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Problems from Another Time

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

Golden Spheres
A California miner has a spherical ball of gold, 2 inches in diameter, which he wants to exchange for spherical balls 1 inch in diameter. How many of the smaller spheres should he receive?
Money Makes the World Go Around
You have two sums of money, the difference of which is 2 dirhems; you divide the smaller sum by the larger and the quotient is equal to 1/2. What are the two sums of money?
Logarithms: The Early History of a Familiar Function - Parallel Insights and the Reception of Mathematical Ideas
The authors recount the 'great tale' of Napier's and Burgi's parallel development of logarithms and urge you to use it in class.
Loaves and Bishops
A certain bishop ordered that 12 loaves be divided among his clergy.
Loaf of Bread
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?
Crown of Metal
Make a crown of gold, copper, tin, and iron weighing 60 minae: gold and copper shall be 2/3 of it; gold and tin, 3/4 of it; and gold and iron, 3/5 of it. Find the required weights of gold, copper, tin, and iron.
'He Advanced Him 200 Lambs of Gold': The Pamiers Manuscript
Problems from a 15th-century French manuscript, including one with negative solutions.
Circular Cone
The frustum of a circular cone has height 15.
Walk Around the Triangle
If an equilateral triangle whose area is equal to 10,000 square feet be surrounded by a walk of uniform width, and equal to the area of the inscribed circle, what is the width of the walk?
Multiplying Like Rabbits
Assume that the human population after the flood was 6 and that 200 years later the population was 1,000,000. Find the annual rate of growth of the population.

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