SOLIDS
Projects

A) Implement this in code.
B) Study translating the code (say C++) to run as an iPhone App.
C) Develop an intelligent agent to play Laskers with an iPhone opponent.

Cells
A) Examine the file thoroughly.
B) Develop a program to automatically search for solutions.
C) Extend such Flash files as Factorial (a joint effort of 2 students working under my direction, one as the voice, the other as animation designer) to the interactive solution of Hess' problem.

Solids [Here is a graphic image with vertices equidistant from the object's center, either in the hexagonal equator plane or triangular zones above or below it.]
A) Create a display of a solid with Twelve Vertices. Make your image oriented to small children.
B) That image was created by Mathematica code; create it another way.
C) Display other geometrical images to stimulate small children to enjoy math, e.g., Nested Shapes

The above require independent work.

Some Interesting Irrationals

 √2, Square Root of 2 e, Natural Logarithms' Base Numerically π, Circle Circumference/Diameter Ratio φ, Golden Ratio Π, Hard to compute irrational number

Approximations

= 2.718290995*

### (2143/22)(1/4)

= 3.1415926**

*Brewster, G.W. The Mathematical Gazette, 25-263, 49, Feb. 1941; cited in Gaither, C. C. and Cavazos-Gaither, A. E., Mathematically Speaking, A Dictionary of Quotations, 1998 ; the exponent for 2 is 5/2 raised to the 2/5.
**Ramanujan; cited by Gardner, M.
The golden ratio φ = (1+ √5)/2 = 1.61803...

The golden ratio conjugate Φ = 1/φ ≈ 0.6180339887

Φ/2 = (√5 - 1)/4 = sin 18 ° = sin π/10 ≈ 0.309

(2sin π/10)(1+ √5)/2 ≈ 1
For further Exploration there are many issues that can lead to projects based on adapting exposition to computer capabilities.
 12/23/2016 Version http://www.cs.ucla.edu/~klinger/nmath/projects.html ©2010 Allen Klinger