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Problems from Another Time

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

Seven men held equal shares in a grinding stone 5 feet in diameter. What part of the diameter should each grind away?
After a terrible battle it is found that 70% of the soldiers have lost an eye.
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.
Discussion of 15th century French manuscript, with translation of its problems, including one with negative solutions
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.
A wooden beam is stood vertically against a wall. The length of the beam is 30 units.
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?
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 circles of varying radius are mutually tangent. The area of the triangle connecting their centers is given. Find the radius of the third circle.
A certain man says that he can weigh any amount from 1 to 40 pounds using only 4 weights. What size must they be?

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