Teacher resources and professional development across the curriculum

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Unit 8

Geometries Beyond Euclid

Hyperbolic Disc Hyperbolic Disc

Our first exposure to geometry is to that of Euclid; in which all triangles have 180 degrees. As it turns out, triangles can have more or less than 180 degrees. This unit explores these curved spaces that are at once otherworldly, yet firmly of this world—and present the key to understanding the human brain.

Unit Goals

Video Transcript

Video

We live in a world — a reality — ruled by straight lines. Our streets, houses, cubicles — virtually all of our space is parceled into rectilinear grids. Mathematicians were also ruled by straight lines — some would say imprisoned by them — for two thousand years. But what is a straight line? And when is a straight line not "straight"?

Textbook

Textbook

Math encompasses far more than the study of numbers. At its heart, it is the application of logic in the search for order in the world around us. A fundamental question in this search is how to divide up, or describe, space.


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