Problems from Another Time

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

Make a crown of gold, copper, tin, and iron weighing 60 minae: gold and copper shall be 2/3 of it; gold and tin, 3/4 of it; and gold and iron, 3/5 of it. Find the required weights of gold, copper, tin, and iron.

'He Advanced Him 200 Lambs of Gold': The Pamiers Manuscript

Problems from a 15th-century French manuscript, including one with negative solutions.

Circular Cone

The frustum of a circular cone has height 15.

Circle and Square

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

Circumscribed Circle #2

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

In the Gentleman's Garden

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?