbb {R}$?
* Can you understand the circle without understanding the the real numbers?
* Does there exist a relation with the Intermediate value theorem?
# Unit circle/Integral of square root of 1-x^2/Example

The upper curve of the unit circle is the set
    ${\left\{(x,y)\mid x^{2}+y^{2}=1,\,-1\leq x\leq 1,\,y\geq 0\right\}}.$
For a given $x$, $-1\leq x\leq 1$, there exists exactly one $y$ fulfilling this condition, namely $y={\sqrt {1-x^{2}}}$. Hence, the area of the upper half of the unit circle is the area beneath the graph of the function $x\mapsto {\sqrt {1-x^{2}}}$, above the interval $[-1,1]$, that is
    $\int _{-1}^{1}{\sqrt {1-x^{2}}}\,dx.$
Applying substitution with
    $x=\cos t{\text{ and }}t=\arccos x$
(where $\cos :[0,\pi ]\rightarrow [-1,1]$ is bijective, due to fact), we obtain, using example, the identities
    ${\begin{aligned}\int _{a}^{b}{\sqrt {1-x^{2}}}\,dx&=\int _{\arccos a}^{\arccos b}{\sqrt {1-\cos ^{2}t}}(-\sin t)\,dt\\&=-\int _{\arccos a}^{\arccos b}\sin ^{2}t\,dt\\&={\frac {1}{2}}(\sin t\cos t-t)|_{\arccos a}^{\arccos b}.\end{aligned}}$
In particular, we get that
    ${\frac {1}{2}}{\left(x\cdot \sin {\left(\arccos x\right)}-\arccos x\right)}={\frac {1}{2}}{\left(x\cdot {\sqrt {1-x^{2}}}-\arccos x\right)}\,$
is a primitive function for ${\sqrt {1-x^{2}}}$. Therefore,
    ${\begin{aligned}\int _{-1}^{1}{\sqrt {1-x^{2}}}\,dx&={\frac {1}{2}}{\left(x\cdot {\sqrt {1-x^{2}}}-\arccos x\right)}|_{-1}^{1}\\&={\frac {1}{2}}(-\arccos 1+\arccos(-1))\\&=\pi /2.\end{aligned}}$
# Unit fractions/Sum n+1 to 2n/ln 2/Hint/Exercise

Show that for every $n\in \mathbb {N} _{+}$ the estimate
    ${\frac {1}{n+1}}+{\frac {1}{n+2}}+\cdots +{\frac {1}{2n}}\leq \ln 2\,$
holds. Hint: Consider the function $f(x)={\frac {1}{x}}$ on the interval $[1,2]$.
# Unit Testing/xUnit.net/View Test Coverage

View test coverage.
* Run the following command and observe the results:
** dotnet test --coverage:"Code Coverage"
* Add tests and then repeat the command above to achieve 100% coverage.
# Unit circle/Circle length/Bisection/Program/Exercise

We consider the unit circle, i.e.
    ${\left\{{\begin{pmatrix}x\\y\end{pmatrix}}\mid x^{2}+y^{2}=1\right\}}\subseteq \mathbb {R} ^{2}\,.$
We put $P_{0}={\begin{pmatrix}1\\0\end{pmatrix}}$ and $P_{1}={\begin{pmatrix}0\\1\end{pmatrix}}$, and we define recursively the sequence $P_{n}$ (in the plane) by
    $Q_{n}={\frac {1}{2}}{\left(P_{0}+P_{n-1}\right)}\,$
(that is, $Q_{n}$ is the bisection point of the line segment between $P_{0}$ and $P_{n-1}$), and $P_{n}$ is the intersection point of the half-line through ${\begin{pmatrix}0\\0\end{pmatrix}}$ and $Q_{n}$ and the circle. We consider the lengths $d_{n}=d(P_{0},P_{n})$ as an approximation for the length of the circle arc between $P_{0}$ and $P_{n}$, and therefore
    $x_{n}=2^{n}d_{n}\,$
is an approximation for the length of the half circle arc (that is, $\pi$). Since in the computation of the points $P_{n}$ and the lengths $d_{n}$, square roots occure (due to the Pythagorean theorem), we can approximate these by rational numbers only with certain errors.
Write a computer-program (in pseudocode), which computes and prints a sequence $y_{n}$ of approximations ($n\geq 1$) for $x_{n}$. In the computation of $y_{n}$, all square roots, which are used in the computation of $x_{n}$, shall be computed with $n$ steps of Heron's method, starting with the initial value $1$. Also, the program shall use better and better approximations for the auxiliary points, the computation of $y_{n}$ requires that better and better approximations for $P_{2},\ldots ,P_{n}$ are determined.
The program shall run to infinity and write down the approximations $y_{1},y_{2},y_{3},...$.
# Unit circle/Real/Definition

