Wikipedia and James Simons give a great demonstration on this: https://en.wikipedia.org/wiki/Topological_property where you can read the transcript from his interview: http://www.ted.com/talks/jim_simons_a_rare_interview_with_the_mathematician_who_cracked_wall_street/transcript?language=en
So if you watch the Ted Talk you will see a Sphere and a lattice around it. This is what was observed by Leonhard Euler the Mathematician from the 1700's. With 8 vertices, 12 edges, and six faces. If you look at the difference -- Vertices - Edges + Faces you get 2. No if you exchange that with Triangles you get 12 vertices and 30 edges and 20 faces, and 20 tiles. Vertices - Edges + Faces = 2.
What Simons points out that I'm nerdy enough to want to write about so I can always reference this is that it doesnt change. The Euler Characteristic. This is a Topological Invariant. So no matter how you do this and how many vertices and edges are added the answer will always be the same. Pretty awesome stuff!
Another thing to note about James Simons one of the most successful traders of all time said that he hired the smartest people from science and data backgrounds and didn't do it all on his own. Definitely watch the Ted Talk.
So if you watch the Ted Talk you will see a Sphere and a lattice around it. This is what was observed by Leonhard Euler the Mathematician from the 1700's. With 8 vertices, 12 edges, and six faces. If you look at the difference -- Vertices - Edges + Faces you get 2. No if you exchange that with Triangles you get 12 vertices and 30 edges and 20 faces, and 20 tiles. Vertices - Edges + Faces = 2.
What Simons points out that I'm nerdy enough to want to write about so I can always reference this is that it doesnt change. The Euler Characteristic. This is a Topological Invariant. So no matter how you do this and how many vertices and edges are added the answer will always be the same. Pretty awesome stuff!
Another thing to note about James Simons one of the most successful traders of all time said that he hired the smartest people from science and data backgrounds and didn't do it all on his own. Definitely watch the Ted Talk.
