Problems from Another Time

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

'He Advanced Him 200 Lambs of Gold': The Pamiers Manuscript - Barter Transactions

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

Now a pile of rice is against a wall with a base circumference 60 chi and an altitude of 12 chi.

Now a good horse and an inferior horse set out from Chang'an to Qi. Qi is 3000 li from Chang'an.

Given a guest on horseback rides 300 li in a day. The guest leaves his clothes behind. The host discovers them after 1/3 day, and he starts out with the clothes.

A Circular Problem

Three circles of varying radius are mutually tangent. The area of the triangle connecting their centers is given. Find the radius of the third circle.

On the Run

A certain slave fled from Milan to Naples going 1/10 of the whole journey each day. At the beginning of the third day, his master sent a slave after him and this slave went 1/7 of the whole journey each day.

Prove the Straight Lines

Given two circles tangent at the point P with parallel diameters AB and CD, prove that APD and BPC are straight lines.

Area of an Equilateral Triangle

Suppose the area of an equilateral triangle be 600. The sides are required.

A Triangular Problem

In a right triangle, having been given the perimeter, a, and the length of the perpendicular from the right-angled vertex to the hypotenuse, b, it is required to find the length of the hypotenuse.

A Grinding Stone

Seven men held equal shares in a grinding stone 5 feet in diameter. What part of the diameter should each grind away?