Transferred from en.wikipedia to Commons by Maksim.

File:Normal subgroup illustration.svg is a vector version of this file. It should be used in place of this PNG file when not inferior. File:Normal subgroup illustration.png → File:Normal subgroup illustration.svg For more information, see Help:SVG. In other languages Alemannisch ∙ Bahasa Indonesia ∙ Bahasa Melayu ∙ British English ∙ català ∙ čeština ∙ dansk ∙ Deutsch ∙ eesti ∙ English ∙ español ∙ Esperanto ∙ euskara ∙ français ∙ Frysk ∙ galego ∙ hrvatski ∙ Ido ∙ italiano ∙ lietuvių ∙ magyar ∙ Nederlands ∙ norsk bokmål ∙ norsk nynorsk ∙ occitan ∙ Plattdüütsch ∙ polski ∙ português ∙ português do Brasil ∙ română ∙ Scots ∙ sicilianu ∙ slovenčina ∙ slovenščina ∙ suomi ∙ svenska ∙ Tiếng Việt ∙ Türkçe ∙ vèneto ∙ Ελληνικά ∙ беларуская (тарашкевіца) ∙ български ∙ македонски ∙ нохчийн ∙ русский ∙ српски / srpski ∙ татарча/tatarça ∙ українська ∙ ქართული ∙ հայերեն ∙ বাংলা ∙ தமிழ் ∙ മലയാളം ∙ ไทย ∙ 한국어 ∙ 日本語 ∙ 简体中文 ∙ 繁體中文 ∙ עברית ∙ العربية ∙ فارسی ∙ +/−

 

Summary

Made by myself with Matlab

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.

Source code

function main ()

N=12; line_thickness=2.2; font_size=25; d=0.13; big_rad=10; ball_rad=0.5; ii=sqrt(-1);
red=[1, 0, 0]; green=[0, 1, 0]; blue=[0, 0, 1];
All=[red' green' blue'];

figure(1); clf; hold on; axis equal; axis off;

Theta=0:0.1:3*pi;
X=big_rad*cos(Theta);
Y=big_rad*sin(Theta);
plot(X, Y, 'linewidth', line_thickness, 'color', [0 0 0]);

for i=0:(N-1)
   z=big_rad*exp(i*ii*2*pi/N);
   place_text_smartly (z, font_size, i, d, sprintf('%d\\pi/%d', i, N/2), N);
   color_ball(real(z), imag(z), ball_rad, All(:, mod(i, 3)+1)');
end

scale=1.4;plot(scale*big_rad,  scale*big_rad)
scale=-1.4;plot(scale*big_rad,  scale*big_rad)

saveas(gcf, 'Normal_subgroup_illustration.eps', 'psc2')
saveas(gcf, 'Normal_subgroup_illustration.png')

function place_text_smartly (z, font_size, pos, d, tx, N)
 p=cos(2*pi/N)+sqrt(-1)*sin(2*pi/N);
 z = z + p^pos * d * font_size;
 shiftx=0.0003; shifty=0.03;
 x = real (z); y=imag(z);
 H=text(x+shiftx*font_size, y+shifty*font_size, tx);
 set(H, 'fontsize', font_size, 'HorizontalAlignment', 'c', 'VerticalAlignment', 'c')

 function color_ball(x, y, r, color)
    Theta=0:0.1:2*pi;
    X=r*cos(Theta)+x;
    Y=r*sin(Theta)+y;
    H=fill(X, Y, color);
    set(H, 'EdgeColor', 'none');

Original upload log

Legend: (cur) = this is the current file, (del) = delete this old version, (rev) = revert to this old version.

Click on date to download the file or see the image uploaded on that date.

• (del) (cur) 13:18, 27 October 2005 . . en:User:Oleg_Alexandrov Oleg Alexandrov ( en:User_talk:Oleg_Alexandrov Talk) . . 648x623 (49214 bytes) (Made by myself with Matlab.)