CS 39R:  Symmetry & Topology
Lecture #11 -- Mon. 11/13, 2017.


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Warm-up:

Discuss with your neighbors any conceptual issues
you may have with regular polytopes in 4D ...




5 Project Presentations:

presentation
            schedule


Learning three essential skills:
-- Giving an oral presentation with good visuals (PPT).
-- Writing an extended abstract (2-4 pages).
-- Preparing an "elevator speech" (60-90 seconds).

Stepping into the 4th dimension !

What is the 4th Dimension?   Does it exist?  -->>  Conceptually, there are infinitely many spatial dimensions
How many mutually orthogonal coordinate axes are there?     -->>  Four:  x, y, z, w.

How many mutually orthogonal coordinate planes are there?  -->>  Six:  xy, xz, xw, yz, yw, zw.

Regular Polytopes in Four and Higher Dimensions



Homework Assignments:  Due: Nov. 20, 2017.

To round off this section on higher dimensions, you may want to watch again:
Perfect Shapes in Higher Dimensions --
Numberphile

In preparation for the last technical topic in CS 39,
compare the symmetry classes of different wall-paper patterns.

Prepare Your Course Project Presentations.



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