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| Keywords: Thomae function (0,1).svg validSVG Thomae's function on the interval 0 1 Shown are all rational points with denominator at most 200 Created using the following Java code <source lang java > public class Thomae static int gcd int a int b while a>0 b>0 if a>b a - a/b b; else b - b/a a; return a>0 a b; public static void main String args int max 200; int width 1280; int height 660; int border 20; int x0 border; int x1 width - border; double dx x1-x0; int y0 height - border; double dy -dx; int r 5; System out println < xml version \ 1 0\ standalone \ no\ > ; System out println < DOCTYPE svg PUBLIC \ -//W3C//DTD SVG 1 1//EN\ \ http //www w3 org/Graphics/SVG/1 1/DTD/svg11 dtd\ > ; System out println <svg width \ + width + \ height \ + height + \ xmlns \ http //www w3 org/2000/svg\ version \ 1 1\ > ; for int q 1; q<max; q++ for int p 0; p<q; p++ if gcd p q 1 System out println <circle cx \ + x0+dx p/q + \ cy \ + y0+dy 1/q + \ r \ + r + \ fill \ black\ stroke \ none\ /> ; System out println </svg> ; </source> Own Smithers888 2008-10-09 Continuity functions | ||||
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