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 Door and the Rod

Given a door and a measuring rod of unknown dimensions, the rod is used to measure the door.

Steamboat

The cost per hour of running a certain steamboat is proportional to the cube of its velocity in still water. At what speed should it be run to make a trip up stream against a four-mile current most economically?

Japanese Temple Problem

Given two circles tangent to each other and to a common line, determine a relationship between the radii and the distance between the tangent points.

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