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Problems from Another Time

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

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.
Be Careful Where You Step!
A ladder has 100 steps. On the first step sits 1 pigeon; on the second, 2; on the third, 3; and so on up to the hundredth. How many pigeons in all?
'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?
Gun Metal
Gun metal of a certain grade is composed of 16% tin and 84% copper. How much tin must be added to 410 pounds of this gun metal to make a composition of 18% tin?

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