# Deep Spaces: Geometry Labs Bring Beautiful Math to the Masses [Slide Show]

They don't wear white coats or protective goggles, but mathematicians around the country have captured the imagination of students in ever more creative ways

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A loxodrome is a spiral that arises from following a particular direction from the north or south pole of a sphere, meeting every line of latitude in the same (non-right) angle....[More]

A visualization created at the Experimental Geometry Lab (EGL) of how the complex plane changes when a certain function, called a Möbius transformation, is applied repeatedly....[More]

Hyperbolic geometry is one alternative to Euclidean geometry, which is taught in high school, and the hyperbolic plane is the analogue of the standard two-dimensional plane....[More]

The Apollonian gasket is a fractal that arises when studying circle packing, which concerns how to most efficiently store round objects. This is an overlay of two different images that show different circle packings and how they interact....[More]

An early 20th-century thread model from the archives of the math building at the University of Illinois at Urbana–Champaign. A group at the Illinois Geometry Lab (IGL) is documenting the models so they can be easily accessed and understood....[More]

Both the octagon on the left and the L-shaped table on the right can be "folded" into genus-2 surfaces, which look like the thin layer of glaze on top of a two-holed donut....[More]

When can a knotted-up loop of string be unknotted without cutting it? It turns out that this question is best studied by looking at the geometry of the space around the string rather than at the loop itself....[More]

Middle school students learn about spherical geometry by drawing on balloons during a presentation by members of the Experimental Algebra and Geometry Lab (EAGL)....[More]

A model of the hyperbolic plane crocheted by students at the EAGL.

Sean Lawton/EAGL

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1. 1. 1958OxfordMorris 12:13 PM 7/15/12

I don't like to add a comment.

2. 2. Daina 08:33 PM 7/15/12

very nice visualization! How to visualize hyperbolic geometry through "hyperbolic crochet" you can see in this TEDxRiga talk:

3. 3. Daina 03:33 PM 7/28/12

since YouTube version is missing some slides I posted a transcribed version with all slides of my TEDxRiga talk here: http://hyperbolic-crochet.blogspot.com/2012/07/my-tedxriga-talk-transcribed-full.html

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