OpenLLM-France/wikimedia huggingface dataset:
# United States Postage Meter Stamp Catalog/Sub-group PC-A – E-stamp
#### Sub-group PC-A: Franks from E-Stamp software, ID numbers with 05#E prefix

* All stamps have large, negative “e” logo at top right and "PDF417" bar code across the bottom with identification number at bottom right.
* "US Postage" and date are at top center, usually below a mail classification statement.
* Found both with and without FIM barcode at top left and also with and without slogan or directional slug at left.
* One hundred FD covers were prepared by E-Stamp in cooperation with the National Postal Museum on March 31, 1998. Trials took place for several more months. The first day of national availability was September 27, 1999.
* E-stamp ceased operations at the end of 2000.
Type RA1a in 2001 edition
PC-A1.1. March 31, 1998. [RR]
    This stamp is found only on the First Day Covers prepared by E-Stamp and the National Postal Museum. (See above). They were sold for $100 each.
    The value figures are large, 4mm tall.
    With "FIM" barcode at top left.
    Mail class: "First Class" (without hyphen).
    Idenification number with 051E prefix.
    V/F: $0.00$^o$ (large figures, 4mm tall)
Type RA1e in 2001 edition
PC-A1.2. 1998. [S]
    As Type PC-A1.1 but with smaller value figures, 2 to 3mm tall.
    "e-stamp.com" normally at bottom left below the barcode.
    ID# with 051E, 052E or 053E prefix.
    V/F: $0.00 (small figures, 2-3mm tall)
    Mail classes: $^♦$
       A. First-Class (with hyphen)
       B1. Priority [R]
       B2. Priority Mail [R]
       a. With "Additional" instead of mail class above "US Postage" [R]
       b. With recipient's identity instead of "e-stamp.com" at left below bar code field [RR]
       c. With 4-digit ZIP code
♦ "Express" (or "Express Mail") was an option but has not been reported by collectors.
Types RA1c and d in 2001 edition
PC-A1.3. [S]
    As Type PC-A1.2 but value figures show decimal fractions of a cent and have wide spacing between the dollar sign and the decimal digit with the other figures.
    ID# with 051E, 052E or 053E prefix.
    The mail classes are the same as for PC-A1.2.
       A. V/F regular: $0.00$^o$
       B. V/F italic: $0.00$^o$
       a. With "Additional" instead of mail class above "US Postage" [R]
Type RA1b in 2001 edition
PC-A1.4. [S]
    As PC-A1.3B but the value figures are spaced closely together.
    "e-stamp.com" at bottom left below the barcode.
    ID# with 053E prefix.
    The mail classes are the same as for PC-A1.2.
    V/F italic: $0.00$^o$
       a. With "Additional" instead of mail class above "US Postage" [R]
Type RA2 in 2001 edition
PC-A2. March 2000. [S]
    As Type PC-A1.2 but the inscriptions are larger.
    "e-stamp.com" at bottom left below the barcode.
    ID# with 053E prefix.
    V/F: $ 0.00
    Mail classes: $^♦$
       A. First-Class (with hyphen)
       B. Priority Mail [S]
       a. With "Additional" instead of mail class above "US Postage" (see below) [R]
       b. "Mailed From ZIP Code" town line with 4-digit ZIP code instead of normal 5-digit code [RR]
♦ "Express" (or "Express Mail") was an option but has not been reported by collectors.
# Super Mario Bros. 3/Enemies/Angry Sun

The Angry Sun is an enemy that appears in Super Mario Brothers 3. It appears in World 2-Desert, and attacks Mario by swooping down at him.
# Super Mario Bros. 3/Enemies/Koopa Paratroopa

Koopa Paratroopas are a variant of Koopa Troopas that have wings. Like their regular counterpart, Koopa Paratroopas have either a red or green shell.
# Super Mario Bros. 3/Codes
## The Lost Levels

