# Mathematics

More ideas (maybe):

- The mathematics of rotation in
`ℝ`^{n}and representing the orientation of a-dimensional polytope in*k*`ℝ`^{n}(related to the Hyper screen saver)

- The most interesting mathematical subject I’ve encountered since graduation: geometric algebra
- The noncentral
*t*-distribution and the noncentral-distribution*χ*^{2} - Introduction to the most basic concepts of topology and measure theory (leading to continuous functions and measurable functions)
- Some math related to the problem of unbiased sampling of particulate
material (and laboratory subsampling) —
For a lot consisting of
particles, the sampling schemes that are guaranteed to be unbiased can be represented as a convex polytope in a high-dimensional real vector space (but how many vertices does this polytope have?)*n*

**Problem 1**: Tom, Dick, and Harry competed in a track-and-field meet where
points were awarded for first, second, and third place in each event. At the end
of the meet, Tom had 22 points, Dick and Harry had 9 points each, and nobody else had any points.

If Dick won the javelin throw, who finished second in the 100-yard dash?

One may assume:

- The scoring was the same for all events.
- More points were awarded for first place than second, and for second place than third.
- No fractional points were awarded.

**Problem 2**: The following algorithm calculates the first several terms (`0` through ` n`) of a well-known integer sequence.
Can you determine which one?

**for**

`= 0`

*i***to**

*n***do**

`[`

*a*`] ← 1;`

*i***for**

`= 2`

*m***to**

*n***do**

**for**

`=`

*j*

*m***to**

*n***do**

`[`

*a*`] ←`

*j*`[`

*a*`] +`

*j*`[`

*a*`−`

*j*`];`

*m*