# Mathematician:Euclid

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## Mathematician

Greek mathematician about whom little is known, apart from:

- He taught in Alexandria (then a Macedonian colony, the hub of the Hellenic world);
- 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.)

Not to be confused with the Socratic philosopher Euclid of Megara.

## 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

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 Norm
- Euclidean Norm of Matrix, otherwise known as a Frobenius Norm

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

Results named for **Euclid** can be found here.

Definitions of concepts named for **Euclid** can be found here.

## Publications

- 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)

## Misattributions

*The laws of nature are but the mathematical thoughts of God.*

- This misattribution seems first to have appeared in
*A Mathematical Journey*by Stanley Gudder ($1976$), p. xv.

- This misattribution seems first to have appeared in

- It is suspected that it originated from Kepler.

- Many sources have propagated this mistake, and many of those use it as an excuse to preach sermons on the subject.

## Anecdotes (of questionable accuracy)

*Ptolemy once asked Euclid if there was any shorter way to a knowledge of geometry than that of the*Elements*, and he replied that there is no royal road to geometry.*

*Someone who had begun to read geometry with Euclid, when he had learned the first proposition, asked him: "What shall I get from learning these things?" Euclid called his slave and said, "Give this person a penny, since he must make a profit out of what he learns."*- -- Stobaeus

## Critical View

*[Abraham Lincoln] studied and nearly mastered the six books of Euclid since he was a member of Congress.**He began a course of rigid mental discipline with the intent to improve his faculties, especially his powers of logic and language. Hence his fondness for***Euclid**, which he carried with him on the circuit till he could demonstrate with ease all the propositions in the six books; often studying far into the night, with a candle near his pillow, while his fellow-lawyers, half a dozen in a room, filled the air with interminable snoring.- -- Abraham Lincoln:
*Short Autobiography*($1860$) - -- Quoted in 1937: Eric Temple Bell:
*Men of Mathematics*:*They Say: What Say They? : Let Them Say*

- -- Abraham Lincoln:

## Also known as

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

Proounced: ** Yoo-klid**.

## Sources

- 1921: Sir Thomas Heath:
*A History of Greek Mathematics: Volume $\text { I }$*... (previous) ... (next): Preface - 1926: Sir Thomas L. Heath:
*Euclid: The Thirteen Books of The Elements: Volume 1*(2nd ed.) ... (previous) ... (next): Introduction: Chapter $\text{I}$. Euclid and the Traditions About Him - 1926: Sir Thomas L. Heath:
*Euclid: The Thirteen Books of The Elements: Volume 1*(2nd ed.) ... (previous) ... (next): Introduction: Chapter $\text{II}$. Euclid's Other Works - 1937: Eric Temple Bell:
*Men of Mathematics*... (previous) ... (next):*They Say: What Say They? : Let Them Say* - 1937: Eric Temple Bell:
*Men of Mathematics*... (previous) ... (next): Chapter $\text{II}$: Modern Minds in Ancient Bodies - 1952: T. Ewan Faulkner:
*Projective Geometry*(2nd ed.) ... (previous) ... (next): Chapter $1$: Introduction: The Propositions of Incidence: $1.1$: Historical Note - 1980: David M. Burton:
*Elementary Number Theory*(revised ed.) ... (previous) ... (next): Chapter $1$: Some Preliminary Considerations: $1.3$ Early Number Theory - 1986: David Wells:
*Curious and Interesting Numbers*... (previous) ... (next): A List of Mathematicians in Chronological Sequence - 1989: Ephraim J. Borowski and Jonathan M. Borwein:
*Dictionary of Mathematics*... (previous) ... (next):**Euclid**(pronounced*You*-clid) - 1991: David Wells:
*Curious and Interesting Geometry*... (previous) ... (next): A Chronological List Of Mathematicians - 1992: George F. Simmons:
*Calculus Gems*... (previous) ... (next): Chapter $\text {A}.4$: Euclid (flourished ca. $300$ B.C.) - 1997: David Wells:
*Curious and Interesting Numbers*(2nd ed.) ... (previous) ... (next): A List of Mathematicians in Chronological Sequence - 1998: David Nelson:
*The Penguin Dictionary of Mathematics*(2nd ed.) ... (previous) ... (next):**Euclid**(*c.*300-260 bc) - 2008: David Nelson:
*The Penguin Dictionary of Mathematics*(4th ed.) ... (previous) ... (next):**Euclid**(*c.*300-260 bc) - 2008: Ian Stewart:
*Taming the Infinite*... (previous) ... (next): Chapter $2$: The Logic of Shape: Euclid - 2014: Christopher Clapham and James Nicholson:
*The Concise Oxford Dictionary of Mathematics*(5th ed.) ... (previous) ... (next):**Euclid**(about 300 bc)

- For a video presentation of the contents of this page, visit the Khan Academy.

*Beware: the entry starts with the above misattributed quote, and then launches into a biography of Abraham Lincoln. The politically squeamish may wish to avoid this link.*