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Description  Illustration of en:Cauchy sequence 
Date  20:58, 3 June 2007 (UTC) 
Source  selfmade, with en:matlab 
Author  Oleg Alexandrov 
Permission ( Reusing this file) 
Public domain 

This chart was created with MATLAB. 
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Source code ( MATLAB)
% draw an illustration of a sequence that is not Cauchy function main() % prepare the screen and define some parameters figure(1); clf; hold on; axis equal; axis off; fontsize=30; thick_line=3; thin_line=2; black=[0, 0, 0]; red=[1, 0, 0]; blue=[0, 0, 1]; arrowsize=0.5; arrow_type=1; arrow_angle=30; % (angle in degrees) circrad=0.07; % radius of ball showing up in places B=9; X=0:0.06:B; f=inline('(X+2)./(X+0.8)', 'X'); Y=sin(5*X).*f(X); for i=1:length(X) ball(X(i), Y(i), circrad, blue); end X=0:0.05:(B+0.3); Z=f(X); plot(X, Z, 'r', 'linewidth', thin_line) plot(X, Z, 'r', 'linewidth', thin_line) % draw the coordinate axes shift=3; Kx=1.1; Ky=1.3; L=max(Y); arrow([1 shift], [Kx*B, shift], thin_line, arrowsize, arrow_angle, arrow_type, black) arrow([1, shift], [1, Ky*L], thin_line, arrowsize, arrow_angle, arrow_type, black) text(Kx*B+0.6, shift, '\it{n}', 'fontsize', fontsize, 'HorizontalAlignment', 'c') text(1, Ky*L+0.8, '\it{x_n}', 'fontsize', fontsize, 'HorizontalAlignment', 'c') % save to disk saveas(gcf, 'Cauchy_sequence_illustration2.eps', 'psc2') % export to eps function ball(x, y, r, colour) Theta=0:0.1:2*pi; X=r*cos(Theta)+x; Y=r*sin(Theta)+y; H=fill(X, Y, colour); set(H, 'EdgeColor', 'none'); function arrow(start, stop, th, arrow_size, sharpness, arrow_type, colour) % Function arguments: % start, stop: start and end coordinates of arrow, vectors of size 2 % th: thickness of arrow stick % arrow_size: the size of the two sides of the angle in this picture > % sharpness: angle between the arrow stick and arrow side, in degrees % arrow_type: 1 for filled arrow, otherwise the arrow will be just two segments % color: arrow colour, a vector of length three with values in [0, 1] % convert to complex numbers i=sqrt(1); start=start(1)+i*start(2); stop=stop(1)+i*stop(2); rotate_angle=exp(i*pi*sharpness/180); % points making up the arrow tip (besides the "stop" point) point1 = stop  (arrow_size*rotate_angle)*(stopstart)/abs(stopstart); point2 = stop  (arrow_size/rotate_angle)*(stopstart)/abs(stopstart); if arrow_type==1 % filled arrow % plot the stick, but not till the end, looks bad t=0.5*arrow_size*cos(pi*sharpness/180)/abs(stopstart); stop1=t*start+(1t)*stop; plot(real([start, stop1]), imag([start, stop1]), 'LineWidth', th, 'Colour', colour); % fill the arrow H=fill(real([stop, point1, point2]), imag([stop, point1, point2]), colour); set(H, 'EdgeColor', 'none') else % twosegment arrow plot(real([start, stop]), imag([start, stop]), 'LineWidth', th, 'Colour', colour); plot(real([stop, point1]), imag([stop, point1]), 'LineWidth', th, 'Colour', colour); plot(real([stop, point2]), imag([stop, point2]), 'LineWidth', th, 'Colour', colour); end
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