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Problems from Another Time

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

Given four numbers whose sum is 9900; the second exceeds the first by 1/7 of the first...
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.
The authors recount the 'great tale' of Napier's and Burgi's parallel development of logarithms and urge you to use it in class.
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?
A man, woman, and two boys desire to cross a river, but their boat has weight restrictions!
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.

How a translation of Peano's counterexample to the 'theorem' that a zero Wronskian implies linear dependence can help your differential equations students
A certain man says that he can weigh any amount from 1 to 40 pounds using only 4 weights. What size must they be?
Heron of Alexandria (ca 200) wrote on many aspects of applied mathematics.
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?

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