File:Relatives Numbers Representation.png
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File:Relative numbers representation.svg is a vector version of this file. It should be used in place of this PNG file when not inferior.
File:Relatives Numbers Representation.png → File:Relative numbers representation.svg
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Summary
DescriptionRelatives Numbers Representation.png |
English: A figure representing the equivalence classes of the relative numbers constructed as a pair of natural numbers. Any relative number (eg. -5) has an infinity of equivalent possible representation, eg. (2,7), (0,5), ...
The equivalent representations (in red) are on the same blue dotted line, and the number in blue at the end on the line is the corresponding relative number
Français : Une figure représentant les classes d'équivalences entres les paire d'entiers construisant les nombre relatifs.
Chaque nombre relatif (par exemple -5) a une infinité de paire qui le représentent de manière équivalente, ( par exemple (2,7), (0,5). Toutes ces représentation équivalente sont sur la même pointillé bleu, et le nombre relatif qu'elle représentent est au bout de la ligne. |
Date | |
Source | Own work |
Author | Thomas Douillard, thomas.douillard gmail.com, with "asymptote" |
generated using "asymptote" software with the following code
Generation code
In asymptote programming language ( http://en.wikipedia.org/wiki/Asymptote_%28vector_graphics_language%29 )
// import settings;
import graph;
// pdfviewer="evince";
// psviewer="evince";
// returns a pair representation of a relative number of the equivalent class
pair pairRepresentation(int n){
if(n>0){
return(n,0);
}else{
return(0,-n);
}
}
string nullString(real r){
return "";
}
void drawCoordinates(pair point, align align=NoAlign){
label("$("+string(point.x)+","+string(point.y)+")$",point,align);
}
unitsize(50,50);
int num = 10;
int i;
for (i=-1*num ; i<=num ; ++i) {
pair point = pairRepresentation(i) ;
dot(point,red);
// equivalence classes labelled with usual names, in blue
label("$\mathbf{"+string(i)+"}$",point,5SW,fontsize(17)+blue);
int j;
for(j=abs(i);j<num;++j) {
drawCoordinates(point,E);
pair nextpoint = point + (1,1);
draw(point -- nextpoint,blue+Dotted+linewidth(2));
dot(point,red+linewidth(5));
point=nextpoint;
}
dot(point,red);
draw(point -- point+(0.5,0.5),blue+Dotted+linewidth(2));
dot(point,red+linewidth(5));
drawCoordinates(point,E);
}
// axes
real decay=-0.2;
ticks tick=RightTicks(N=0,n=1,end=false,nullString);
xaxis("$n_1$",YEquals(decay),decay,num+1.0,tick,Arrow);
yaxis("$n_2$",XEquals(decay),decay,num+1.0,LeftTicks(N=0,n=1,end=false,nullString),Arrow);
Other svg version : File:Relatifs.svg unfortunately does not render correctly with wikimedia, but is OK with inkscape
Licensing
Public domainPublic domainfalsefalse |
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. |
Items portrayed in this file
depicts
25 November 2009
File history
Click on a date/time to view the file as it appeared at that time.
Date/Time | Thumbnail | Dimensions | User | Comment | |
---|---|---|---|---|---|
current | 23:58, 25 November 2009 | 664 × 645 (57 KB) | wikimediacommons>TomdFr | Uploaded a version from -5 to 5, the previous one was uselessly too big ... |
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