Checked content

File:Cauchy sequence illustration2.png

Description Illustration of en:Cauchy sequence
Date 20:58, 3 June 2007 (UTC)
Source self-made, with en:matlab
Author Oleg Alexandrov
( Reusing this file)

Public domain

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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
   f=inline('(X+2)./(X+0.8)', 'X');
   for i=1:length(X)
          ball(X(i), Y(i), circrad, blue);
   plot(X, Z, 'r--', 'linewidth', thin_line)
   plot(X, -Z, 'r--', 'linewidth', thin_line)
   % draw the coordinate axes
   Kx=1.1; Ky=1.3; 
   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)
   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
   start=start(1)+i*start(2); stop=stop(1)+i*stop(2);
% points making up the arrow tip (besides the "stop" point)
   point1 = stop - (arrow_size*rotate_angle)*(stop-start)/abs(stop-start);
   point2 = stop - (arrow_size/rotate_angle)*(stop-start)/abs(stop-start);
   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(stop-start); stop1=t*start+(1-t)*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 % two-segment 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);

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