Problems from Another Time

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

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?

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 - Introduction

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

Square in the Circle

There is a circle from within which a square is cut, the remaining portion having an area of 47.6255 square units.

Inscribed Circle and Trapezoid

A circle is inscribed in an isosceles trapezoid. Find the relationship of the radius to the sides.