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Problems from Another Time

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

Perimeters of Similar Triangles
The perimeters of two similar triangles are 45 and 135 respectively. One side of the first triangle has length 11 and a second side has length 19. Find the lengths of the sides of the second triangle.
Area of Elliptical Segment
Find the area of the elliptical segment cut off parallel to the shorter axis;
A Lion in a Well
There is a lion in a well whose depth is 50 palms. He climbs and slips back a certain amount each day. In how many days will he get out of the well?
Sum of Squares
There are two numbers which are to each other as 5 and 6 and the sum of their squares is 2196. What are the numbers?
Pearls of Wisdom
The third part of a necklace of pearls, broken in a lover's quarrel, fell to the ground...
Farmer's Best Deal
How many calves, goats and pigs did the farmer buy?
Traveling Men
Two men starting from the same point begin walking in different directions. Their rates of travel are in the ratio 7:3.
Logarithms: The Early History of a Familiar Function - Introduction
The authors recount the 'great tale' of Napier's and Burgi's parallel development of logarithms and urge you to use it in class.
Landscaping
A person has a circular yard that is 150 ft. in diameter, and wishes a walk of equal width made round it within the fence...
Woodcutter
A woodcutter starts to fell a tree 4 feet in diameter, and cuts half way through. One face of the cut is horizontal, and the other face is inclined to the horizontal at an angle of 45 degrees. Find the volume of the wood cut out.

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