Notice: Use of undefined constant bub - assumed 'bub' in /home/pat/website/public/math/fun/bubbles/header.inc on line 3 Notice: Use of undefined constant bub - assumed 'bub' in /home/pat/website/public/math/fun/bubbles/header.inc on line 4 Notice: Use of undefined constant bub - assumed 'bub' in /home/pat/website/public/math/fun/bubbles/header.inc on line 6 Notice: Use of undefined constant cats - assumed 'cats' in /home/pat/website/public/math/fun/bubbles/header.inc on line 6 Notice: Use of undefined constant bub - assumed 'bub' in /home/pat/website/public/math/fun/bubbles/header.inc on line 8 Notice: Use of undefined constant cats - assumed 'cats' in /home/pat/website/public/math/fun/bubbles/header.inc on line 8 Notice: Use of undefined constant bub - assumed 'bub' in /home/pat/website/public/math/fun/bubbles/header.inc on line 12 Notice: Use of undefined constant cats - assumed 'cats' in /home/pat/website/public/math/fun/bubbles/header.inc on line 12 Notice: Use of undefined constant bub - assumed 'bub' in /home/pat/website/public/math/fun/bubbles/header.inc on line 12 Notice: Use of undefined constant cats - assumed 'cats' in /home/pat/website/public/math/fun/bubbles/header.inc on line 12 Notice: Use of undefined constant bub - assumed 'bub' in /home/pat/website/public/math/fun/bubbles/header.inc on line 12 Notice: Use of undefined constant cats - assumed 'cats' in /home/pat/website/public/math/fun/bubbles/header.inc on line 12 Notice: Use of undefined constant bub - assumed 'bub' in /home/pat/website/public/math/fun/bubbles/header.inc on line 12 Notice: Use of undefined constant cats - assumed 'cats' in /home/pat/website/public/math/fun/bubbles/header.inc on line 12 Notice: Use of undefined constant bub - assumed 'bub' in /home/pat/website/public/math/fun/bubbles/header.inc on line 12 Notice: Use of undefined constant cats - assumed 'cats' in /home/pat/website/public/math/fun/bubbles/header.inc on line 12 Notice: Use of undefined constant bub - assumed 'bub' in /home/pat/website/public/math/fun/bubbles/header.inc on line 12 Notice: Use of undefined constant cats - assumed 'cats' in /home/pat/website/public/math/fun/bubbles/header.inc on line 12 Notice: Use of undefined constant bub - assumed 'bub' in /home/pat/website/public/math/fun/bubbles/header.inc on line 12 Notice: Use of undefined constant cats - assumed 'cats' in /home/pat/website/public/math/fun/bubbles/header.inc on line 12 Notice: Use of undefined constant bub - assumed 'bub' in /home/pat/website/public/math/fun/bubbles/header.inc on line 12 Notice: Use of undefined constant cats - assumed 'cats' in /home/pat/website/public/math/fun/bubbles/header.inc on line 12 Notice: Use of undefined constant cat - assumed 'cat' in /home/pat/website/public/math/fun/bubbles/category.php on line 3 Notice: Use of undefined constant cat - assumed 'cat' in /home/pat/website/public/math/fun/bubbles/category.php on line 4 Notice: Use of undefined constant bub - assumed 'bub' in /home/pat/website/public/math/fun/bubbles/category.php on line 8 Notice: Use of undefined constant cats - assumed 'cats' in /home/pat/website/public/math/fun/bubbles/category.php on line 8 Notice: Use of undefined constant bub - assumed 'bub' in /home/pat/website/public/math/fun/bubbles/category.php on line 12 Notice: Use of undefined constant cat - assumed 'cat' in /home/pat/website/public/math/fun/bubbles/category.php on line 12 Notice: Use of undefined constant bub - assumed 'bub' in /home/pat/website/public/math/fun/bubbles/category.php on line 16 Notice: Use of undefined constant subcats - assumed 'subcats' in /home/pat/website/public/math/fun/bubbles/category.php on line 16 Notice: Use of undefined constant bub - assumed 'bub' in /home/pat/website/public/math/fun/bubbles/category.php on line 20 Notice: Use of undefined constant subcats - assumed 'subcats' in /home/pat/website/public/math/fun/bubbles/category.php on line 20 Notice: Use of undefined constant bub - assumed 'bub' in /home/pat/website/public/math/fun/bubbles/category.php on line 20 Notice: Use of undefined constant subcats - assumed 'subcats' in /home/pat/website/public/math/fun/bubbles/category.php on line 20 Notice: Use of undefined constant bub - assumed 'bub' in /home/pat/website/public/math/fun/bubbles/category.php