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The incircle O(r) of triangle ABC touches AB at D, BC at E and AC at F. Find r in terms of AD, BE and CF.

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 Size of a City

A square walled city of unknown dimensions has four gates, one at the center of each side.

Harvest Time

A man plants 4 kernels of corn, which at harvest produce 32 kernels: these he plants the second year; now, supposing the annual increase to continue 8 fold, what would be the produce of the 15th year, allowing 1000 kernels to a pint?

Peano on Wronskians: A Translation

How a translation of Peano's counterexample to the 'theorem' that a zero Wronskian implies linear dependence can help your differential equations students

Squared Proof

Prove that if the sums of the squares of opposite sides of any quadrilateral are equal, its diagonals intersect at right angles.