* The lost levels in Super Mario Bros. 3 are unused, abandoned levels that were programmed into the game, but were deleted from the final version. Some of these levels feature lost enemies that are also programmed into the game. The level that sheds some light on the subject is the level that can be accessed with the Game Genie code AOZULT. This code forces entry into a lost level found inside the START panel in World 1. The level seems like it was deleted from World 6 for being too short and too easy. This is generally true of all the levels, especially ones matching motifs that appear later in the game. This suggests that these may either have been in the early stages of development before being deleted from the completed game, developmental versions of in-game, final cut levels, or may have served some other purpose such as use in conjunction with development tools.
Other codes include:
* KZNUGGXE-OZNUIKUU, a lost plains stage similar to Worlds 3-9 and 5-3.
* LZXUAGPZ-SINUGGXE-ELNUIKUL, a grassy, hilly stage featuring Goomba's shoe, Lakitu, a coin heaven and continuous Starman power-ups. Possibly an early version of World 7-3.
* LZXUAGPZ-ZGNUGGXA-KLNUIKUL, an underground level with big doors and Buzzy Beetles. The layout of this level is reminiscent of World 1-5, but without the coin heaven.
* ZZXUAGPZ-GINUGGXA-NLNUIKUL, unused Tanooki Suit bonus rooms with castle music.
* GZXUAGPX-XLNUGGXE-NLNUIKUL, an auto-scrolling underwater ice level reminiscent of World 6 with Jelectros from World 7-4 and gold Cheep-Cheeps, an unused enemy in the final game. The middle of this level consists of an island filled with Munchers.
* AZXUAGPX-APNUGGXE-NZNUIKUU, a vertical level with waterfalls and pipes.
* IZXUAGPX-OZNUGGXE-KZNUIKUU, a cloud level filled with red Parabeetles and the unused, fast-moving green Parabeetles.
* GZXUAGPZ-SGNUGGXE-SZNUIKUU, obviously a harder version of World 1-6.
* GZXUAGPZ-KGNUGGXA-ELNUIKUL, another variation of the above level. No goal, cut short.
* IZXUAGPX-UZNUGGXE-SZNUIKUU, an unused cloud level. May be an attempt at a nighttime cloud level.
* GGNUGGXE-NZNUIKUL, an unused level, presumably an early version of a World 7 level.
Caution: When using these codes, the pointers and enemies may load up incorrectly, or the screen may glitch all together and make the level unplayable.

## Miscellaneous codes

| Code | Effect |
| KKKZSPIU | Enables the debug mode. On the title screen: Press Up/Down to select the starting world. Press A to add five lives to your starting value. In the game: Press Select to cycle between Mario's forms. A+B+Select toggles Kuribo's Shoe (may be graphically glitched in certain areas, but works otherwise fine) |
| YPXXLVGE | Mario (but not Luigi) can reuse his items infinitely |
| SLXPLOVS | Infinite lives |
| ESKKKTEY | Allows you to enter any level, including levels that have already been beaten |
| OXKIPZOS | Free movement mode on the world map |
| GZUXNGEI | Infinite jumps |
| AOSUZSSI | Grab ice blocks from anywhere, including solid walls |
# Super Mario Bros. 3/Enemies/Koopa Troopa

Koopa Troopas are turtle enemies in the Mario games. They are a basic enemy, slightly more dangerous than Goombas. They come in two colors, green and red, the former type being more common. Koopa Troopas appear in most levels.
# Super Mario Bros. 3/Enemies/Venus Fire Trap

Venus Fire Traps are variants of Piranha Plants that appear as early as World 1-1. They appear from pipes to spit fireballs at Mario or Luigi. In some desert levels, they appear from the quicksand, starting with World 2-2.
# The Legend of Zelda: Ocarina of Time/Grottos

There are many open and hidden grottos located throughout Hyrule. Many of them contain helpful or valuable items.

## Pink Fairy Fountains

Fairies are useful for restoring your health, and even reviving you when you lose all of your hearts and die. If you are low on health, or have a bottle to keep one for later, the following locations will be the best places to find a fairy quickly.
* Desert Colossus: Go to rock where dried up pool and palm trees are and play the Song of Storms and pool will fill up with water making fairies appear.
* Gerudo Fortress: Out the door where you rescued the first carpenter with another door to left play Song of Storms and hole will open drop in to find fairy fountain.
* Hyrule Field: Across stream to west smash boulder with the Megaton Hammer.
* Graveyard: Grave with flowers in the front down behind chest bomb wall and follow corridor.
* Scared Forest Meadow: Climb ladder at end of maze and drop into hole down another ladder and you will find the fairy fountain.
* Zora's River: Bomb boulder on highest place.
* Zora's Domain: On island in water play Song of Storms and drop in hole that appears to find a fairy fountain.
# Trigonometry/Trigonometric Unit Circle and Graph Reference

