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Discovering Life in Higher Dimensions: Mapping the World Roadtrip

Join mathematician Alan Edelman on a journey through higher dimensional geometry, from real number lines to regular polytopes and the Mercator World Map myth. Explore the world's fastest computers and Beowulf clusters, diving into the realms of pure mathematics and cutting-edge technology. Uncover the hidden secrets of our multidimensional universe and expand your perspective beyond the 3D world we know.

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Discovering Life in Higher Dimensions: Mapping the World Roadtrip

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  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 aren’t 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. N Rd P S Stereographic Projection Project P to sphere along the line to the north pole. Mercator Map Ster Proj Log z Not cylindicrical projection!

  10. 3. World’s 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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