ProofWiki:Mathematicians/Euclid

In Greek: Εὐκλείδης (Eukleídēs), also known as Euclid of Alexandria.

Little is known about him, apart from:

• He taught in Alexandria (then a Macedonian colony);
• He assembled the geometry text The Elements, possibly the most famous mathematics text book of all time.

There is controversy as to whether he did actually exist. It has been suggested that the name Euclid was a pseudonym for a team of mathematicians working as a team. (See Bourbaki for a modern example of this.)

Nationality

Greek

History

• Born: c. 325 BCE
• Died: c. 265 BCE, Alexandria, Egypt

Theorems and Definitions

• The field of Euclidean geometry.
• Euclid's Lemma
• Euclid's Theorem
• Euclid's Algorithm
• Euclidean Relation
• Euclid Numbers (erroneously so named - such numbers derive from a version of the proof of Euclid's Theorem that he himself never made.)

Several concepts are named after him, but they were so named because they possess properties inherited from concepts which Euclid introduced:

• Euclidean Domain
• Euclidean Metric, Euclidean Space and Euclidean Topology
• Euclidean Relation
• Euclidean Valuation

Books and Papers

• c. 300 BCE: The Elements.
• The Pseudaria (or Pseudographemata) (referred to by Proclus, believed irreparably lost), a more elementary primer on geometry.
• The Data elementary exercises in analysis, supplementary to The Elements.
• On Divisions (of Figures) (mentioned by Proclus, lost in Greek but survived in Arabic), concerns dissection of geometric figures.
• The Porisms, a collection of theorems and problems in more advanced geometry.
• The Surface-Loci (mentioned by Pappus, now considered lost), may have concerned surfaces of revolution.
• The Conics, now lost, but according to Pappus may have been the basis of the work of the same name by Apollonius. It was well-known to Archimedes who quoted it extensively.
• The Phaenomena, a work of astronomy and spherical geometry which still exists.
• The Optics.
• Elements of Music (but it is disputed as to whether he actually wrote this).

Also see

• John J. O'Connor and Edmund F. Robertson: "Euclid": MacTutor History of Mathematics archive

• George F. Simmons: Calculus Gems (1992), Chapter $\text {A}.4$