## Postscript source: tile.psPut the text from "%!PS-Adobe" through "showpage" in a file "tile.ps", then view it with a postscript viewer (ghostview, ghostscript), or print it on a postscript printer to get an image much higher in quality than the .gif file created from it. %!PS-Adobe % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % % % % % Program to draw tiling of hyperbolic plane by ideal triangles. % % These have area pi in the Poincare metric (constant curvature -1). % % % % --- J. Carlson, November 1, 1991 % % % % % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%% DEFINITIONS %%%%%%%%%%%%%%%%%%%%%%%%%%%%% % set inch scale and line width /inch {72 mul} def % define one inch 0.1 setlinewidth % define parameters of figure: /R 2.5 inch def % the scale: radius of limit circle /a 60 def % the central half-angle /b 90 a sub 2 mul def % the angle subtended by the arc /c a 2 mul def % the angle of rotation /r R a sin a cos div mul def % initial radius /n 3 def % the number of arcs /N 7 def % number of layers % define basic arc (rotate after drawing it to get ready for next one): /ARC { r R r 180 180 b add arc stroke c rotate } def % procedure to update parameters for successive layers of tiling: /update { /a a 2 div def % update a: a <== a/2 /b 90 a sub 2 mul def % update b: b <== (90 - a)/2 /c a 2 mul def % update c: c <== 2a /r R a sin a cos div mul def % update r: r <== R tan a /n n 2 mul def % update n: n <== 2n } def %%%%%%%%%%%%%%%%%%%%% NOW DRAW THE FIGURE %%%%%%%%%%%%%%%%%%%%% gsave % save graphics state 4.25 inch 6.0 inch translate % put origin near center of page % draw unit circle: newpath 0 0 R 0 360 arc stroke % draw first layer of arcs: 1 1 n {ARC} for % finally, draw N-1 more layers: 1 1 N 1 sub { update 1 1 n {ARC} for } for grestore % restore graphics state %%%%%%%%%%%%%%%%%%%%% FINALLY, ADD LEGEND %%%%%%%%%%%%%%%%%%%%% /Times-BoldItalic findfont 36 scalefont setfont 1.5 inch 1.5 inch moveto (Tiling of Hyperbolic Plane) show showpage
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