Problems from Another Time

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

The sum of the two digits of a 2-digit number is 9. If 45 is subtracted from the number, the result will be expressed by the digits in reverse order. Find the number.

A Clothes Call

A man went to a draper and bought a length of cloth 35 braccia long to make a suit of clothes.

10 Into 3 Parts

Make of 10 three parts such that one part multiplied by 3 makes as much as the other multiplied by 4 and as the other multiplied by 5.

Long Time to Fill the Tub

A water tub holds 73 gallons; the pipe which fills it usually admits 7 gallons in 5 minutes; and the tap discharges 20 gallons in 17 minutes.

Horsing Around

One military horse cannot pull a load of 40 dan; neither can 2 ordinary horses, nor can three inferior horses...

Squared Proof

Prove that if the sums of the squares of opposite sides of any quadrilateral are equal, its diagonals intersect at right angles.

Water Reeds

A pond has two water reeds, where the one grows 3 feet and the other 1 foot on the first day. The growth of the first becomes every day half of that of the preceding day, while the other grows twice as much as on the day before.

Logarithms: The Early History of a Familiar Function - Logarithms: A 'Great Tale' for Use in the Classroom

The authors recount the 'great tale' of Napier's and Burgi's parallel development of logarithms and urge you to use it in class.

Two Equal Parts of a Triangle

The three sides of a triangular piece of land, taken in order, measure 15, 10, and 13 chains respectively.

Series of Circles

A series of circles have their centers on an equilateral hyperbola and pass through its center. Show that their envelope is a lemniscate.