Henry's interests

Henry's posts

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Video of my talk at MoMath, "3D Shadows: Casting Light on the Fourth Dimension".

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Gyroid made from a single shape of developable strip

13/04/2017

2 Photos - View album

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I'll be giving a public lecture at Duke University, Durham NC on Tuesday April 18!

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Open source social network mastodon seems to be picking up steam - I am henryseg@mastodon.cloud

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In Edinburgh 12 May - 4 June? Come see our "Brilliant Geometry" exhibition! Light, shadow, and a 4d zoetrope.

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An article on hyperbolic virtual reality, featuring my work with Vi Hart, Andrea Hawksley and Sabetta Matsumoto, and David Dumas's work with Horalia Armas, Brandon Reichman and Hai Tran.

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In which I provide some pi day provocation.

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**As the world turns, but the map stays still**

The animation below was suggested by Michael Hardy, whose question on MathOverflow about the properties of a 2-to-1, almost-everywhere-conformal map from the torus to the sphere got me interested in the subject.

In a previous post, I showed a fixed mapping of two copies of the surface of the Earth onto a torus, and then rotated the resulting torus to reveal more of its surface than can be seen in any one fixed view.

But in this animation, while the torus itself stays fixed, the Earth rotates around its axis relative to the coordinate system used for the mapping.

The result makes it clear just how strange things are at some points on this map (in the previous view, the strangeness was deliberately hidden in the ocean). There are four

**branch points**on the torus; if you walk around these points, the version of you mapped to the Earth will complete

**two**circles around the corresponding point. You can only see two of the branch points in this view, but the positions of the other two are easy to imagine from the symmetry.

My previous post on the torus map:

https://plus.google.com/113086553300459368002/posts/8XXBvq9hjoK

Michael Hardy's question on MathOverflow:

http://mathoverflow.net/questions/260202/jacobis-elliptic-functions-and-plane-sections-of-a-torus

+Henry Segerman's interactive 3D model (which uses essentially the same map, but orients the Earth differently relative to the torus):

https://skfb.ly/MYpC

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+Greg Egan Here's +Saul Schleimer's and my unwrapped square torus.

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