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Problems from Another Time

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

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.

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.
There is a circle from within which a square is cut, the remaining portion having an area of 47.6255 square units.
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?
If an arc of 45 degrees on one circumference is equal to an arc of 60 degrees on another circle, what is the ratio of the areas of the circle?
How a translation of Peano's counterexample to the 'theorem' that a zero Wronskian implies linear dependence can help your differential equations students
A wooden log is encased in a wall. If we cut part of the wall away to a depth of 1 inch...
Knowing the base, b, and the altitude, a, of a triangle. Find the expression for a side of the inscribed square.
Now there are 100 deers [being distributed] in a city. If one household has one deer there is a remainder...Find the number of households in the city.

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