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Showing posts from August, 2014

This image by Roice Nelson shows the boundary of the {7,3,3} honeycomb featured previously on the Visual Insight...

Originally shared by American Mathematical Society

This image by Roice Nelson shows the boundary of the {7,3,3} honeycomb featured previously on the Visual Insight blog. The black circles are holes, not contained in the boundary of the {7,3,3} honeycomb. There are infinitely many holes, and the actual boundary, shown in white, is a fractal with area zero. Read more from John Baez: http://blogs.ams.org/visualinsight/2014/08/14/733-honeycomb-meets-plane-at-infinity/

#images #mathimagery #fractals #mathematics  
http://blogs.ams.org/visualinsight/2014/08/14/733-honeycomb-meets-plane-at-infinity

It feels great contributing to Visual Insight images!

Image
It feels great contributing to Visual Insight images!

Originally shared by John Baez

{7,3,3} meets the plane at infinity

Maryam Mirzakhani won the Fields medal largely for her work on hyperbolic geometry.  The hyperbolic plane is something we can all enjoy: it's not flat, but curved like a saddle, and triangles have angles that add up to less than 180 degrees.  We can draw it crushed down to a disk, as in this picture by Roice Nelson.  All the light blue circles should really be the same size - but the ones near the edge have been squashed.

Instead of learning Euclidean geometry in school, you could have learned hyperbolic geometry - it's almost the same, with some big differences.  The main thing is that the parallel postulate is false in hyperbolic geometry: there are many ways to draw a line through a point parallel to another line!  This is how Lobachevsky  discovered hyperbolic geometry in 1823: by seeing what would happen if you changed the rules this way.

And instead of lear…

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