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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 circle, a square and an equilateral triangle all have the same perimeter equal to 1 meter. Compare their areas.
Two bicyclists travel in opposite directions around a quarter-mile track and meet every 22 seconds. When they travel in the same direction on this track, the faster passes the slower once every 3 minutes and 40 seconds. Find the rate of each rider
To find three quantities x.y, and z...
Gun metal of a certain grade is composed of 16% tin and 84% copper. How much tin must be added to 410 lbs. of this gun metal to make a composition of 18% tin?
Now there are six-headed four legged animals and four-headed two-legged birds. Find the total number of animals and birds.
A water tub holds 73 gallons; the pipe which fills it usually admits 7 gallons in 5 minutes; and the tap discharges 20 gallons in 17 minutes.
Suppose a ladder 60 feet long is placed in a street so as to reach a window 37 feet above the ground on one side of the street...
Seven men held equal shares in a grinding stone 5 feet in diameter. What part of the diameter should each grind away?
Given a pyramid 300 cubits high, with a square base 500 cubits to a side, determine the distance from the center of any side to the apex.
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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