28sep19GF

Review
Wednesday: (1IH No projector and screen)

1. Five minute reports by students.
2. Greenboard presentation of dim(Sierpinski Gasket)=irrational (Barnsley)

Thursday: (IGL 121AH with TV screen )

1. Sinewheel
2. Tavares's cubes
3. Thurston's sphere eversion by corrugations
4. 3D Koch aka Fahauer fractals, aka Yulia's recursive kochblue.py

Homework
Please consider using David Eck's superb and free-on-line computer graphics
The University of Minnesota has a nice webpage for both on-line and hard-back
copies here:
https://open.umn.edu/opentextbooks/textbooks/introduction-to-computer-graphics

Hobar&Smith Prof. David Eck (http://math.hws.edu/eck/) is both mathematician
and computer scientist, who did his PhD at Brandeis with Richard Palais.

The important thing about his approach is that it is "hands-on" even when he
is discussing obsolete or OpenGL languages. He does that by simulating the
older languages and libraries with HTML5/CANVAS/Javascript/WebGL software.
And (!) he is offering his glsim.js  Python/OpenGL excerpt for translating
such RTICAs into WebGL painlessly.

But the final two chapter has eye-candy quality examples in full-blown
WebGL applications.  Everything is inspectable. Nothing is hidden.
And it's free! (except the hardback, which is cheap!).

Mini Projects Continued
From Sinewheel to Allerton
Background: sinewheel.html is a HTML5/CANVAS implementation by Zach
Reizner of a 40 year of Apple BASIC rtica to explain trigonometric functions
by how their graph is generated, or (geometrically) how to pass from the
parametrization of a circle from polar coordinates ($r= const$) to Cartesian
($x=r \sin t, y= r \cos t$) coordinates.

Question: Does this rtica (animated yes, but barely interactive) illustrate
this well enough? Did you catch it's meaning when you played with it?

As such, it became the beginning of a lesson on how to graph functions in
you learned in high school. Note that the sine function graph is generated
as an illusion by the corners of a sequence of polygons:

If you buy it that for the first(!) polygon the distance along the circle is
the same as the distance moved on the positive reals, and then count steps,
then the endpoint falls a distance equal to the circumferential distance
travelled then the corner sits on the graph of the sine of the arclength

The second part was a similar generation of the parabola $y=x(1-x)$ in the
unit square. This lead to using a cobweb graph to illustrate logistic
chaos. See Lisa Li and Manting Huang's IGL project

Miniproject: Improve the way sinewheel tells its story. Make it
interactive. E.g. have the student step through the formation of the
illusion. Try a 2D animation explaining both sine and cosine. Invent!

Resources:

http://new.math.uiuc.edu/quasiweb17/allertonJSweb.html
Tools: 2D line drawing using HTML5/CANVAS only