File:Paradoxical decomposition F2.png
預覽大小:623 × 599 像素。 其他解析度:249 × 240 像素 | 499 × 480 像素 | 798 × 768 像素 | 1,064 × 1,024 像素 | 2,129 × 2,048 像素 | 2,977 × 2,864 像素。
原始檔案 (2,977 × 2,864 像素,檔案大小:104 KB,MIME 類型:image/png)
File:Paradoxical decomposition F2.svg是本檔案的向量版本。 如果品質不低,就應該優先使用該檔案,而非PNG檔案。
File:Paradoxical decomposition F2.png → File:Paradoxical decomposition F2.svg
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摘要
描述Paradoxical decomposition F2.png |
English: Illustration for the paradoxical decomposition of used in the proof of the Banach-Tarski paradox. |
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來源 | 自己的作品, made using MetaPost program. | ||||||||
作者 | David Benbennick | ||||||||
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Linethickness = 1pt; beginfig(1); recursion_depth := 6; const := 2.2; numeric length; length := 1.3in / (const**recursion_depth); pickup pencircle scaled Linethickness; picture p, q, r; for i = 1 upto recursion_depth - 2: draw (0,0) -- (length,0); draw (0,-length) -- (0,length); length := length * const; currentpicture := currentpicture shifted (length,0); p := currentpicture rotated 90; q := p yscaled -1; addto currentpicture also p; addto currentpicture also q; endfor; draw (0,0) -- (length,0); draw (0,-length) -- (0,length); length := length * const; currentpicture := currentpicture shifted (length,0); p := currentpicture rotated 90; q := p yscaled -1; r := currentpicture xscaled -1; addto currentpicture also p; addto currentpicture also q; addto currentpicture also r; draw (-length,0) -- (length,0); draw (0,-length) -- (0,length); dotlabel.urt(btex$e$etex, (0,0)); dotlabel.ulft(btex$a$etex, (length,0)); dotlabel.lrt(btex$b$etex, (0,length)); pair P, Q, R; P := (-0.5length, 0.5length); Q := (-length, 0.9length); draw P .. Q .. (-2length,0) .. Q yscaled -1 .. P yscaled -1 .. cycle withcolor red; label.top(btex$S(a^{-1})$etex, (-1.2length, 0.9length)) withcolor red; Q := (length, length); R := (0, 2length); draw P xscaled -1 --- Q .. R .. (-2.2length, 0) .. R yscaled -1 .. Q yscaled -1 --- P scaled -1 .. cycle withcolor blue; label.rt(btex$aS(a^{-1})$etex, (1.1length,1.1length)) withcolor blue; currentpicture := currentpicture shifted (10cm,10cm); endfig; end;
I saved the above as Paradoxical_decomposition_F2.mp, and the following LaTeX program as Paradoxical_decomposition_F2.tex:
%&latex \documentclass[12pt]{article} \usepackage{graphicx} \pagestyle{empty} \begin{document} \includegraphics{Paradoxical_decomposition_F2.1} \end{document}
I then ran the following commands:
mpost Paradoxical_decomposition_F2 tex Paradoxical_decomposition_F2 dvips -mode ljfzzz -D 1200 Paradoxical_decomposition_F2 -o convert -density 1200 Paradoxical_decomposition_F2.ps Paradoxical_decomposition_F2.pnm pnmcrop Paradoxical_decomposition_F2.pnm | pnmtopng > Paradoxical_decomposition_F2.png advpng -z4 Paradoxical_decomposition_F2.png
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檔案歷史
點選日期/時間以檢視該時間的檔案版本。
日期/時間 | 縮圖 | 尺寸 | 用戶 | 備註 | |
---|---|---|---|---|---|
目前 | 2011年1月27日 (四) 07:22 | 2,977 × 2,864(104 KB) | ChrstphrChvz | ImageOptim with PNGOUT | |
2005年6月12日 (日) 06:54 | 2,977 × 2,864(121 KB) | Dbenbenn | higher resolution version, 2977x2864 | ||
2004年12月13日 (一) 04:30 | 514 × 494(9 KB) | Dbenbenn | Illustration for the paradoxical decomposition of F_2 |
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