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An Introduction to Hyperbolic Geometry<br />By Amber Case<br />Cyborg Anthropologist<br />Ignite Portland 8<br />Twitter: ...
M. C.  Escher<br />
Euclid, 300 B. C. <br />Once upon a time…<br />
5 Postulates<br />
The 5th Postulate…<br />
János Bolyai<br />
v<br />Klein<br />Lobachevsky<br />Gauss<br />
ALWAYS 180°!<br />Less than 180°! <br />
The Spherical Triangle!<br />270°!<br />
Riemann<br />Hyperbolic<br />Manifolds<br />
1997: Daina Taimina, Cornell<br />
Ancient City Model<br />
Present Day<br />
Thank You! CyborgCampOctober 2010Cyborgcamp. com Twitter: @caseorganiccaseorganic@gmail. com<br />
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Introduction to Hyperbolic Geometry by Amber Case | Ignite Portland 8


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Traditional geometry is something we all learned in school. Some of us like it, and the rest of us didn't. In traditional geometry, parallel lines stay parallel, and triangles are always 180 degrees. Theses are the rules, and they cannot be broken.

Enter Hyperbolic Geometry. It's not new, but it is an AWESOME field of mathematics. Basically, it breaks all the rules.

In this presentation, I demonstrate some of the history and implications of this field, a field that has inspired Escher and sent Euclid rolling in his grave. I also explain the mysterious 5th Postulate and how all of this applies to the web.

Sound complicated? Don't panic! I'll use a lot of pictures and analogies. And with all of the beer you'll all be consuming, the ideas should enter your brain smoothly and enjoyable. This won't hurt a bit.


Amber Case is a Cyborg Anthropologist studying the interaction between humans and computers and how technology affects culture. She consults with a number of large and small companies on extending online presence. In her free time, she does independent research and has exceedingly long conversations.

Case gave her first lecture on Hyperbolic Geometry to her mathematics class at age 14. She hasn't given one since, but uses the mathematics all the time.

Published in: Education, Technology
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