Problems from Another Time

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

A woodcutter starts to fell a tree 4 feet in diameter, and cuts half way through. One face of the cut is horizontal, and the other face is inclined to the horizontal at an angle of 45 degrees. Find the volume of the wood cut out.

Round Pond in Rectangular Garden

A round pond sits in a rectangular garden. Its center is inaccessible; however, you know the distances from each corner of the garden to the circumference of the pond: 60, 52, 28, and 40 yards. What is the radius of the pond?

Peano on Wronskians: A Translation - Additional References in the Articles

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

Gardening

An oblong garden is a half yard longer than it is wide and consists entirely of a gravel walk...

The Speculator's Buy

A speculator bought stock at 25% below par and sold it at 20% above par. He gained $1560. How much did he invest?

Contractors

A carpenter has undertaken to build a house in 20 days. He takes on another man and says; "If we build the house together, we can accomplish the work in 8 days!" How long would it take this other man to build the house working alone?

'He Advanced Him 200 Lambs of Gold': The Pamiers Manuscript - A Source of the Two-Trains Problem?

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

Historical Activities for the Calculus Classroom

Curve sketching, tangent lines, and optimization, explored via interactive applets

Viete: Triangle

In a right triangle, let the perpendicular be 5 and the sum of the base and hypotenuse 25. Find the lengths of the base and hypotenuse

Square Battalions

A general formed his men into a square, that is, an equal number in rank and file, and he found that he had an excess of 59 men.