on line 23 Notice: Use of undefined constant cat - assumed 'cat' in /home/pat/website/public/math/fun/bubbles/category.php on line 23 Notice: Use of undefined constant bub - assumed 'bub' in /home/pat/website/public/math/fun/bubbles/category.php on line 27 Notice: Use of undefined constant cats - assumed 'cats' in /home/pat/website/public/math/fun/bubbles/category.php on line 27 Notice: Use of undefined constant bub - assumed 'bub' in /home/pat/website/public/math/fun/bubbles/category.php on line 28 Notice: Use of undefined constant cat - assumed 'cat' in /home/pat/website/public/math/fun/bubbles/category.php on line 28 Notice: Use of undefined constant bub - assumed 'bub' in /home/pat/website/public/math/fun/bubbles/category.php on line 28 Notice: Use of undefined constant cat - assumed 'cat' in /home/pat/website/public/math/fun/bubbles/category.php on line 28 Notice: Use of undefined constant bub - assumed 'bub' in /home/pat/website/public/math/fun/bubbles/category.php on line 28 Notice: Use of undefined constant cat - assumed 'cat' in /home/pat/website/public/math/fun/bubbles/category.php on line 28 Notice: Use of undefined constant bub - assumed 'bub' in /home/pat/website/public/math/fun/bubbles/category.php on line 28 Notice: Use of undefined constant cat - assumed 'cat' in /home/pat/website/public/math/fun/bubbles/category.php on line 28 Notice: Use of undefined constant bub - assumed 'bub' in /home/pat/website/public/math/fun/bubbles/category.php on line 28 Notice: Use of undefined constant cat - assumed 'cat' in /home/pat/website/public/math/fun/bubbles/category.php on line 28 Notice: Use of undefined constant bub - assumed 'bub' in /home/pat/website/public/math/fun/bubbles/category.php on line 28 Notice: Use of undefined constant cat - assumed 'cat' in /home/pat/website/public/math/fun/bubbles/category.php on line 28 Notice: Use of undefined constant bub - assumed 'bub' in /home/pat/website/public/math/fun/bubbles/category.php on line 28 Notice: Use of undefined constant cat - assumed 'cat' in /home/pat/website/public/math/fun/bubbles/category.php on line 28 Notice: Use of undefined constant bub - assumed 'bub' in /home/pat/website/public/math/fun/bubbles/category.php on line 28 Notice: Use of undefined constant cat - assumed 'cat' in /home/pat/website/public/math/fun/bubbles/category.php on line 28 Notice: Use of undefined constant bub - assumed 'bub' in /home/pat/website/public/math/fun/bubbles/category.php on line 36 Notice: Use of undefined constant cats - assumed 'cats' in /home/pat/website/public/math/fun/bubbles/category.php on line 36 Notice: Use of undefined constant bub - assumed 'bub' in /home/pat/website/public/math/fun/bubbles/category.php on line 36 Notice: Use of undefined constant cats - assumed 'cats' in /home/pat/website/public/math/fun/bubbles/category.php on line 36 Notice: Use of undefined constant bub - assumed 'bub' in /home/pat/website/public/math/fun/bubbles/category.php on line 37 Notice: Use of undefined constant cats - assumed 'cats' in /home/pat/website/public/math/fun/bubbles/category.php on line 37 Notice: Use of undefined constant bub - assumed 'bub' in /home/pat/website/public/math/fun/bubbles/category.php on line 37 Notice: Use of undefined constant cats - assumed 'cats' in /home/pat/website/public/math/fun/bubbles/category.php on line 37 Notice: Use of undefined constant bub - assumed 'bub' in /home/pat/website/public/math/fun/bubbles/category.php on line 37 Notice: Use of undefined constant cats - assumed 'cats' in /home/pat/website/public/math/fun/bubbles/category.php on line 37 Minimal surfaces and soap films
previousreturnnext
Notice: Use of undefined constant bub - assumed 'bub' in /home/pat/website/public/math/fun/bubbles/category.php on line 91 Notice: Use of undefined constant cat - assumed 'cat' in /home/pat/website/public/math/fun/bubbles/category.php on line 91 A cube
Notice: Use of undefined constant bub - assumed 'bub' in /home/pat/website/public/math/fun/bubbles/category.php on line 93 Notice: Use of undefined constant subcats - assumed 'subcats' in /home/pat/website/public/math/fun/bubbles/category.php on line 93
The minimal area surface which contains each of the edges of a cube in its boundary has 13 faces.
