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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?
Having been given the perimeter and perpendicular of a right angled triangle, it is required to find the triangle.
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.
Determine the dimensions of the least isosceles triangle ACD that can circumscribe a given circle.
Determine the greatest cylinder that can be inscribed in a given cone.
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 square walled city measures 10 li on each side. At the center of each side is a gate. Two persons start walking from the center of the city.
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 authors recount the 'great tale' of Napier's and Burgi's parallel development of logarithms and urge you to use it in class.
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.

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