The Unit Circle
The unit circle is a commonly used tool in trigonometry because it helps the user to remember the special angles and their trigonometric functions. The unit circle is a circle drawn with its center at the origin of a graph(0,0), and with a radius of 1. All angles are measured starting from the x-axis in quadrant one and may go around the unit circle any number of degrees. Points on the outside of the circle that are in line with the terminal (ending) sides of the angles are very useful to know, as they give the trigonometric function of the angle through their coordinants. The format is (cos, sin).
Note that in trigonometry, an angle can be of any size, positive or negative. An angle larger than 360º means that you have gone round the circle more than once.
# Trigonometry/The summation of finite series
## Problem Statement

Find a closed form for
    $\sin(a)+\sin(a+b)+\sin(a+2b)+\cdots +\sin(a+(n-1)b)$
Note: A 'closed form' is not mathematically defined, but just means a simplified formula which does not involve '...', or a summation sign. In our problem, we should look for a formula that only involves variables $a,b,n$, and known operations like the four operations, radicals, exponents, logarithm, and trigonometric functions.

## Method 1

To sum the series
    $\sin(a)+\sin(a+b)+\sin(a+2b)+\cdots +\sin(a+(n-1)b)=S$
Multiply each term by
    $2\sin \left({\tfrac {b}{2}}\right)$
Then we have
    $2\sin(a)\sin \left({\tfrac {b}{2}}\right)=\cos \left(a-{\tfrac {b}{2}}\right)-\cos \left(a+{\tfrac {b}{2}}\right)$
and similarly for all terms to
    $2\sin {\bigla+(n-1)b{\bigr )}\sin \left({\tfrac {b}{2}}\right)=\cos \left(a+(2n-3){\tfrac {b}{2}}\right)-\cos \left(a+(2n-1){\tfrac {b}{2}}\right)$
Summing, we find that nearly all the terms cancel out and we are left with
    $2S\sin \left({\tfrac {b}{2}}\right)=\cos \left(a-{\tfrac {b}{2}}\right)-\cos \left(a+(2n-1){\tfrac {b}{2}}\right)=2\sin \left(a+(n-1){\tfrac {b}{2}}\right)\sin \left({\tfrac {nb}{2}}\right)$
Hence
    $S=\sin \left(a+(n-1){\tfrac {b}{2}}\right){\frac {\sin \left(n{\tfrac {b}{2}}\right)}{\sin \left({\tfrac {b}{2}}\right)}}$
Similarly, if
    $C=\cos(a)+\cos(a+b)+\cos(a+2b)+\cdots +\cos {\bigla+(n-1)b{\bigr )}$
then
    $C=\cos \left(a+(n-1){\tfrac {b}{2}}\right){\frac {\sin \left(n{\tfrac {b}{2}}\right)}{\sin \left({\tfrac {b}{2}}\right)}}$

## Method 2

Consider the following sum
    $s=e^{ai}+e^{(a+b)i}+\cdots +e^{(a+(n-1)b)i}$
Since $s$ is a geometric series with common ratio $e^{bi}$, we get
    $s={\frac {e^{ai}(e^{nbi}-1)}{e^{bi}-1}}={\frac {e^{ai}(e^{nbi}-1)}{e^{bi}-1}}={\frac {e^{ai}e^{\frac {nbi}{2}}(e^{\frac {nbi}{2}}-e^{-{\frac {nbi}{2}}})}{e^{\frac {bi}{2}}(e^{\frac {bi}{2}}-e^{-{\frac {bi}{2}}})}}$
    $s={\frac {\sin \left(n{\tfrac {b}{2}}\right)}{\sin \left({\tfrac {b}{2}}\right)}}\cdot e^{\left(a+(n-1){\tfrac {b}{2}}\right)i}$
Therefore,
    $\sin(a)+\sin(a+b)+\sin(a+2b)+\cdots +\sin {\bigla+(n-1)b{\bigr )}={\rm {Im}}(s)=\sin \left(a+(n-1){\tfrac {b}{2}}\right){\frac {\sin \left(n{\tfrac {b}{2}}\right)}{\sin \left({\tfrac {b}{2}}\right)}}$
    $\cos(a)+\cos(a+b)+\cos(a+2b)+\cdots +\cos {\bigla+(n-1)b{\bigr )}={\rm {Re}}(s)=\cos \left(a+(n-1){\tfrac {b}{2}}\right){\frac {\sin \left(n{\tfrac {b}{2}}\right)}{\sin \left({\tfrac {b}{2}}\right)}}$
# Trigonometry/The solution of cubic equations

