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Problems from Another Time

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

Discussion of 15th century French manuscript, with translation of its problems, including one with negative solutions
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.
A circle is inscribed in an isosceles trapezoid. Find the relationship of the radius to the sides.
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.
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?
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 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?
The third part of a necklace of pearls, broken in a lover's quarrel, fell to the ground...
A general formed his men into a square, that is, an equal number in rank and file, and he found that he had an excess of 59 men.
Given the fraction ax/ (a-x ), convert it into an infinite series.

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