Problems from Another Time

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

Heron of Alexandria (c. 10 - 75 CE) wrote on many aspects of applied mathematics.

Prove that a square circumscribed about a given circle is double in area to a square inscribed in the same circle.

Find the isosceles triangle of smallest area that circumscribes a circle of radius a.

A gentleman has a garden of rectangular form and wants to construct a walk of equal width half way round to take up half the garden. What must be the width of this walk?

Gun Metal

Gun metal of a certain grade is composed of 16% tin and 84% copper. How much tin must be added to 410 pounds of this gun metal to make a composition of 18% tin?

Purse of Denari

Four men already having denari found a purse of denari; each man has a different amount of denari before they found the purse. Find out how much denari each man has.

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.