*An elementary proof of Heron's Formula*

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*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 \(\lim_{n \rightarrow \infty} \frac{\sqrt[n]{n!}}{n} = \frac {1}{e}\).*