Background:

Euclid (Euclid of Alexandria), was a Greek mathematician who is thought to have lived in Egypt during the reign of Ptolemy I (323 BC-283 BC). His book; “Elements” is still the most successful textbook in history of mathematics covering geometry and topics from number theory.

Very little is known about Euclid other than his writings. What little biographical information we do have comes largely from commentaries by Proclus and Pappus of Alexandria: Euclid was active at the great Library of Alexandria and may have studied at Plato's Academy in Greece. Euclid's exact lifespan and place of birth are unknown. Some writers in the Middle Ages confused him with Euclid of Megara, a Greek Socratic philosopher who lived approximately one century earlier.

The Elements:

·        Euclid deduces the fundamental principles of geometry from a small set of axioms (initial propositions).

·        The relationship between Mersenne primes and perfect numbers

·        The proof of the infinitude of prime numbers

·        Lemma (on factorization which lead to the fundamental theorem of arithmetic on uniqueness of prime factorizations.

·        The Euclidean algorithm that finds the greatest common factor of two numbers.

Other Work:

Euclid also wrote works on perspective, conic sections, spherical geometry, and possibly quadric surfaces.

As well as the Elements, 5 other works of Euclid have survived to the present day.

• Data deals with the nature and implications of "given" information in geometrical problems; the subject matter is closely related to the first four books of the Elements.
• On Divisions of Figures, which survives only partially in Arabic translation, concerns the division of geometrical figures into two or more equal parts or into parts in given ratios. It is similar to a third century (AD) work by Heron of Alexandria.
• Optics, the earliest surviving Greek treatise on perspective, contains propositions on the apparent sizes and shapes of objects viewed from different distances and angles.
• Catoptrics, which concerns the mathematical theory of mirrors, particularly the images formed in plane and spherical concave mirrors.

All of these works follow the basic logical structure of the Elements, containing definitions and proved propositions.

There are four works credibly attributed to Euclid which have been lost.

• Conics was a work on conic sections that was later extended by Apollonius of Perga.
• Porisms might have been an outgrowth of Euclid's work with conic sections, but the exact meaning of the title is unknown.
• Pseudaria (Book of Fallacies) was a text about errors in reasoning.
• Surface Loci concerned either loci (sets of points) on surfaces or loci which were themselves surfaces.

Furthermore, Euclid's method of proving mathematical theorems by logical reasoning from accepted first principles remains the backbone of mathematics and is responsible for that field's characteristic rigor.

Trivia:

• The asteroid 4354 Euclides is named after Euclid.
• Euclides is a lunar crater named after him.
• Euclid Avenue in Cleveland, Ohio.
• In Benton Harbor, Michigan, Euclid Avenue runs parallel to Napier Avenue, a street that shares its name with the 17th century mathematician John Napier.
• There is a city called Euclid in Ohio with a population of 52,000+
• In Colorado there is a Euclid Middle school located on Euclid Avenue.
• The Euclid math competition, from the University of Waterloo.
• Euclid was ranked 14^th in the book "The 100: A Ranking of The Most Influential Persons in History" by Michael H. Hart's .
• Euclid is the name of a town in the SNES game, Tales of Phantasia.
• Euclid was the computer's name in the movie Pi.

Euclid of Alexandria

Pages from Euclid's Elements

Euclid Labs