The set
    $E:={\left\{(x,y)\in \mathbb {R} ^{2}\mid x^{2}+y^{2}=1\right\}}\,$
is called the unit circle.
# United Kingdom Law

* Welcome to the United Kingdom Learning Project, within the School of Law. The UK has a complex legal system with three main jurisdictions (England and Wales; Scotland; and Northern Ireland), each with their own legal principles and history. However, some laws apply to the entire UK, and this is the area that this project has learning resources on.
* History
* 2 September 2008 - department founded.
* 16 December 2008 - reorganization of the department page.
* 23 April 2017 - overhauled in line with revamp of School of Law.
* Resources
* English Law
* Northern Ireland Law
* United Kingdom Law/Bill of Rights
* Brexit
* Children, Schools and Families Bill
* United Kingdom Law/Company
* Comparative law and justice/Northern Ireland
* Comparative law and justice/Scotland
* Criminal Justice Act 2003
* United Kingdom Law/Freedom of Information
* United Kingdom Law/Great Repeal Bill 2008
* Protection from Harassment Act 1997
* United Kingdom Law/Reform
* United Kingdom Law/Reform/Draft Repeals Bill/Notes
* United Kingdom Law/Reform/Great Reform Bill
* United Kingdom Law/Reform/Great Reform Bill/Debate
* United Kingdom Law/Reform/Great Reform Bill/entry
* United Kingdom Law/Reform/Great Reform Bill/set
* United Kingdom Law/Statutes
* United Kingdom Law/Data Protection Act
* Active participants
* The histories of Wikiversity pages indicate who the active participants are. If you are an active participant in this department, you can list your name here (this can help small departments grow and the participants communicate better; for large departments a list of active participants is not needed).
* DarkObsidian - (Founder)
* Green Giant
# Unit Testing/xUnit.net/Test Exceptions
## Create a C# Program

Create the following C# program. Save it as Multiply.cs

## Create a Test Program

Create the following C# test program. Save it as MultiplyTest.cs

## Test Success

Test the program by running it in a terminal or command prompt in the same folder as the project above and observe the results.

## Test Failure

Change the multiply source code somehow, such as multiplying the string by a positive number. Test the program by running Jest again and observe the results.
# Unit circle/Description as graph/Exercise

Describe the upper half of the unit circle and the lower half of the unit circle as graphs of functions.
# Real function/Exponential equation/Continuous/Exponential function/Exercise

Let
    $f\colon \mathbb {R} \longrightarrow \mathbb {R}$
be a continuous function $\neq 0$, with the property that
    $f(x+y)=f(x)\cdot f(y)\,$
for all $x,y\in \mathbb {R}$. Prove that $f$ is an exponential function, i.e. there exists a $b>0$ such that $f(x)=b^{x}$.
# Real function/Extrema/Higher derivatives/Fact/Proof

Under the given conditions, the Taylor formula becomes
    $f(x)-f(a)={\frac {f^{(n+1)}(c)}{(n+1)!}}(x-a)^{n+1}\,,$
with some $c$ (depending on $x$) between $a$ and $x$. Depending on whether $f^{(n+1)}(a)>0$ or $f^{(n+1)}(a)<0$ holds, we have (due to the continuity of the $(n+1)$-th derivative) $f^{(n+1)}(x)>0$ or $f^{(n+1)}(x)<0$ for $x\in [a-\epsilon ,a+\epsilon ]$, for a suitable $\epsilon >0$. For these $x$, we have $c\in [a-\epsilon ,a+\epsilon ]$, so that the sign of $f^{(n+1)}(c)$ depends on the sign of $f^{(n+1)}(a)$. For $n$ even, $n+1$ is odd and therefore the sign of $(x-a)^{n+1}$ changes at $x=a$ (for $x<a$, the sign is negative, and for $x>a$, the sign is positive). Since the sign of $f^{(n+1)}(c)$ does not change, the sign of $f(x)-f(a)$ is changing. This means that there can not be an extremum. Suppose now that $n$ is odd. Then $n+1$ is even, hence $(x-a)^{n+1}>0$ for all $x\neq a$ in the neighborhood. This means, in the neighborhood, in case $f^{(n+1)}(a)>0$, that $f(x)>f(a)$ holds, and we have an isolated minimum in $a$. If $f^{(n+1)}(a)<0$, then $f(x)<f(a)$ holds, and we have an isolated maximum in $a$.
# Real function/Extrema/3x^3-7x^2+6x-3/From -4 to 4/Exercise

Determine local and global extrema of the function
    $f\colon [-4,4]\longrightarrow \mathbb {R} ,x\longmapsto f(x)=3x^{3}-7x^{2}+6x-3.$
# Real function/Extrema/2x^3-5x^2+4x-1/From -2 to 5/Exercise

Determine local and global extrema of the function
    $f\colon [-2,5]\longrightarrow \mathbb {R} ,x\longmapsto f(x)=2x^{3}-5x^{2}+4x-1.$
# Real function/Extrema/Higher derivatives/Fact

