File:Rational Representation.svg

Original file (SVG file, nominally 629 × 629 pixels, file size: 132 KB)

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
Source Own work
Author TomT0m
Other versions File:RationalRepresentation.pdf

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));
add(damier.fit(),(0,0));
// drawing the equivalent classes

Licensing

Public domain I, the copyright holder of this work, release this work into the public domain. This applies worldwide.
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I grant anyone the right to use this work for any purpose, without any conditions, unless such conditions are required by law.

Licensing

I, the copyright holder of this work, hereby publish it under the following license:
w:en:Creative Commons
attribution share alike
This file is licensed under the Creative Commons Attribution-Share Alike 4.0 International license.
You are free:
  • to share – to copy, distribute and transmit the work
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Under the following conditions:
  • attribution – You must give appropriate credit, provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use.
  • share alike – If you remix, transform, or build upon the material, you must distribute your contributions under the same or compatible license as the original.

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1 April 2015

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134,922 byte

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Date/TimeThumbnailDimensionsUserComment
current20:55, 1 April 2015Thumbnail for version as of 20:55, 1 April 2015629 × 629 (132 KB)TomT0mUser created page with UploadWizard

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