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HOM SIGMAA 2012 Student Paper Contest Winners

Download the two winning essays to learn about using indivisibles to find the area under a cycloid arch in the 17th century and about the Radon transform and its use in x-ray tomography in the 20th century.

Kepler's Conjecture

A survey of the attempts to prove Kepler's conjecture over the past 400 years.

Leibniz - Bernoulli correspondence

This is from a letter of June, 1695 in which Leibniz is discussing differentiation with Johann Bernoulli. The work in which these letters appear is the Virorum Celeberr. Got. Gul. Leibnitii et Johann Bernoulli Commercium Philosophicum et Mathematica, originally published in 1740.

The Right and Lawful Rood

The "rood", a linear measure dating from many centuries ago, is calculated anew in today's classrooms.

The Cog-Wheel Revolution

Two cog-wheels, one having 26 cogs, and the other 20 cogs, run together. In how many revolutions of the larger wheel will the smaller gain in 12 revolutions?

The Ambitious Horse

Problems taken from Chinese sources

The Cost of War

After a terrible battle it is found that 70% of the soldiers have lost an eye.

An Investigation of Historical Geometric Constructions

Dynamic geometry software is used to demonstrate early Greek attempts at the trisection of an angle and the squaring of a circle.

Dimensions of a Triangle

Determine the dimensions for a right-angled triangle, having been given the hypotenuse, and the side of the inscribed square.

Investigating Euler's Polyhedral Formula Using Original Sources

The author shows how teachers can use Leonhard Euler's original works in the classroom to explore Euler's famous polyhedral formula,
V + F = E + 2.