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Summary of: SHAPE: The Hidden Geometry of Information, Biology, Strategy, Democracy, and Everything Else by Jordan Ellenberg

Summary of: SHAPE: The Hidden Geometry of Information, Biology, Strategy, Democracy, and Everything Else by Jordan Ellenberg

          
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About the Book

Notice to Readers
This is not the main book; it is just a summary by BRIGHT GURUS. It is not meant to replace the original book.


RECAP OF THE BOOK
We can either junk the very appealing idea that putting a hole in a thing increases the number of holes by one, or we can junk the very appealing idea that it's nuts to talk about a negative number of holes.
straw: Euler characteristic 0, 1 hole popped balloon: Euler characteristic 1, 0 holes unpopped balloon: Euler characteristic 2, -1 holes A way to describe the Euler characteristic, if you want it to seem less weird, is as a difference between two numbers, the number of even-dimensional holes and the number of odd-dimensional holes.
(1 zero-dimensional hole + 1 two-dimensional hole) - (0 onedimensional holes) A capital B has one zero-dimensional hole and two one-dimensional holes, so it has Euler characteristic -1.* Snip the bottom loop of the B and it becomes an R, which has Euler characteristic 0; there's one fewer (one-dimensional) hole, so the Euler characteristic goes up.
0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0 .
The process can't go on forever, because with each swing the numbers in the tree get smaller, and a sequence of positive whole numbers that decreases at each step must, eventually, hit bottom and stop.* At the end of the axefest we're left with a tree each of whose leaves is a number that can't be factored-that is, a prime-and those prime numbers, multiplied together, give the number we started with.
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Product Details
  • ISBN-13: 9798510965919
  • Publisher: Independently Published
  • Publisher Imprint: Independently Published
  • Height: 229 mm
  • No of Pages: 64
  • Spine Width: 3 mm
  • Width: 152 mm
  • ISBN-10: 8510965919
  • Publisher Date: 27 May 2021
  • Binding: Paperback
  • Language: English
  • Returnable: N
  • Weight: 100 gr


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Summary of: SHAPE: The Hidden Geometry of Information, Biology, Strategy, Democracy, and Everything Else by Jordan Ellenberg
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