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Problems from Another Time

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

Look Out Below!
Suppose a ladder 60 feet long is placed in a street so as to reach a window 37 feet above the ground on one side of the street...
Radii of Three Circles
Determine the radii of three equal circles described within and tangent to a given circle, and also tangent to each other.
Numbers Game #1
The sum of two numbers is 10 and their product is 40. What are the numbers?
Logarithms: The Early History of a Familiar Function - Bibliography
The authors recount the 'great tale' of Napier's and Burgi's parallel development of logarithms and urge you to use it in class.
Asking a Woman Her Age
A lady being asked how old she was at the time of her marriage replied that the age of her oldest son was 13; that he was born 2 years after her marriage...
Circle and Equilateral Triangle
A circle ABDC is circumscribed around an equilateral triangle ABC.  Prove that the straight line AD is equal to the sum of the two straight lines BD and DC.
Looking for Bargains
One says that 10 garments were purchased by two men at a price of 72 dirhams. The garments varied in value. The price of each garment of one man is 3 dirhams more than the price for each garment of the other. How many garments did each man buy?
'He Advanced Him 200 Lambs of Gold': The Pamiers Manuscript - Proportionality Techniques
Discussion of 15th century French manuscript, with translation of its problems, including one with negative solutions
Log Stuck in a Wall
Now given a cylindrical log of unknown size buried in a wall...
Harvest Time
A man plants 4 kernels of corn, which at harvest produce 32 kernels: these he plants the second year; now, supposing the annual increase to continue 8 fold, what would be the produce of the 15th year, allowing 1000 kernels to a pint?

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