Problems from Another Time

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

Having been given the sum of two numbers, a, and the difference of their squares, b, find the numbers.

A Tree with Branches, Nests, Eggs and Birds

There is a tree with 100 branches. How many nests, eggs and birds are there?

A father wills his estate valued at $40,000 to his three children. Before the settlement one of the children dies. What should the other two receive?

Pyramid Calculation

Given a pyramid 300 cubits high, with a square base 500 cubits to a side, determine the distance from the center of any side of the base to the apex.

A Wealth of Plantains

Twenty-three weary travelers entered a delightful forest. There they found 63 numerically equal piles of plantain fruit.

The Door and the Rod

Given a door and a measuring rod of unknown dimensions, the rod is used to measure the door.

Steamboat

The cost per hour of running a certain steamboat is proportional to the cube of its velocity in still water. At what speed should it be run to make a trip up stream against a four-mile current most economically?

Japanese Temple Problem

Given two circles tangent to each other and to a common line, determine a relationship between the radii and the distance between the tangent points.

Peano on Wronskians: A Translation - Survey of Infinitesimal Analysis

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

The Cost of War

After a terrible battle it is found that 70% of the soldiers have lost an eye.