Problems from Another Time

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

An erect pole of 10 cubits has its base moved 6 cubits. Determine the new height and the distance the top of the pole is lowered.

Why It Pays to Learn Math

In order to encourage his son in the study of arithmetic, a father agrees to pay him 8 pennies for every problem solved correctly and to charge him 5 pennies for each incorrect solution.

The Size of a City

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

Tomato Can

A cylindrical tin tomato can is to be made which shall have a given capacity. Find what should be the ratio of the height to the radius of the base that the smallest possible amount of tin shall be required.

Area Problem

Three equal circles with radii 12 feet are tangent to each other. Compute the area enclosed between them.

Peano on Wronskians: A Translation - Survey of Infinitesimal Analysis

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

The Cost of War

After a terrible battle it is found that 70% of the soldiers have lost an eye.

Inheritance of Three Sons

A man died leaving 3 sons, to whom he bequeathed his estate in the following manner: to the eldest he gave 184 dollars; to the second 155 dollars and to the third 96 dollars;

The Ant Race

Two ants are 100 paces apart, crawling back and forth along the same path. The first goes 1/3 pace forward a day and returns 1/4 pace; the other goes forward 1/5 pace and returns 1/6 pace. How many days before the first ant overtakes the second?

'He Advanced Him 200 Lambs of Gold': The Pamiers Manuscript - First Shoots of Capitalism

Discussion of 15th century French manuscript, with translation of its problems, including one with negative solutions