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Problems from Another Time

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

Given a right triangle where you know the length of the base and the sum of the perpendicular side and the hypotenuse.

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.
If 40 oranges are worth 60 apples, and 75 apples are worth 7 dozen peaches, and 100 peaches are worth 1 box of grapes and three boxes of grapes are worth 40 pounds of pecans, how many peaches can be bought for 100 oranges?
The third part of a necklace of pearls, broken in a lover's quarrel, fell to the ground...
One hundred men besieged in a castle, have sufficient food to allow each one bread to the weight of 14 lot a day for ten months.
Given the fraction ax/ (a-x ), convert it into an infinite series.
A merchant woman buys and sells apples and pears for Denaros. How much did she invest in apples; how much in pears?
A two door gate of unknown width is opened so that a 2 inch gap exists between the two doors.
The authors recount the 'great tale' of Napier's and Burgi's parallel development of logarithms and urge you to use it in class.
Prove that if the sums of the square opposite sides of any quadrilateral are equal, its diagonals interect at right angles.

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