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A history of attempts to develop formulas expressing the sums of powers of the first n positive integers from the Pythagoreans to Jakob Bernoulli. With exercises.

Teaching Leonardo: An Integrated Approach

The work of the great Renaissance artist/scientist Leonardo da Vinci can be taught in secondary schools through an integrated approach of several disciplines. This article explores the approach of the Ross School.

Area of an Equilateral Triangle

Suppose the area of an equilateral triangle be 600. The sides are required.

A Swarm of Bees

The square root of half the number of bees in a swarm has flown out upon a jessamine bush; 8/9 of the swarm has remained behind.

Pioneers in Mathematics

A five-volume set of biographies of mathematicians from ancient times to the twentieth century, aimed at secondary students.

X Marks The Spot

What is the value of X...

Age

My age is a number consisting of two digits, 1/7 of this number is a mean proportional between these two digits, and two years hence, my age will be a third proportional to the same two digits, directly as they stand in my present age.

The Geometry of Rene Descartes

Images from Frans van Schooten's 1659 edition of The Geometry of Rene Descartes

Creatures with Four or Six Heads

Now there are six-headed four-legged animals and four-headed two-legged birds. Find the total number of animals and birds.

Maximization

Find the greatest value of y in a given equation.