You are here

Home » MAA Publications » Periodicals » Convergence » Problems from Another Time

Problems from Another Time

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

A Circular Problem
Three circles of varying radius are mutually tangent. The area of the triangle connecting their centers is given. Find the radius of the third circle.
On the Run
A certain slave fled from Milan to Naples going 1/10 of the whole journey each day. At the beginning of the third day, his master sent a slave after him and this slave went 1/7 of the whole journey each day.
Prove the Straight Lines
Given two circles tangent at the point P with parallel diameters AB and CD, prove that APD and BPC are straight lines.
Area of an Equilateral Triangle
Suppose the area of an equilateral triangle be 600. The sides are required.
A Triangular Problem
In a right triangle, having been given the perimeter, a, and the length of the perpendicular from the right-angled vertex to the hypotenuse, b, it is required to find the length of the hypotenuse.
A Grinding Stone
Seven men held equal shares in a grinding stone 5 feet in diameter. What part of the diameter should each grind away?
Mutually Tangent Circles
Three congruent circles of radius 6 inches are mutually tangent to one another. Compute the area enclosed between them.
Pennies for the Poor
If I were to give 7 pennies to each beggar at my door, I would have 24 pennies left in my purse. How many beggars are there and how much money do I have?
The Size of a City
A square walled city of unknown dimensions has four gates, one at the center of each side.
Tomato Can
A cylindrical tin tomato can is to be made which shall have a given capacity. Find what should be the ratio of the height to the radius of the base that the smallest possible amount of tin shall be required.

Pages