A cubic equation is an equation of the form
    $ax^{3}+bx^{2}+cx+d=0$
to be solved for x. There are three possible values for x, known as the roots of the equation, though two or all three of the values may be equal (repeated root). If a, b, c and d are all real numbers, at least one value of x must be real. There are two possible cases: the other two roots may be real, or they may be a pair of complex conjugate numbers.
The roots can always be expressed exactly as surds. However, if all three roots are real, the surds involve the cube roots of complex numbers. In that case, they are in general most easily calculated using trigonometric functions.
In the above equation, a is non-zero (or the equation would be quadratic). Divide through by a to get the equation in the form
    $x^{3}+Ax^{2}+Bx+C=0$
Let
$Q={\frac {3B-A^{2}}{9}},\qquad R={\frac {9AB-27C-2A^{3}}{54}},\qquad D=Q^{3}+R^{2}$
D is called the discriminant. If $D>0$ , two roots are complex; if $D=0$ there is a (real) repeated root; if $D<0$ there are three unequal real roots.
Assume $D<0$ . Clearly, $Q^{3}=D-R^{2}$ must be less than $D$ so is also negative; thus, $-Q^{3}$ and $-Q$ are both positive. Let
$\cos(\theta )={\frac {R}{\sqrt {-Q^{3}}}}$
Then the three roots are
    $x_{1}=2{\sqrt {-Q}}\cos \left({\tfrac {\theta }{3}}\right)-{\frac {A}{3}}$
    $x_{2}=2{\sqrt {-Q}}\cos \left({\tfrac {\theta }{3}}+120^{\circ }\right)-{\frac {A}{3}}$
    $x_{3}=2{\sqrt {-Q}}\cos \left({\tfrac {\theta }{3}}+240^{\circ }\right)-{\frac {A}{3}}$
Example: solution to $x^{3}-3x+1=0$: $A=0$, $B=-3$, and $C=1$. One finds $Q=-1$, $R=-1/2$, $D=-3/4$, and $\theta =2\pi /3,4\pi /3$, with the result that $x=2\cos(4\pi /9)=2\sin(\pi /18)=0.347296$, $x=2\cos(2\pi /9)=1.53209$, $x=-2\cos(\pi /9)=-1.87939$, the first being the critical threshold for bond percolation on the triangular lattice (Sykes and Essam 1964).
[Add example and/or exercise]
# Trigonometry/The distance and dip of the horizon

Since the Earth is (approximately) a sphere, an observer close to its surface can only see a limited area, bounded by a circle centred on the observer. This circle is called the horizon. Further, a point on this circle is slightly below the plane drawn through the observer and perpendicular to a line from the observer to the centre of the Earth. The angle between this plane and the line from the observer to a point on the horizon is called the dip of the horizon.
[Insert diagram]
let the radius of the Earth be r, the distance to the horizon be d and the height of the observer above the Earth be h. Then by Pythagoras' theorem
    $\displaystyle (r+h)^{2}=r^{2}+d^{2}$
or, rearranging,
    $\displaystyle d={\sqrt {h(2r+h)}}$.
In normal circumstances, h will be so much less than r that it is accurate enough to write
    $\displaystyle d={\sqrt {2hr}}$.
This formula may be inverted to find how high you must be to see to a given distance:
    $\displaystyle h={\frac {d^{2}}{2r}}$.
The dip θ is equal to the angle at the centre of the Earth between the observer and the horizon, so
    $\displaystyle \tan(\theta )={\frac {d}{r}}$.
It will be proved in Book 3 that for small angles
    $\displaystyle \tan(\theta )\approx \theta {\text{ radians }}={\frac {180\theta }{\pi }}{\text{ degrees}}$.
* Worked Example
* Suppose the radius of the Earth is 3960 miles and the observer is 100 feet high. Converting the height to miles,
* $\displaystyle h={\frac {100}{5280}}$
* $\displaystyle d={\sqrt {2hr}}={\sqrt {2\,{\frac {100}{5280}}\,3960}}={\sqrt {\frac {800}{3}}}\approx 16.3{\text{ miles}}$.
* $\theta \approx {\frac {16.3}{3960}}{\text{ radians }}\approx 0.004116{\text{ radians }}\approx 0.236{\text{ degrees}}$.
Note that in practice light rays are bent slightly by the Earth's atmosphere, so in general the horizon is slightly farther, and the dip slightly less, than these simple rules predict.
# Trigonometry/Trigonometric Form of the Complex Number

