# CS 39:  Symmetry & Topology Lecture #1 -- Mon. 1/28, 2019.

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## Warm-Up:

What is Symmetry?

How would you define Symmetry?

Try to draw your name or your initials in a symmetrical manner.

## Introductions -- Let's get to know one another!

Brief statements about yourself -- and what you hope to get out of this course.

## Working with Symmetry:

Sort all letters of the alphabet into 4 different symmetry classes.   (Why only FOUR classes?)

Try to find at least two different symmetrical arrangements of  4 identical rectangular tables placed in a square room.
(Subsequently we will compare and classify results.) -- How many conceptually different arrangements are there?

Try to find a concise and general definition for "symmetry".

What is  symmetry good for?

Make a name tag using your first name; try to make it symmetrical.
(Inspiration from Scott Kim).

## First important concepts:

Bilateral and rotational symmetries of finite 2D objects.
A 2D pattern with a rotational center is either Cn-symmetric, if a rotation through 360/n degrees places it back onto itself;
or it is Dn-symmetric if in addition it also has reflective mirror symmetry on n axes going through the center.
A pattern with only one mirror-symmetry axis would be D1.

2D symmetry in art and architectural facades.

Symmetry in floor plans.

ASSIGNMENT:
Try to find many different symmetry groups in hub caps and in company logos; document (photo) the most extreme cases you find.

What is "antisymmetry" ?

Are there other symmetry operations ?

## Some remarks on my teaching style:

"AIDA" ( == Attention --> Interest --> Desire --> Action! )
Learning by doing!
Many small homework assignments, to deepen understanding, and to "close the  feedback loop".
Interactive lectures, Q&A;  ==>  I want everybody to participate actively!

#### --- Later course contents will be tailored somewhat to the interests of course participants. ==> Please state your interests on the  Background Questionnaire (later).

• Course Projects:
Some individual study (with heavy use of the web): "The Role of Symmetry in: <Your Favorite Area>".

• Quizzes/Exams:
Perhaps one or two short quizzes, to provide feedback whether the key concepts have sunk in.
NO  Final Exam!

## First Homework Assignment:

Try to find many different rotational symmetry groups represented in hub caps and in company logos; document the most extreme ones (Cn, Dn: max & min n).
While evaluating the type of symmetry, focus on the "grand pattern" and ignore details such as the typically 5 mounting holes, the air valves, or small brand names that might break all symmetries.

Take an I-phone picture or make a sketch.
DUE: either electronically before 9am, Monday, Feb. 4, -- or on paper at 4:00pm before the beginning of the next lecture.

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