Problems from Another Time

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

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

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.

Walk Around the Triangle

If an equilateral triangle whose area is equal to 10,000 square feet be surrounded by a walk of uniform width, and equal to the area of the inscribed circle, what is the width of the walk?

Multiplying Like Rabbits

Assume that the human population after the flood was 6 and that 200 years later the population was 1,000,000. Find the annual rate of growth of the population.

Lunchtime at the Fish Pond

A fish sees a heron looking at him from across a pool, so he quickly swims towards the south. When he reaches the south side of the pool, he has the unwelcome surprise of meeting the heron.

Dimensions of a Box

The dimensions of a rectangular box in inches are expressed by three consecutive numbers. The surface of the box is 292 square inches. Find the dimensions.

A Tower on a Cliff

A cliff with a tower on its edge is observed from a boat at sea; find the height of the cliff and the tower.