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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 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 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 - 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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
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This is two circles intersecting twice at right angles. The minimal surface you get has 5 faces (one appears in the middle).
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The Pringle's chip is a minimal surface! It is easy to see the curvature.
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This minimal surface with octahedral boundary has 9 faces. One is a rhombus in the middle.
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various attempts to illustrate a monkey saddle (a saddle that you would be comfortable sitting in if you had a large tail).
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This is a failed attempt to get a nice surface bounding the figure eight knot.
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This is the skelaton of a pentagonal prism. The minimal surface shown has 16 faces.
  • one pentagonal face in the center
  • ten trapazoidal faces
  • five triangular faces
(Compare to the cube)
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