File:Rational Representation.svg
Jump to navigation
Jump to search
Size of this PNG preview of this SVG file: 600 × 600 pixels. Other resolutions: 240 × 240 pixels | 480 × 480 pixels | 768 × 768 pixels | 1,024 × 1,024 pixels | 629 × 629 pixels.
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
|
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. |
Licensing
I, the copyright holder of this work, hereby publish it under the following license:
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
- to remix – to adapt the work
- 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.
File history
Click on a date/time to view the file as it appeared at that time.
| Date/Time | Thumbnail | Dimensions | User | Comment | |
|---|---|---|---|---|---|
| current | 14:55, 1 April 2015 | | 629 × 629 (132 KB) | TomT0m | User created page with UploadWizard |
File usage
The following 2 pages use this file:
