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Problems from Another Time

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

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 - Introduction
Discussion of 15th century French manuscript, with translation of its problems, including one with negative solutions
Heron's Formula
Heron of Alexandria (c. 10 - 75 CE) wrote on many aspects of applied mathematics.
Circle and Square
Prove that a square circumscribed about a given circle is double in area to a square inscribed in the same circle.
Circumscribed Circle #2
Find the isosceles triangle of smallest area that circumscribes a circle of radius a.
In the Gentleman's Garden
A gentleman has a garden of rectangular form and wants to construct a walk of equal width half way round to take up half the garden. What must be the width of this walk?

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