Problems from Another Time

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

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?

Mutually Tangent Circles

Three congruent circles of radius 6 inches are mutually tangent to one another. Compute the area enclosed between them.

Pennies for the Poor

If I were to give 7 pennies to each beggar at my door, I would have 24 pennies left in my purse. How many beggars are there and how much money do I have?

Two Men Meet

A square walled city measures 10 li on each side. At the center of each side is a gate. Two persons start walking from the center of the city.