Problems from Another Time

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

The edge of a cloud is at an altitude of 20 degrees and the sun above it at 35 degrees. The shadow cast by the edge of the cloud fall on a object 2300 yards away, how high is the cloud?

Bicyclists on a Track

Two bicyclists travel in opposite directions around a quarter-mile track and meet every 22 seconds. When they travel in the same direction on this track, the faster passes the slower once every 3 minutes and 40 seconds. Find the rate of each rider

To Each His Due

A man has four creditors. To the first he owes 624 ducats; to the second, 546; to the third, 492; and to the fourth 368.

Three Vertical Posts

Three vertical posts along a straight canal, each rising to the same height above the surface of the water. By using measurments of the posts, determine, to the nearest mile, the radius of the earth.

A Circular Problem

Determine the dimensions of the least isosceles triangle ACD that can circumscribe a given circle.

Ladder Day Question

A ladder is placed perpendicular to the plane of the horizon, and in coincidence with the plane of an upright wall.

Walk Around the World

Suppose a person whose height is 5 feet 7 inches travels 10000 miles in the arc of a great circle. How much further will the person's head have gone compared to their feet, the circumference of the Earth being 21600 miles?

Faster Than a Speeding Horse

A horse, halving its speed each day, travels 700 miles in 7 days. How far does it travel each day?

Logarithms: The Early History of a Familiar Function - Before Logarithms: The Computational Demands of the Late Sixteenth Century

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

Another Numbers Game

Determine a number having remainders 2, 3, and 2 when divided by 3, 5, and 7 respectively.