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Problems from Another Time

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

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.
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?
Show that the curves x2 - y2 = a2 and 2 xy = b2 cross at right angles.
The highest point of the Andes is about 4 miles above sea level.
Suppose a ladder 60 feet long is placed in a street so as to reach a window 37 feet above the ground on one side of the street...
A circle is inscribed in an isosceles trapezoid. Find the relationship of the radius to the sides.
A carpenter has undertaken to build a house in 20 days. He takes on another man and says; "If we build the house together, we can accomplish the work in 8 days!" How long would it take this other man to build the house working alone?
Twenty-three weary travelers entered a delightful forest. There they found 63 numerically equal piles of plantain fruit.
A certain bishop ordered that 12 loaves be divided among his clergy.
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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