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Problems from Another Time

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

Heron of Alexandria (ca 200) wrote on many aspects of applied mathematics.
A cylindrical tin tomato can is to be made which shall have a given capacity. Find what should be the ratio of the height to the radius of the base that the smallest possible amount of tin shall be required.
Discussion of 15th century French manuscript, with translation of its problems, including one with negative solutions
A round pond sits in a rectangular garden. Its center is inaccessible; however, you know the distances from each corner of the garden to the center of the pond: 60, 52, 28, and 40 yards. What is the radius of the pond?
There is a garden is the shape of a rhombus whose side is 768.52 feet. Within the garden is an inscribed square flower bed whose side is 396 feet. What is the area of the garden?
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?
The purchase price for an apple and an orange is 100 yen. When n oranges and n + 3 apples are bought the price is 520 yen. Find the number n of oranges and the price of one orange.
Having been given the perimeter and perpendicular of a right angled triangle, it is required to find the triangle.
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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