Problems from Another Time

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

The dimensions of a rectangular box in inches are expressed by three consecutive numbers. The surface of the box is 292 square inches. Find the dimensions.

A Tower on a Cliff

A cliff with a tower on its edge is observed from a boat at sea; find the height of the cliff and the tower.

A Linear Hypocycloid

Prove geometrically that the hypocycloid is a straight line when the radius of the rolling circle is one-half the radius of the fixed circle.

Triangular Numbers

What is the sum of the reciprocals of the triangular numbers?

Ages of Father and Son

When knowing the sum of their ages along with another equation, determine how old a father and son are.

Stinkin' Pile of Money

Three men have a pile of money, their shares being 1/2, 1/3 and 1/6. Each man takes some money from the pile until nothing is left.

Money Changers

Two men have a certain amount of money. The first says to the second, "If you give me 5 denari, I will have 7 times what you have left."

Trisecting a Log

There is a log of precious wood 18 feet long whose bases are 5 feet and 2.5 feet in circumference. Into what lengths should the log be cut to trisect its volume?

Division Problem

The number 50 is divided by a certain number. If the divisor is increased by 3, the quotient decreases by 3.75. What is the number?

Logarithms: The Early History of a Familiar Function - Conclusion

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