# File:RationalRepresentation.pdf

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## Summary

 Description English: Representation of rational numbers (Q) as pairs of integers, equivalent pairs on the same line. Français : Représentation des nombres rationnels comme des paires de nombres entiers, les paires équivalentes sur le même ligne. Date 11 December 2009 Source Own work Author TomT0m
File:Rational Representation.svg is a vector version of this file. It should be used in place of this PDF file when not inferior.

File:RationalRepresentation.pdf → File:Rational Representation.svg

Source of the file, in the en:asymptote graphic programming language: fr:Utilisateur:TomT0m/RationalRepresentation.asy

```import settings;
import graph;
import math;

pdfviewer="/usr/bin/evince";
psviewer="evince";

// parameters

int num=10;

int gcd(int a,int b){
if(b==0){
return a;
}else{
return gcd(b,a-quotient(a,b)*b);
}
}
bool isPrimeWith(int a,int b){
return gcd(a,b)==1;
}

pen color_rational(int x,int y){

if(y==0){
return white;
}else{
real ratio = x
/y;
return rgb(0.5*(1+ratio),0.7*(1+ratio),0.3*(1-ratio));
}
}
unitsize(2,2);

picture damier;
// unitsize(damier,1,1);
size(damier,5000,5000,(-100,-100),(100,100));

dot(damier,(0,0));
dot(damier,(-num,-num),invisible);
dot(damier,(num,num),invisible);

for(int x=-num; x<=num;++x){

for(int y=-num; y<=num;++y){

pen p=color_rational(x,y);

if(y>0){
pair far;
if(isPrimeWith(abs(x),abs(y)) ){
far=(x*100,y*100);
drawline(damier,(0,0),far,p);
}
}

if(y==0){

dot(damier,(x,y));
dot(damier,(x,y),rgb(0.9,0.9,0.9));

}else
dot(damier,(x,y),p);

}
}

dot(damier,(0,0));
dot(damier,(0,0),rgb(0.9,0.9,0.9));
// drawing the equivalent classes
```

## Licensing

 I, the copyright holder of this work, release this work into the public domain. This applies worldwide.In some countries this may not be legally possible; if so:I grant anyone the right to use this work for any purpose, without any conditions, unless such conditions are required by law.

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Date/TimeThumbnailDimensionsUserComment
current21:59, 11 December 20091,047 × 1,047 (7 KB)TomT0m{{Information |Description={{en|1=Representation of rational numbers (Q) as pairs of integers, equivalent pairs on the same line.}} {{fr|1=Représentation des nombres rationnels comme des paires de nombres entiers, les paires équivalentes sur le même li

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