Problems from Another Time

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

Seven men held equal shares in a grinding stone 5 feet in diameter. What part of the diameter should each grind away?

Three congruent circles of radius 6 inches are mutually tangent to one another. Compute the area enclosed between them.

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?

Two Men Meet

A square walled city measures 10 li on each side. At the center of each side is a gate. Two persons start walking from the center of the city.

Area of a Polygon

Prove that the area of a regular polygon can be given by the product of its perimeter and half the radius of the inscribed circle.

Circumscribed Circle

The radius of a circle is 3.20 meters. Compute to within .001 square meters the areas of the inscribed and circumscribed equilateral triangles.

Peano on Wronskians: A Translation - On the Wronskian Determinant

How a translation of Peano's counterexample to the 'theorem' that a zero Wronskian implies linear dependence can help your differential equations students

Arbelos

In Archimedes' Book of Lemmas (ca 250), he introduces a figure that, due to its shape, has historically been known as "the shoemaker's knife" or arbelos.

Disjoint Congruent Circles

A set of n disjoint, congruent circles packs the surface of a sphere S so that each region of the surface exterior to the circles is bounded by arcs of three of the circles.

Loafing About

There were two men, of whom the first had 3 small loaves of bread and the other, 2.