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Problems from Another Time

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

A California miner has a spherical ball of gold, 2 inches in diamter, which he wants to exchange for spherical balls 1 inch in diameter. How many of the smaller spheres should he receive?
The sum of two numbers is 10 and their product is 40. What are the numbers?
Find the greatest value of y in the equation a4 x2= (x2 + y2)3.
Determine the different values of x, when a certain function hits a minimum.
Given a door and a measuring rod of unknown dimensions, the rod is used to measure the door.
It is required to determine whether 30 horses can be put into 7 stalls; so that in every stall there may be, either a single horse, or an odd number of horses.
One says that 10 garments were purchased by two men at a price of 72 dirhams. The garments varied in value. The price of each garment of one man is 3 dirhams more than the price for each garment of the other. How many garments did each man buy?
The authors recount the 'great tale' of Napier's and Burgi's parallel development of logarithms and urge you to use it in class.
Now there is a wall 5 feet thick and two rats tunnel from opposite sides.
There are two columns in the ruins of Persepolis left standing upright; one is 70 ft. above the plane, and the other 50 ft;