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 ∙ العربية ∙ беларуская (тарашкевіца) ∙ български ∙ বাংলা ∙ català ∙ нохчийн ∙ čeština ∙ dansk ∙ Deutsch ∙ Ελληνικά ∙ English ∙ British English ∙ Esperanto ∙ español ∙ eesti ∙ euskara ∙ فارسی ∙ suomi ∙ français ∙ Frysk ∙ galego ∙ Alemannisch ∙ עברית ∙ हिन्दी ∙ hrvatski ∙ magyar ∙ հայերեն ∙ Bahasa Indonesia ∙ Ido ∙ italiano ∙ 日本語 ∙ ქართული ∙ 한국어 ∙ lietuvių ∙ македонски ∙ മലയാളം ∙ Bahasa Melayu ∙ မြန်မာဘာသာ ∙ norsk bokmål ∙ Plattdüütsch ∙ Nederlands ∙ norsk nynorsk ∙ norsk ∙ occitan ∙ polski ∙ prūsiskan ∙ português ∙ português do Brasil ∙ română ∙ русский ∙ sicilianu ∙ Scots ∙ slovenčina ∙ slovenščina ∙ српски / srpski ∙ svenska ∙ தமிழ் ∙ ไทย ∙ Türkçe ∙ татарча / tatarça ∙ українська ∙ vèneto ∙ Tiếng Việt ∙ 中文 ∙ 中文（中国大陆） ∙ 中文（简体） ∙ 中文（繁體） ∙ 中文（马来西亚） ∙ 中文（新加坡） ∙ 中文（臺灣） ∙ +/−

 

Made by myself with Matlab

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.

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');

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.)