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Problems from Another Time

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

I have two fields of grain. From the first field I harvest 2/3 a bushel of grain/unit area; from the second, 1/2 bushel/unit area.
A person has a circular yard that is 150 ft. in diameter, and wishes a walk of equal width made round it within the fence...
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?
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.
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?
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.

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