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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 square circumscribed about a given circle is double in area to a square inscribed in the same circle. True of false? Prove your answer.
Given a guest on horseback rides 300 li in a day. The guest leaves his clothes behind. The host discovers them after 1/3 day, and he starts out with the clothes.
Prove geometrically that the hypocycloid is a straight line when the radius of the rolling circle is one-half the radius of the fixed circle.
One military horse cannot pull a load of 40 dan; neither can 2 ordinary horses, nor can three inferior horses.
The dimensions of a rectangular box in inches are expressed by three consecutive numbers. The surface of the box is 292 square inches. Find the dimensions.
Given two circle tangent at the point P with parallel diameters AB, CD, prove that APD and BPC are straight lines.
Three men have a pile of money, their shares being 1/2, 1/3 and 1/6. Each man takes some money from the pile until nothing is left.
A person has a circular yard that is 150 ft. in diameter, and wishes a walk of equal width made round it within the fence...
In a given square, inscribe 4 equal circles so that...
The authors recount the 'great tale' of Napier's and Burgi's parallel development of logarithms and urge you to use it in class.

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