Euclid of Alexandria and His Contributions to Geometry

Painting of Euclid drawing on a slate
De Agostini / A. Dagli Orti, Getty Images

Euclid of Alexandria lived in 365-300 BC (approximately). Mathematicians usually refer to him simply as "Euclid," but he's sometimes called Euclid of Alexandria to avoid confusion with the Green Socratic philosopher Euclid of Megara. Euclid of Alexandria is considered to be the Father of Geometry.

Very little is known about Euclid's life except that he taught in Alexandria, Egypt. He may have become educated at Plato's Academy in Athens, or possibly from some of Plato's students. He is an important historical figure because all of the rules we use in Geometry today are based on the writings of Euclid, specifically The Elements.

The Elements includes the following Volumes:

  • Volumes 1-6: Plane Geometry
  • Volumes 7-9: Number Theory
  • Volume 10: Eudoxus' Theory of Irrational Numbers
  • Volumes 11-13: Solid Geometry

The first edition of the Elements was actually printed in 1482 in a very logical, coherent framework. More than one thousand editions have been printed throughout the decades. Schools only stopped using the Elements in the early 1900s, some were still using it in the early 1980s, however, the theories continue to be those that we use today.

Euclid's book the Elements also contains the beginnings of number theory. The Euclidean algorithm, which is often referred to as Euclid's algorithm, is used to determine the greatest common divisor (gcd) of two integers. It is one of the oldest algorithms known and was included in Euclid's Elements. Euclid's algorithm does not require factoring. Euclid also discusses perfect numbers, infinite prime numbers, and Mersenne primes (the Euclid-Euler theorem).

The concepts presented in The Elements weren't all original. Many of them had been proposed by earlier mathematicians. Possibly the greatest value of Euclid's writings is that they present the ideas as a comprehensive, well-organized reference. The principals are supported by mathematical proofs, which geometry students learn even to this day.

Main Contributions

He is famous for his treatise on geometry: The Elements. The Elements makes Euclid one of if not the most famous mathematics teacher. The knowledge in the Elements has been the foundation for teachers of mathematics for over 2000 years

Geometry tutorials wouldn't be possible without the work of Euclid.

Famous Quote: "There is no royal road to geometry."

In addition to his brilliant contributions to linear and planar geometry, Euclid wrote about number theory, rigor, perspective, conical geometry, and spherical geometry.

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Euclidean Geometry vs Non-Euclidean Geometry

At the time, and for many centuries, Euclid's work was simply called "geometry" because it was assumed to be the only possible method of describing space and the position of figures. In the 19th century, other types of geometry were described. Now, Euclid's work is called Euclidean geometry to distinguish it from the other methods.