Saturday May 10: Euler Characteristic, the 5 Platonic Solids, and Cryptography

Advanced Series

Title: The Euler Characteristic and the 5 Platonic Solids

Speaker: Professor Gyan Bhanot

Time & Date: 2pm-3pm, Saturday May 10

Location: Princeton Public Library, teen room (3rd floor)

Abstract: For any planar figure made from any combination of polygons, there is a seemingly mysterious relationship between the number of edges (E), the number is vertices (V) and the number of faces (F), namely that X = V+F-E = 1. The quantity X = V+F-E is called the Euler Characteristic of any surface of polyhedra. We will give an elementary proof that X = 1 in 2-dimensions and X = 2 in 3-dimensions.

A “Platonic Solid” is a convex 3-d object made from regular polygons with the same number of faces meeting at each vertex. We will use the result X = 2 in 3-d to prove that there are only five “Platonic Solids”: the Cube, the Tetrahedron, the Octahedron, the Dodecahedron and the Icosahedron, which are shown in the figure.

Figure: Platonic_Solids

Chili peppers: 1 out of 4

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Recreational Series

Topic: Cryptography

Leader: Harini Subrahmanyam Fredrickson

Location: Princeton Public Library, teen room (3rd floor)

Time & Date: 3:14pm-4:14pm, Saturday May 10

Description: The description is a secret for now (it’s encrypted!); stay tuned for us to update the website with one, or come to the talk to find out what cryptography is about!

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