Problems from Another Time

Individual problems from throughout mathematics history, as well as articles that include problem sets for students.

Given four integers which, if added together three at a time, their sums are: 20, 22, 24, and 27. What are the integers?

Golden Spheres

A California miner has a spherical ball of gold, 2 inches in diameter, which he wants to exchange for spherical balls 1 inch in diameter. How many of the smaller spheres should he receive?

Money Makes the World Go Around

You have two sums of money, the difference of which is 2 dirhems; you divide the smaller sum by the larger and the quotient is equal to 1/2. What are the two sums of money?

Logarithms: The Early History of a Familiar Function - Parallel Insights and the Reception of Mathematical Ideas

The authors recount the 'great tale' of Napier's and Burgi's parallel development of logarithms and urge you to use it in class.

Loaves and Bishops

A certain bishop ordered that 12 loaves be divided among his clergy.

Loaf of Bread

In baking a hemispherical loaf of bread of 10" radius, the crust was everywhere of an equal thickness, and the solidity of the crust was equal to half the solid content of the whole loaf. What were the dimensions of the interior soft part?

Crown of Metal

Make a crown of gold, copper, tin, and iron weighing 60 minae: gold and copper shall be 2/3 of it; gold and tin, 3/4 of it; and gold and iron, 3/5 of it. Find the required weights of gold, copper, tin, and iron.

'He Advanced Him 200 Lambs of Gold': The Pamiers Manuscript

Problems from a 15th-century French manuscript, including one with negative solutions.

Circular Cone

The frustum of a circular cone has height 15.

Circle and Square

Prove that a square circumscribed about a given circle is double in area to a square inscribed in the same circle.