* Intuition of "a group": D4
12
diamond clock 9 3
6
How many transformations back onto same diamond shape?
* count 'em
* table of successive transformations - a "binary operation". (Cayley Table)
* Supposed only allowed to flip top-bottom, and rotate to right.
Can you get all the other transformations? How do you find the right way?
* Are there any other groups with eight elements?
(And how can we tell if two groups are the "same", anyway?)
* Mathematics:
- formal systems and "proof" : definitions, postulates, rules -> theorems
* Formal definition of a group
* Group with 1 element
* Group with 2 elements
* Cyclic groups, Cn (integers, mod n, under addition)
* Is there another group with 4 elements?
================ didn't do this stuff yet
* definition: "abelian". (" a*b=b*a ")
* definition: "isomorphic." ("_really_ the same")
* definition: "cycle" of an element
* definition: "order" of an element
* patterns in how many groups?
* solid cube group : heading towards thinking about Rubik's Cube