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Problems from Another Time

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

Area of a Polygon
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.
Circumscribed Circle
The radius of a circle is 3.20 meters. Compute to within .001 square meters the areas of the inscribed and circumscribed equilateral triangles.
Peano on Wronskians: A Translation - Introduction
How a translation of Peano's counterexample to the 'theorem' that a zero Wronskian implies linear dependence can help your differential equations students
Square in the Circle
There is a circle from within which a square is cut, the remaining portion having an area of 47.6255 square units.
Inscribed Circle and Trapezoid
A circle is inscribed in an isosceles trapezoid. Find the relationship of the radius to the sides.
Cat on a Hot Tin Wall
A cat sitting on a wall 4 cubits high saw a rat prowling 8 cubits from the foot of the wall.
'He Advanced Him 200 Lambs of Gold': The Pamiers Manuscript - Currency Exchange
Discussion of 15th century French manuscript, with translation of its problems, including one with negative solutions
Three Piles of Rice
Now a pile of rice is against a wall with a base circumference 60 chi and an altitude of 12 chi.
Horses to Qi
Now a good horse and an inferior horse set out from Chang'an to Qi. Qi is 3000 li from Chang'an.
Beyond the Call of Duty
Given a guest on horseback rides 300 li in a day. The guest leaves his clothes behind. The host discovers them after 1/3 day, and he starts out with the clothes.

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