CS 39: Symmetry & Topology
Lecture #13 -- Mon. 5/6, 2019.
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Preparation: Modular
construction of a "cubist Moebius band"
Warm-up:
Compare your own "Cubist
Moebius Band" with your neighbors' models:
Discuss: How would you
do a "Cubist Klein Bottle"?
"Cubist
Approximations"
How did we get here?
Wallpaper Symmetries ==> Tiling
Patterns ==> Modular Constructions ...
Some key numbers to remember:
1D: 1 Point Lattice type (Bravais
Lattice); 7
Frieze Patterns.
2D: 5 Point Lattice
types (Bravais Lattices); 17 Wallpaper
Patterns (groups).
3D: 14 Point
Lattice types (Bravais Lattices); 230 Wallpaper
Patterns (groups).
Tiling:
Use one or more repeated shapes to fill some 2D or 3D space.
==> Floor tiling, brick walls, voxelization in computer
graphics, LEGO blocks, 2D pixel arrays, LED TV screens ...
Turn on a subset of all tiles to represent a shape.
Modular Construction:
Exploit symmetry to decompose a complex shape into smaller, easier
to fabricate parts.
Example: Sculpture: "Torus
Knot 3_5" was made from 3 identical parts.
Optional Material (for a time
when things are more relaxed ...)
Tubular
Sculptures, Lego
Knots,
Today's Project Presentations:
Next Week's Project Presentations:
Please send me your real project
titles!
Learning some
essential professional skills:
-- Giving an oral presentation with good visuals (PPT).
-- Preparing an "Elevator Speech" (60-90 seconds).
-- Writing an extended
abstract (2-4 pages).
-- Building your Portfolio.
What
does it take to succeed at UC Berkeley ?
Discussion: What are Good Work
Habits ?
New Homework Assignments:
Prepare your Course Project presentations.
All Project
Presentations will be posted here.
Prepare your Elevator Speech.
Start working on your Project Report
Please, do the course
evaluations! Your feedback is valuable!!
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