$z=a+bi=r\left(\cos \phi \ +i\sin \phi \right)$
where
* i is the imaginary number $\left(i\ ={\sqrt {-1}}\right)$
* the modulus $r=\operatorname {mod} (z)=|z|={\sqrt {a^{2}+b^{2}}}$
* the argument $\phi =\arg(z)$ is the angle formed by the complex number on a polar graph with one real axis and one imaginary axis. This can be found using the right angle trigonometry for the trigonometric functions.
This is sometimes abbreviated as $r\left(\cos \phi \ +i\sin \phi \right)=r\operatorname {cis} \phi$ and it is also the case that $r\operatorname {cis} \phi =re^{i\phi }$ (provided that $\phi$ is in radians). The latter identity is called Euler's formula.
Euler's formula can be used to prove DeMoivre's formula: $(\cos \phi \ +i\sin \phi )^{n}=\cos(n\phi )+i\sin(n\phi ).$ This formula is valid for all values of n, real or complex.
Next Page: Trigonometric Unit Circle and Graph Reference | Previous Page: Vectors and Dot Products
Home: Trigonometry
# Trigonometry/The sine of 15 degrees

We have
    $\sin(\theta )={\sqrt {\frac {1-\cos(2\theta )}{2}}}$
    $\cos(\theta )={\sqrt {\frac {1+\cos(2\theta )}{2}}}$
If $\theta =15^{\circ }$ then
    $\cos(2\theta )=\cos(30^{\circ })={\frac {\sqrt {3}}{2}}$
so after some manipulation (left as an exercise),
    $\sin(15^{\circ })={\frac {{\sqrt {6}}-{\sqrt {2}}}{4}}=\cos(75^{\circ })$
    $\cos(15^{\circ })={\frac {{\sqrt {6}}+{\sqrt {2}}}{4}}=\sin(75^{\circ })$
These results may be combined with those from the previous section to find the sines and cosines of $=3^{\circ }$ and its multiples.
# Trigonometry/The sine of 18 degrees

The trigonometric functions of angles that are multiples of 3º can all be expressed as surds. This page will only deal with angles that are multiples of 18º.
Consider the equation
    $\sin(5x)-1=0$ .
Clearly, the only solutions are that 5x = 90º, 90º + 360º, 90º + 2x360º, 90º + 3x360º ... Thus x = 18º, 90º, 162º, 234º or 306º. (There is no need to go further, since increasing x by 360º does not affect its sine.) $\sin(x)$ is, after using various simplifications, sin(18º) twice, 1, -sin(54º) twice.
This equation can be solved in another way. Using the formula for $\sin(a+b)$ , we can expand $\sin(5x)$ to get
    $16\sin ^{5}(x)-20\sin ^{3}(x)+5\sin(x)-1=0$
If we write $s=\sin(x)$ , this becomes a quintic equation in s,
    $16s^{5}-20s^{3}+5s-1=0$
i.e.
    $(s-1)(4s^{2}+2s-1)^{2}=0$
so either $s=1$ (corresponding to x = 90º) or
    $s={\frac {{\sqrt {5}}-1}{4}}$
(corresponding to x = 18º or 54º). Thus
    $\sin(18^{\circ })={\frac {{\sqrt {5}}-1}{4}}\approx 0.30902$ .
    $\sin(54^{\circ })={\frac {{\sqrt {5}}+1}{4}}\approx 0.80902$.
* Exercise: More angles
* By considering the equation
* $\sin(5x)=0$
* show that
* $\sin(36^{\circ })={\frac {\sqrt {10-2{\sqrt {5}}}}{4}}\approx 0.58779$ .
* $\sin(72^{\circ })={\frac {\sqrt {10+2{\sqrt {5}}}}{4}}\approx 0.95106$ .
The cosines are found immediately, e.g. cos(18º) = sin(72º).
# Ruby on Rails/Getting Started/Running the Server
## Running the Rails server
### The bundled WEBrick server

