# Problems from Another Time

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

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?
Discussion of 15th century French manuscript, with translation of its problems, including one with negative solutions
Heron of Alexandria (c. 10 - 75 CE) wrote on many aspects of applied mathematics.
Prove that a square circumscribed about a given circle is double in area to a square inscribed in the same circle.
Find the isosceles triangle of smallest area that circumscribes a circle of radius a.
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 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?
Four men already having denari found a purse of denari; each man has a different amount of denari before they found the purse. Find out how much denari each man has.
Prove geometrically that the hypocycloid is a straight line when the radius of the rolling circle is one-half the radius of the fixed circle.
What is the sum of the reciprocals of the triangular numbers?