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Problems from Another Time

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

In baking a hemispherical loaf of bread of 10" radius, the crust was everywhere of an equal thickness, and the solidity of the crust was equal to half the solid content of the whole loaf. What were the dimensions of the interior soft part?
A wooden log is encased in a wall. If we cut part of the wall away to a depth of 1 inch...
Given a triangular piece of land having two sides 10 yards in length and its base 12 yards, what is the largest square that can be constructed within this piece of land so that one of its sides lies along the base of the triangle?
Discussion of 15th century French manuscript, with translation of its problems, including one with negative solutions
What is the sum of the following series, carried to infinity: 11, 11/7, 11/49, etc.?
Having been given the lengths, a and b, of two straight lines drawn from the acute angles of a right triangle to the middle of the opposite sides, determine the length of those sides.
Suppose that the propability of success in an experiment is 1/10. How many trials of the experiment are necessary to insure even odds on it happening at least once?
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.
Two merchants, A and B, loaded a ship with 500 hhds (hogshead) of rum; A loaded 350 hhds, and B the rest; in a storm the seamen were obliged to throw overboard 100 hhds; how much must each sustain of the loss?
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.

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