Problems from Another Time

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

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

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

Circle With a Chord

In a circle whose circumference is 60 units, a chord is drawn forming a segment whose sagitta is 2 units. What is the length of the chord?

Right Triangle

Given a right triangle where you know the length of the base and the sum of the perpendicular side and the hypotenuse...