Problems from Another Time

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

There is a regular pentagon. The length of its side is a. Find the area of the pentagon. Generalize your result for a nonagon.
I owe a man the following notes: one of $800 due May 16; one of$660 due on July 1; one of $940 due Sept. 29. He wishes to exchange them for two notes of$1200 each and wants one to fall due June 1. When should the other be due?
Show that the curves x2 - y2 = a2 and 2 xy = b2 cross at right angles.
The highest point of the Andes is about 4 miles above sea level.
A certain man had in his trade four weights with which he could weigh integral pounds from one up to 40. How many pounds was each weight?
Given a semicircle, Prove that if O is the circle's center, DO=OE.
In order to encourage his son in the study of arithmetic, a father agrees to pay him 8 pennies for every problem solved correctly and to charge him 5 pennies for each incorrect solution.
There is a round town 8000 feet in circumference.
Of a collection of mango fruits, the king took 1/6; the queen 1/5 the remainder, and the three princes took 1/4, 1/3 and 1/2 (of the same remainder); and the youngest child took the remaining 3 mangoes.
Three vertical posts along a straight canal, each rising to the same height above the surface of the water. By looking at the line of vision, determine, to the nearest mile, the radius of the earth.