CS 39:  Symmetry & Topology
Lecture #13 -- Mon. 5/6, 2019.

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Preparation:  Modular construction of a "cubist Moebius band"


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:
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).

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 SculpturesLego 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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