Let $I$ denote a real interval,
    $f\colon I\longrightarrow \mathbb {R}$
an $(n+1)$-times continuously differentiable function, and $a\in I$ an inner point of the interval. Suppose that
    $f'(a)=f^{\prime \prime }(a)=\ldots =f^{(n)}(a)=0{\text{ and }}f^{(n+1)}(a)\neq 0$
is fulfilled. Then the following statements hold.
* If $n$ is even, then $f$ does not have a local extremum in $a$.
* Suppose that $n$ is odd. In case $f^{(n+1)}(a)>0$, the function $f$ has an isolated local minimum in $a$.
* Suppose that $n$ is odd. In case $f^{(n+1)}(a)<0$, the function $f$ has an isolated local maximum in $a$.
# Real function/Extrema/Second derivative/Fact

Let $I$ denote a real interval,
    $f\colon I\longrightarrow \mathbb {R}$
a twice continuously differentiable function, and $a\in I$ an inner point of the interval. Suppose that $f'(a)=0$ holds. Then the following statements hold.
* If $f^{\prime \prime }(a)>0$ holds, then $f$ has an isolated local minimum in $a$.
* If $f^{\prime \prime }(a)<0$ holds, then $f$ has an isolated local maximum in $a$.
# Real function/Even and odd/Zero function/Exercise

Show that there exists exactly one function $f\colon \mathbb {R} \rightarrow \mathbb {R}$, which is at the same time even and odd.
# Real function/Extrema/4x^3+3x^2-x+2/Tangent from -3 to 3/Exercise

Consider the function
    $f\colon \mathbb {R} \longrightarrow \mathbb {R} ,x\longmapsto f(x)=4x^{3}+3x^{2}-x+2.$
Find the point $a\in [-3,3]$ such that the tangent of the function at $a$ is parallel to the secant between $-3$ and $3$.
# Real function/Extrema/Second derivative/Fact/Proof/Exercise

Let $I$ be a real interval,
    $f\colon I\longrightarrow \mathbb {R}$
a twice continuously differentiable function, and let $a\in I$ be an inner point of the interval. Suppose that $f'(a)=0$. Show the following statements.
* If $f^{\prime \prime }(a)>0$ holds, then $f$ has an isolated local minimum in $a$.
* If $f^{\prime \prime }(a)<0$ holds, then $f$ has an isolated local maximum in $a$.
# Real function/Higher derivative/Recursive/Definition

Let $I\subseteq \mathbb {R}$ denote an interval, and let
    $f\colon I\longrightarrow \mathbb {R}$
be a function. The function $f$ is called $n$-times differentiable, if it is $(n-1)$-times differentiable, and the $(n-1)$-th derivative, that is $f^{(n-1)}$, is also differentiable. The derivative
    $f^{(n)}(x):=(f^{(n-1)})'(x)\,$
is called the $n$-th derivative of $f$.
# Textual Criticism of the Bible

Textual Criticism of the Bible is the study of the Bible with the intention of detecting errors in the text and determining what the original text may have been.
It proceeds by analysing the oldest manuscripts, published versions and translations to produce lists of variant readings. Critics then try to decide which is the best reading. Where no satisfactory reading can be found, critics may make conjectural emendations. Sometimes, these conjectures have later been found in previously unknown manuscripts, such as the Dead Sea Scrolls.

## Causes of Textual Corruption

Before the advent of printing, manuscripts had to be copied by hand so were quite rare and expensive. They rarely included the whole Bible, and were often just single books of the Bible.
Textual corruption usually occurs by accident, but sometimes a copyist would deliberately alter what he considered a corrupt or heretical reading. Since such alterations produce sensible readings, they are hard to spot.

## Rules for Deciding on the Best Reading

There are no infallible rules for deciding which of several competing rules are the best, and at the end of the day good critical judgment is needed. However, the following rules are often useful.

## Alternatives to Textual Criticism

It may be that it is not necessary to amend the text of the Bible. It did not seem to make sense, hence seemed to need amendment, because we did not understand it. However, advances in other areas may permit us to understand the text better.

### Archaeology

Archaeology may help us to understand the historical and social background of a passage, hence reveal its meaning.

### Comparative Philology

Examination of languages similar to those of the Bible may suggest new meanings of words. Many English words, such as roe, can have several completely different meanings (a kind of deer, fish eggs), which would make a passage seem corrupt if we only knew one meaning and the other was intended. The same may be true of Hebrew and Greek.
Example: Judges 18:7 seems to say "there was no-one to put them to shame in anything" or "there was no-one to insult them in anything". This assumes that the word kulum means "to humiliate" or "to insult". However, it may be equivalent to the Arabic kallama, "to speak", allowing the more intelligible translation "there was no-one uttering a word".