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Problems from Another Time

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

In Archimedes' Book of Lemmas (ca 250), he introduces a figure that, due to its shape, has historically been known as "the shoemaker's knife" or arbelos.
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.
How a translation of Peano's counterexample to the 'theorem' that a zero Wronskian implies linear dependence can help your differential equations students
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?
In a certain lake, swarming with red geese, the tip of a lotus bud was seen to extend a span [9 inches] above the surface of the water.
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?
Determine by using algebra the number of degrees in the angle A where: cos A = tan A
On an expedition to seize his enemy's elephants, a king marched 2 yojanas the first day.
A fellow said that when he counted his nuts by twos, threes, fours, fives and sixes, there was still one left over; but when he counted them by sevens they came out even. How many did he have?

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