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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 the fraction ax/ (a-x ), convert it into an infinite series.
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 two door gate of unknown width is opened so that a 2 inch gap exists between the two doors.
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.

There is a circle from within which a square is cut, the remaining portion having an area of 47.6255 square units.
A certain man says that he can weigh any amount from 1 to 40 pounds using only 4 weights. What size must they be?
How a translation of Peano's counterexample to the 'theorem' that a zero Wronskian implies linear dependence can help your differential equations students
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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