Problems from Another Time

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

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

Peano on Wronskians: A Translation - On the Wronskian Determinant

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

Arbelos

In Archimedes' Book of Lemmas (ca 250), he introduces a figure that, due to its shape, has historically been known as "the shoemaker's knife" or arbelos.

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...

Circle, Square, and Triangle

A circle, a square and an equilateral triangle all have the same perimeter equal to 1 meter. Compare their areas.