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Some leftovers from TechKnowLedge this morning:<br>
<br>
The Lie Algebraic Group E8 (mathematics) - Wikipedia, the free
encyclopedia<br>
<a class="moz-txt-link-freetext" href="http://en.wikipedia.org/wiki/E8_(mathematics)">http://en.wikipedia.org/wiki/E8_(mathematics)</a> E8 X E8 would be a
functional mapping of E8<br>
onto itself. Functions which do this can operate within String
Theory.<br>
<br>
<a class="moz-txt-link-freetext" href="Http://www.endlessuniverse.net">Http://www.endlessuniverse.net</a><br>
Check out the "Animations" section:<br>
<a class="moz-txt-link-freetext" href="http://www.physics.princeton.edu/~steinh/endlessuniverse/animations.html">http://www.physics.princeton.edu/~steinh/endlessuniverse/animations.html</a><br>
<br>
How the cover image of "Endless Universe" is topologically a Klein
bottle which has swallowed itself:<br>
<a class="moz-txt-link-freetext" href="http://www.ifp.illinois.edu/~sdickson/UIUC_CS/LeTopologicon_inside_back_cover001.PNG">http://www.ifp.illinois.edu/~sdickson/UIUC_CS/LeTopologicon_inside_back_cover001.PNG</a><br>
<br>
The number of interior regions determined by diagonalizing a regular
polygon:<br>
<a class="moz-txt-link-freetext" href="http://www.math.rutgers.edu/~erowland/polygons-project.html">http://www.math.rutgers.edu/~erowland/polygons-project.html</a><br>
n^3 < R(n) < n^4 -- it is a phenomenon of super-cubic
complexity which takes place in the plane. Who knew? It's
practically fractal!<br>
<br>
The topological mesh techniques I came up to do "<a
href="http://emsh.calarts.edu/%7Emathart/sw/objView/thicken.html">thickening</a>"
of mathematical surfaces for sculpture do not cut it for this
problem (4-coloring the interior regions determined by regular
polygons.) Andrew Glassner, "Maintaining Winged-Edge Models",
Graphics Gems II ; James Arvo, ed.; (IV.6 -- pp. 191-201) Academic
Press, Inc.; ISBN: 0-12-064480-0<br>
<br>
I think that the <a
href="http://en.wikipedia.org/wiki/Combinatorial_maps">Combinatorial
Map</a> is required to solve this. I have discovered that I need
to un-think Glassner's model in order to correctly implement the
Combinatorial Map in C++.<br>
<br>
And "Why 19?" <a class="moz-txt-link-freetext" href="http://ekadhikena-purvena.tumblr.com">http://ekadhikena-purvena.tumblr.com</a><br>
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