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Problems from Another Time

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

Prove that the area of a regular polygon can be given by the product of its perimeter and half the radius of the inscribed circle.
Find two number with sum 20 and when squared their sum is 208.
Two circles of radii 25 feet intersect so that the distance between their centers is 30 feet. What is the length of the side of the largest square inscribable within their intersecting arcs?
Given the cats eye as shown. Let the radius of the eye be given by R. What is the area of the pupil?
The incircle O(r) of triangle ABC touches AB at D, BC at E and AC at F. Find r in terms of AD, BE and CF.

Three hundred pigs are to be prepared for a feast.
A certain man says that he can weigh any amount from 1 to 40 pounds using only 4 weights. What size must they be?
The authors recount the 'great tale' of Napier's and Burgi's parallel development of logarithms and urge you to use it in class.
A man plants 4 kernels of corn, which at harvest produce 32 kernels: these he plants the second year; now supposing the annual increase to continue 8 fold, what would be the produce of the 15th year, allowing 1000 kernels to a pint?
A fox, a raccoon, and a hound pass through customs and together pay 111 coins.

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