Problems from Another Time

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

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

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.

A Horse in London

A man hired a horse in London at 3 pence a mile. He rode 94 miles due west to Bristol then due north to Chester, whence he returned toward London for 66 miles, which put him in Coventry.

Square and Round Land

As for a square piece of land that amounts to 100 square cubits, if it is said to you, "Cause it to make a piece of land that amounts to 100 square cubits that is round," what is the required diameter?

Peano on Wronskians: A Translation - Appendix 1: Student Tasks

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

Animal Customs

A fox, a wild-cat, and a hound pass through customs and together pay 111 coins.