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Showing posts from April, 2016

Wacky Conformal Transformation

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Wacky Conformal Transformation

I was trying to conformally stretch out the band model to more of the euclidean plane, and ran across this strange thing.

I don't understand all the features, but it's pretty.  It was generated by first applying the band model transformation to the disk, rotating that 90 degrees and scaling, then applying the band model transformation again.

Anybody know of a conformal transformation of the PoincarĂ© disk that maps to a large area of the euclidean plane while keeping hyperbolic tiles approximately the same size?  I suspect it may not be possible, since the amount of material one needs to fit in grows exponentially.  If it is possible, I bet such a thing would need to be undulating, with some areas of smaller tiles and other areas with larger tiles.

Reference
Vladimir Bulatov's work, "Conformal Models of Hyperbolic Geometry", bulatov.org/math/1001/

A new kind of book with tons of fascinating geometry.

A new kind of book with tons of fascinating geometry.

Illustrations are available as models for 3D printing.

Originally shared by Henry Segerman

My book is now available for preorder!
https://jhupbooks.press.jhu.edu/content/visualizing-mathematics-3d-printing

{7,3} Surfboard Finale

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{7,3} Surfboard Finale

The mathematical surfboard is finished! It turned out perfectly, and I'm so happy with the result. Thanks Sarah Nemec-Nelson for a wonderful 10th anniversary present.

I'll get some pictures or video of it in action up at some point :D

For more, see {7,3} Surfboard Part 1:
plus.google.com/+RoiceNelson/posts/iSmtVvE7xTV

And {7,3} Surfboard Part Deux:
plus.google.com/+RoiceNelson/posts/FL96TdMRvCE

Henry Segerman appears on Numberphile!

Henry Segerman appears on Numberphile!

Originally shared by Numberphile

Extra footage: https://youtu.be/pCCtcqyazOE
https://www.youtube.com/watch?v=uAnCL3vhVIs&feature=autoshare