Problems from Another Time

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

Suppose a lighthouse is built on the top of a rock; the distance between a place of observation and that part of the rock level with the eye is 620 yds.

Apples and Oranges and Peaches

If 40 oranges are worth 60 apples, and 75 apples are worth 7 dozen peaches, and 100 peaches are worth 1 box of grapes and three boxes of grapes are worth 40 pounds of pecans, how many pounds of pecans can be bought for 100 oranges?

The Cog-Wheel Revolution

Two cog-wheels, one having 26 cogs, and the other 20 cogs, run together. In how many revolutions of the larger wheel will the smaller gain in 12 revolutions?

The Recruiting Officers

Two officers each have a company of men, the one has 40 less than the other.

The Time It Takes To Eat a Goat

A lion, a wolf and a fox each take a certain amount of time to eat a goat separately. How long would it take all these animals together to eat the goat?

Maxes and Mins

Determine the different values of x, when a certain function hits a minimum.

Two Numbers

Find two numbers with sum 20 and when squared their sum is 208.

A Room with a View

Find the height of a window.

A Swarm of Bees

The square root of half the number of bees in a swarm has flown out upon a jessamine bush; 8/9 of the swarm has remained behind.

Logarithms: The Early History of a Familiar Function - The Challenges of Parallel Insights in the History of Mathematics

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