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Problems from Another Time

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

A mouse is at the top of a poplar tree 60 braccia high, and a cat is on the ground at its foot. The mouse decends 1/2 a braccia a day and at night it turns back 1/6 of a braccia.
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.
Prove geometrically that the hypocycloid is a straight line when the radius of the rolling circle is one-half the radius of the fixed circle.
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?
The third part of a necklace of pearls, broken in a lover's quarrel, fell to the ground...
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?
Given the fraction ax/ (a-x ), convert it into an infinite series.
Find the isoceles triangle of smallest area that circumscribes a circle of radius 1.
A two door gate of unknown width is opened so that a 2 inch gap exists between the two doors.
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.

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