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?

Drinking Wine by the Barrel

A man and his wife drink a barrel of wine at different rates.

Elephant Hunt

On an expedition to seize his enemy's elephants, a king marched 2 yojanas the first day.

Water in a Fish Pond

There is a round fish pond of certain dimensions, and into the pond is dropped a marble column. How high will the water rise?

Maximization

Find the greatest value of y in a given equation.

Grain and Camels

A certain gentleman ordered that 90 measures of grain were to be transported from his house to another, 30 leucas distant.

Isoceles Trapezoid

Given the dimensions of an isosceles trapezoid, find the length of the transversal drawn parallel to the bases that divides the trapezoid into 2 equal areas.

A Snake in the Hole

A powerful, unvanquished, excellent black snake, 32 hastas in length, enters into a hole at the rate of 7 1/2 angulas in 5/14 of a day, and in the course of 1/4 of a day its tail grows 2 3/4 of an angula.

Logarithms: The Early History of a Familiar Function - Joost Bürgi Introduces Logarithms

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