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One says that 10 is divided into three parts and if the small part is multiplied by itself and added to the middle one multiplied by itself the result is the large one multiplied by itself...

Circle and Equilateral Triangle

A circle ABDC is circumscribed around an equilateral triangle ABC. Prove that the straight line AD is equal to the sum of the two straight lines BD and DC.

How to Submit an Article to Loci

A brief outline of policies for submission of articles to Loci.

Three Vertical Posts

Three vertical posts along a straight canal, each rising to the same height above the surface of the water. By using measurments of the posts, determine, to the nearest mile, the radius of the earth.

Perpendicular Curves

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

Loafing About

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

Prime Numbers: The Most Mysterious Figures in Math

An introduction to the prime numbers in many of their aspects.

Four Integers

Given four integers which, if added together three at a time, their sums are: 20, 22, 24, and 27. What are the integers?

Circle and Square

Prove that a square circumscribed about a given circle is double in area to a square inscribed in the same circle.

Euclidean and Non-Euclidean Geometries: Development and History

This textbook seamlessly combines the history of non-Euclidean geometry with the mathematical ideas.