Life in higher dimensions - PowerPoint PPT Presentation

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Life in higher dimensions

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... geometrical dimensions Regular Polytopes How many? 2. The Mercator World Map Social Studies Teacher Myth The truth Stereographic Projection 3. – PowerPoint PPT presentation

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Title: Life in higher dimensions


1
  • Life in higher dimensions
  • Mapping the World
  • Roadtrip most powerful computer in Japan
  • Alan Edelman
  • June 13, 2006

2
My favorite facts from high school
3
1. Higher dimensional geometry
  • The real number line
  • The Cartesian plane
  • The 3d world
  • Just add dimensions P(w,x,y,z)
  • Mathematician arent afraid
  • Not physics, not time, just four (or more)
    geometrical dimensions

4
Regular Polytopes
5
How many?
2d regular polygons ? infinitely 3d regular
polyhedra ? 5 4d regular polytopes ? 6 5d
regular 5d polytopes ? 3
6
2. The Mercator World Map
7
Social Studies Teacher Myth
8
The truth
Designed for constant compass directions See
Wikipedia
9
Stereographic Projection
Project P to sphere along the line to the north
pole.
Mercator Map
Ster Proj
Log z
Not cylindicrical projection!
10
3. Worlds fastest computers
  • top500

11
Performance Trends
12
Extrapolations
13
Earth Simulator
14
Earth Simulator
15
Beowulf Clusters
Our Experience
16
Beowulfs
17
The First Beowulf
18
Enjoy Mathematics
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