Data 02: Polyhedra

All lecture, Data projects and Exam documets in one 313 page PDF

Unit 00

Unit 01

Unit 02

Unit 03

Unit 04

Unit 05

Unit 06

Unit 07

Unit 08

Data 01

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Unit 10

Unit 11

Unit 12

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Unit 15

Unit 16

Unit 17

Data 02

Unit 18

Unit 19

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Unit 21

Unit 22

Unit 23

Unit 24

Unit 25

Unit 26

Data 03

Unit 27

Unit 28

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Unit 35

Data 04
The second Project (PDF) deals with polyhedra. They are beautiful too and related to calculus. Every network G defines a function fG(x). The problem of computing this function is known to be the hardest problem in computer science: it is NP complete. We learn here how to compute the function from local data. It is interesting that like primes, which were studied initially for purely mathematical reasons and which then exploded to the most important encryption and key exchange technology, also polyhedra were studied originally since Plato for their purity but are now part of a theory of networks which is used in tacking modern problems of communication, computation, logistics and are at the heart of complexity theory: if we were able to compute fG(x) effectively, we could solve essentially all hard problems in computer science as it would settle the P versus NP problem.
Icosahedron Echidnahedron Tetraxishexahedron
The movie ``Travelling Salesman" appeared in 2012. It is a stage play similarly as the Swiss play ``The physicists" written by Dürrenmatt. [ As Singh once pointed out, WW1 was the war of the Chemists (Gas), WW2 was the war of the Physicists (A-Bomb) WW3 most likely will be the war of Mathematicians (Communication).] In the Travelling Salemen movie, the conversation builds on a scenario, in which the NP problem was solved affirmatively. Nobody who works in the field however believes that P=NP holds. The goal is to prove N and NP are different. Like the scenario that extraterrestial life exists which will be able to get in contact with us, the scenario N=NP makes good Holliwood stuff.