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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.

Storm's A' Brewin'

What is the perpendicular height of a cloud when its angles of elevation were 35 degrees and 64 degrees as taken by two observers at the same time...

Websites to Visit

There are a number of wonderful mathematics websites that readers of Convergence should be aware of. We describe some of them here.

The Mathematics of the Heavens and the Earth

A comprehensive history of trigonometry from ancient times to the Renaissance.

Square Battalions

A general formed his men into a square, that is, an equal number in rank and file, and he found that he had an excess of 59 men.

Perpendicular Curves

Show that the curves x2 - y2 = a2 and 2 xy = b2 cross at right angles.

An Apple a Day

A man entered an orchard through 7 gates, and there took a certain number of apples. When he left the orchard, he gave the first guard half the apples he had and 1 apple more.

Numbers Game #1

The sum of two numbers is 10 and their product is 40. What are the numbers?

Unknown Quantity; A Real and Imaginary History of Algebra

A history of algebra from its early beginnings to the twentieth century.

Calculate a Triangle

Having been given the perimeter and perpendicular of a right angled triangle, it is required to find the triangle.