  • one square face in the middle.
  • eight trapezoidal faces
  • four triangular faces
Notice: Use of undefined constant bub - assumed 'bub' in /home/pat/website/public/math/fun/bubbles/category.php on line 107 Notice: Use of undefined constant cat - assumed 'cat' in /home/pat/website/public/math/fun/bubbles/category.php on line 107 Notice: Use of undefined constant bub - assumed 'bub' in /home/pat/website/public/math/fun/bubbles/category.php on line 107 Notice: Use of undefined constant cat - assumed 'cat' in /home/pat/website/public/math/fun/bubbles/category.php on line 107 Notice: Use of undefined constant bub - assumed 'bub' in /home/pat/website/public/math/fun/bubbles/category.php on line 107 Notice: Use of undefined constant cat - assumed 'cat' in /home/pat/website/public/math/fun/bubbles/category.php on line 107
Notice: Use of undefined constant bub - assumed 'bub' in /home/pat/website/public/math/fun/bubbles/category.php on line 107 Notice: Use of undefined constant cat - assumed 'cat' in /home/pat/website/public/math/fun/bubbles/category.php on line 107 Notice: Use of undefined constant bub - assumed 'bub' in /home/pat/website/public/math/fun/bubbles/category.php on line 107 Notice: Use of undefined constant cat - assumed 'cat' in /home/pat/website/public/math/fun/bubbles/category.php on line 107 Notice: Use of undefined constant bub - assumed 'bub' in /home/pat/website/public/math/fun/bubbles/category.php on line 107 Notice: Use of undefined constant cat - assumed 'cat' in /home/pat/website/public/math/fun/bubbles/category.php on line 107
Notice: Use of undefined constant bub - assumed 'bub' in /home/pat/website/public/math/fun/bubbles/category.php on line 107 Notice: Use of undefined constant cat - assumed 'cat' in /home/pat/website/public/math/fun/bubbles/category.php on line 107 Notice: Use of undefined constant bub - assumed 'bub' in /home/pat/website/public/math/fun/bubbles/category.php on line 107 Notice: Use of undefined constant cat - assumed 'cat' in /home/pat/website/public/math/fun/bubbles/category.php on line 107 Notice: Use of undefined constant bub - assumed 'bub' in /home/pat/website/public/math/fun/bubbles/category.php on line 107 Notice: Use of undefined constant cat - assumed 'cat' in /home/pat/website/public/math/fun/bubbles/category.php on line 107
Notice: Use of undefined constant bub - assumed 'bub' in /home/pat/website/public/math/fun/bubbles/category.php on line 107 Notice: Use of undefined constant cat - assumed 'cat' in /home/pat/website/public/math/fun/bubbles/category.php on line 107 Notice: Use of undefined constant bub - assumed 'bub' in /home/pat/website/public/math/fun/bubbles/category.php on line 107 Notice: Use of undefined constant cat - assumed 'cat' in /home/pat/website/public/math/fun/bubbles/category.php on line 107
If you pop one of the triangular faces, you get a new triangle on the inside and 11 other faces.
Notice: Use of undefined constant bub - assumed 'bub' in /home/pat/website/public/math/fun/bubbles/category.php on line 107 Notice: Use of undefined constant cat - assumed 'cat' in /home/pat/website/public/math/fun/bubbles/category.php on line 107
previousreturnnext