# Browse Classroom Capsules and Notes

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Displaying 131 - 140 of 1211

An elementary proof of Heron's Formula

Using a convexity argument to show that you can never lose money by income averaging (on your income tax) as opposed to computing the standard tax

Constructing Pythagorean systems with any number of terms

Generalizations of the Archimedean result that ratio of the volume of a sphere to that of its circumscribing cylinder is the same as the ratio of their respective surface areas

A simple derivation of the formula for the distance from a point to a line

A derivation of the formulas $\max(r,s)=\frac{1}{2}(r+s+|r-s|)$ and $\min(r,s)=\frac{1}{2}2(r+s-|r-s|)$

In the decimal expansion of an irrational square root, not all digits are equally likely to appear.

A discussion of compass and straightedge methods for approximate trisection of an angle

A proof that $\lim_{n \rightarrow \infty} \frac{\sqrt[n]{n!}}{n} = \frac {1}{e}$.

The Factorial Triangle is a relative of Pascal's Triangle with many applications