First,
Just finished reading, _the crest of the peacock_ (ibid lowercase), by George
Gheverghese Joseph. Subtitle is "non-European roots of mathematics." Wonderful
book, highest recommendation and not just to mathematicians.
My three biggest shames in life: losing my fluency in Japanese and Arabic; and
excepting one course in knot theory at UW-Madison, stopping my math education
at calculus in high school. I still love reading about math and mathematicians
but wish I understood more.
To the question/help request. Some roots of my problem:
One) I am studying origami and specifically the way you can, in 2-dimensions,
draw the pattern of folds that will yield a specific 3-D figure. And there are
'families' of 2-D patterns that an origami expert can look at and tell you if
the eventual 3-D figure will have 2, 3, or 4 legs. How it is possible to 'see',
in your mind, the 3-D in the 2-D?
Two) a quick look at several animated hyper-cubes show the 'interior' cube
remaining cubical as the hypercube is manipulated. Must this always be true,
must the six facets of the 3-D cube remain perfect squares? What degrees of
freedom are allowed the various vertices of the hyper-cube?
Three) can find static hyper— for the five platonic solids, but not animations.
Is it possible to provide something analogous to the hypercube animation for
the other solids? I think this is a problem in manifolds as many of you have
talked about.
Question: If one had a series of very vivid, very convincing, visions of
animated hyper-platonic solids with almost complete freedom of movement of the
various vertices (doesn't really apply to hypersphere) — how would one go about
finding visualizations that would assist in confirming/denying/making sense of
the visions?
Please forgive the crude way of expressing/asking my question. I am both math
and computer graphic ignorant.
davew
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