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HOM SIGMAA 2010 Student Paper Contest Winners

Download the three winning essays to learn about medieval Islamic dust boards, Old Babylonian similarity, and the Fermat Problem.

Investing in Apples and Pears

A merchant woman buys and sells apples and pears. How much did she invest in apples; how much in pears?

Swinging Pendulum

Given a pendulum as shown. The height of the pendulum is two units and its horizontal width is 2 units. What is the area of the pendulum?

Loafing About

There were two men, of whom the first had 3 small loaves of bread and the other, 2.

Limit Points and Connected Sets in the Plane

A study of Mullikan's Nautilus, using movies to illustrate the important ideas

The Door and the Rod

Given a door and a measuring rod of unknown dimensions, the rod is used to measure the door.

Nuts Over Counting

A fellow said that when he counted his nuts by twos, threes, fours, fives and sixes, there was still one left over; but when he counted them by sevens they came out even. What is the smallest number of nuts he could have?

When Nine Points Are Worth But Eight: Euler's Resolution of Cramer's Paradox

How Euler resolved the paradox first noted by Maclaurin that nine points should determine a curve of order three, yet two such curves can intersect in nine points

Walk Around the World

Suppose a person whose height is 5 feet 7 inches travels 10000 miles in the arc of a great circle. How much further will the person's head have gone compared to their feet, the circumference of the Earth being 21600 miles?

Lilavati of Bhaskara

Two pages from a 1650 manuscript of the Lilavati of Bhaskara II (1114-1185). The second photo is an illustration of the Pythagorean Theorem.