# Problems from Another Time

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

Given the frustum of a circular cone with height h.
I was employed to survey a field, which I was told was an exact geometrical square, but by reason of a river running through it, I can only obtain partial measurements.
A ladder has 100 steps. On the first step sits 1 pigeon; on the second, 2; on the third, 3; and so on up to the hundredth. How many pigeons in all?
Discussion of 15th century French manuscript, with translation of its problems, including one with negative solutions
An official asks a woman why she has so many bowls to wash. The woman explains that she had dinner guests who ate meat, rice, and soup. Judging by the number of bowls, how many guests were there?
A teacher agreed to teach 9 months for $562.50 and his board. At the end of the term, on account of two months absence caused by sickness, he received only$409.50. What was his board worth per month?
Find the isoceles triangle of smallest area that circumscribes a circle of radius 1.
Two bicyclists travel in opposite directions around a quarter-mile track and meet every 22 seconds. When they travel in the same direction on this track, the faster passes the slower once every 3 minutes and 40 seconds. Find the rate of each rider
In a right triangle, the hypotenuse is 9.434 and the sum of the sides around the right angle is 13. Find the lengths of the sides around the right angle.
Having been given the perimeter and perpendicular of a right angled triangle, it is required to find the triangle.