As you already know, Rails comes with an integrated server: WEBrick. WEBrick is a Ruby-written server to get you started right from the beginning. There are alternatives such as Mongrel or Phusion Passenger (formerly known as mod_ruby, a module for Apache). For local(!!) development WEBrick is a good choice.
To start up the server, simply open up a console, navigate to your Rails application and type
* On Windows, OS X and Linux: ruby script/server
After some seconds, WEBrick has been initialized and you are ready to go. The console with the web server needs to stay open, otherwise the server will shut down. To see if everything is working as expected, open up your web browser and navigate to
You should see the default Rails start page saying that everything is working correctly. You can view the details page (name) for the current version of your environment and some other variables. The server console not only runs the server, but shows how the requests by the browser are processed, including the amount of queries, the used SQL syntax or the data from your submitted forms.
There are several options, including but not limited to:
* -p port: Specify the port to run on
* -b ip: Bind to a specific IP address
* -e name: Use a specific Rails environment (like production)
* -d: Run in daemon mode
* -h: Display a help message with all command-line options

### Mongrel

To start a single mongrel instance:
* On all platforms:
This should be executed in the root directory of the Rails app you wish to run on Mongrel. There are numerous options you can specify, including:
* -p port: run on a specific port
* -e environment: execute with a specific Rails environment, like production
* -d: run in daemon mode
# Ruby on Rails/Plugins

A large portion of the power of Rails comes from the wide range of plugins which are available for download.

## Places to Get Plugins

* AgileWebDevelopment Plugin Repository is currently the best location to find out about plugins available for Rails. This web site provides facilities for rating plugins and provides links to the plugin homepage and Subversion repository.
* Rails Wiki Page for Plugins is the wiki page which contains a list of a large number of plugins.
* RailsLodge Plugin Directory is an easy to use plugin directory with sample code on how to install and use each plugin.

## Popular Plugins

Since other sites like the one above provide detailed information on plugins this book will not attempt to discuss every one of the popular plugins which are available, however there are some plugins which are used often enough and which are the source of enough questions that they are worth mentioning.

### Acts_as_authenticated

This plugin provides a basis for authentication in your Rails app.
# Ruby on Rails/Getting Started/Install on OS X
## Install on OS X
### Option 1

* Download Ruby and RubyGems
* Install Ruby
* Install RubyGems
* Get to the command-line and type:

### Option 2

* Download Locomotive
* Install Ruby on Rails software from Locomotive

### Option 3

* Use the broken Ruby installation on OSX 10.4 and follow this guide

### RMagic

A shellscript has been made that will install everything you need to make RMagic work on your OS X box. Copy the contents, save it as a file and run the file through a terminal (by navigating to the file and type ./name_of_file.
# Ruby on Rails/Getting Started/Is everything installed?

If everything was installed correctly you should be able to do the following:
* Type irb -v on the command line and see the version number for irb, the interactive Ruby interpreter
** What version do you expect to see here??
* Type gem -v on the command line and see the version number for RubyGems
** What version do you expect to see here??
* Type rails -v and the installed Rails version number should be displayed
** What version do you expect to see here??
* Type rails testapp and a new Rails app should be created in a directory called testapp
* Change into the testapp directory and run script/server, launching the built-in Rails server
** Open a browser and go to the URL http://localhost:3000. You should see the What should you see here??.
* Type rake and the Rails application's tests should run
** Will they work out of the box? What is the expected output?
# Ruby on Rails/Introduction

Ruby on Rails, or often seen as RoR or just Rails, is an web application framework written in the programming language Ruby. Rails was created to be a project management tool for "37signals". Quickly, it became one of the most popular frameworks on the web and its ideas and philosophies has inspired many frameworks in different languages.

### Features

* Rails supports agile software development
* Rails has a short and very intuitive language
* Single blocks of code are intended to be short and clear
* Rails is very flexible
* Rails comes with a testing framework
* The framework follows the principles of DRY
* Rails has some conventions: these allow quick development and consistent code
* Rails uses the MVC-Architecture
* Rails comes with an integrated server for local testing
* Applications with Rails are RESTful