|
|
| Line 1: |
Line 1: |
| | <asy> | | <asy> |
| − | // Copyright (c) 2007, Philippe Ivaldi.
| + | draw(circle((0,0),.375),dashed+gray+linewidth(1)); |
| − | // Version: $Id: edvenn_pi.asy,v 0.0 2007/02/19 17:49:31 Philippe Ivaldi Exp $
| + | draw(circle((.375,.375),.375),dashed+gray+linewidth(1)); |
| − | | + | draw(circle((-.375,.375),.375),dashed+gray+linewidth(1)); |
| − | // This program is free software; you can redistribute it and/or modify
| + | draw(circle((-.375,-.375),.375),dashed+gray+linewidth(1)); |
| − | // it under the terms of the GNU General Public License as published by
| + | draw(circle((.375,-.375),.375),dashed+gray+linewidth(1)); |
| − | // the Free Software Foundation; either version 2 of the License, or (at
| + | </asy> |
| − | // your option) any later version.
| |
| − | | |
| − | // This program is distributed in the hope that it will be useful, but
| |
| − | // WITHOUT ANY WARRANTY; without even the implied warranty of
| |
| − | // MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
| |
| − | // General Public License for more details.
| |
| − | | |
| − | // You should have received a copy of the GNU General Public License
| |
| − | // along with this program; if not, write to the Free Software
| |
| − | // Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA
| |
| − | // 02110-1301, USA.
| |
| − | | |
| − | // Commentary:
| |
| − | | |
| − | // THANKS:
| |
| − | | |
| − | // BUGS:
| |
| − | | |
| − | // INSTALLATION:
| |
| − | | |
| − | // Code:
| |
| − | | |
| − | | |
| − | // Venn diagram // Diagramme de Venn
| |
| − | // Edwards' construction // Construction d'Edwards
| |
| − | import roundedpath;
| |
| − | size(10cm,0);
| |
| − | path [] EdVenn(int n)
| |
| − | {
| |
| − | path [] opath;
| |
| − | if (n>=1)
| |
| − | opath.push(shift(-1.4,-.9)*roundedpath(xscale(2.8)*yscale(.9)*unitsquare,.1));
| |
| − | if (n>=2)
| |
| − | opath.push(shift(0,-.9)*roundedpath(xscale(1.4)*yscale(1.8)*unitsquare,.1));
| |
| − | if (n>=3)
| |
| − | opath.push(scale(.5)*unitcircle);
| |
| − | for (int i=1; i<=n-3; ++i)
| |
| − | {
| |
| − | pair pcle=point(opath[2],1/(2^i)),
| |
| − | ccle=intersectionpoint(pcle--(pcle-dir(opath[2],1/(2^i))), (0,0)--(1,0));
| |
| − | path cle=shift(ccle)*scale(abs(pcle-ccle))*unitcircle;
| |
| − | real[] p1=intersect(cle, opath[2]);
| |
| − | path ocle=subpath(cle,-p1[0],p1[0]);
| |
| − | guide tpath;
| |
| − | real step=360/(2^i), a=0;
| |
| − | for (int j=0; j<2^i; ++j)
| |
| − | {
| |
| − | tpath=tpath..rotate(a)*ocle;
| |
| − | a+=step;
| |
| − | }
| |
| − | opath.push(tpath..cycle);
| |
| − | }
| |
| − | return opath;
| |
| − | }
| |
| − | | |
| − | size(10cm,0);
| |
| − | draw(EdVenn(15));</asy>
| |
![[asy] draw(circle((0,0),.375),dashed+gray+linewidth(1)); draw(circle((.375,.375),.375),dashed+gray+linewidth(1)); draw(circle((-.375,.375),.375),dashed+gray+linewidth(1)); draw(circle((-.375,-.375),.375),dashed+gray+linewidth(1)); draw(circle((.375,-.375),.375),dashed+gray+linewidth(1)); [/asy]](http://latex.artofproblemsolving.com/c/3/b/c3b158c5f4298d625471f2378cbbf05cbd5ad4c0.png)
