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Dissecting Hypercubes with Pascal's Triangle | Infinite Series

2017-06-01

[public] 108K views, 4.73K likes, 49.0 dislikes audio only

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What does the inside of a tesseract look like? Pascal’s Triangle can tell us. Start your 60 day free trial of CuriosityStream by going to https://curiositystream.com/infinite/ and using the promo code “infinite.”

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Devil’s Staircase

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Written and Hosted by Kelsey Houston-Edwards

Produced by Rusty Ward

Graphics by Ray Lux

Made by Kornhaber Brown (www.kornhaberbrown.com)

What shape is formed by taking a diagonal slice of a 4-dimensional cube? Or, a 10-dimensional cube? It turns out that a very familiar mathematical object - Pascal’s triangle - can help us answer this question.

Further Resources:

Cube Slices, Pictoral Triangles and Probability

http://www.maa.org/sites/default/files/pdf/upload_library/22/Allendoerfer/1992/0025570x.di021171.02p0016b.pdf

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The Devil's Staircase | Infinite Series by PBS Infinite Series
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Introduction
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Definitions
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Hyperplanes
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Pascals Triangle
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Pascals Rule
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The Devil's Staircase | Infinite Series 257,224 views
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PBS Infinite Series Mathematician Tai-Danae Bradley and physicist Gabe Perez-Giz offer ambitious content for viewers that are eager to attain a greater understanding of the world around them. Math is pervasive - a robust yet precise language - and with each episode you’ll begin to see the math that underpins everything in this puzzling, yet fascinating, universe. Previous host Kelsey Houston-Edwards is currently working on her Ph.D. in mathematics at Cornell University.
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