# Mathematician:Pythagoras of Samos

## Mathematician

Greek philosopher whose contributions to mathematics were perhaps more limited than is generally believed.

Best known for being said to have provided the first known proof of Pythagoras's Theorem (or one of his students did) which had probably been known to the ancient Egyptians.

May have introduced the concept of structuring the study of geometry into a system of definitions, axioms, theorems and proofs.

Supposedly discovered the result: Sum of Angles of Triangle equals Two Right Angles, but there is a plausible case for suggesting that Thales of Miletus had discovered it previously, and passed it on via his teachings.

Legend has it that on discovering what is now known as Pythagoras's Theorem, he sacrificed an ox to give thanks to the deities, but this is unlikely given his vegetarian philosophical stance.

Investigated the mathematics of musical harmony. As a consequence, posited the idea of the "music of the spheres" from the supposition that each of the planets produced a sound proportional to its speed of movement through the sky.

Possibly the first to assert that the earth is spherical.

According to legend, he died in the flames of his school, set on fire by religious bigots who disapproved.

## Nationality

Greek

## History

- Born: between 580 and 572 BCE, Samos, Ionia
- Supposed to have travelled extensively: to Egypt at least, and maybe as far as Babylonia.
- Founded a school in Croton
- Died: between 500 and 490 BCE

## Theorems and Definitions

- Pythagorean Equation
- Pythagorean Mean
- Pythagorean Triple
- Pythagoras's Constant: $\sqrt 2$
- Proposition $47$ of Book $\text{I} $: Pythagoras's Theorem in Euclid's
*The Elements* - Pythagorean Identities

- Has also been credited with Proposition $44$ of Book $\text{I} $: Construction of Parallelogram on Given Line equal to Triangle in Given Angle in Euclid's
*The Elements*.

Results named for **Pythagoras of Samos** can be found here.

Definitions of concepts named for **Pythagoras of Samos** can be found here.

## Writings

No writings of his survive, although many forgeries have circulated.

## Notable Quotes

*God is number.*- -- Quoted in 1937: Eric Temple Bell:
*Men of Mathematics*: Chapter $\text{II}$: Modern Minds in Ancient Bodies

- -- Quoted in 1937: Eric Temple Bell:

*Number rules the universe.*- -- Quoted in 1993: Richard J. Trudeau:
*Introduction to Graph Theory*: $1$. Pure Mathematics: Why study pure mathematics?

- -- Quoted in 1993: Richard J. Trudeau:

## Critical View

*... one tenth of him genius, nine-tenths sheer fudge.*- -- Attribution unknown
- -- Quoted in 1937: Eric Temple Bell:
*Men of Mathematics*: Chapter $\text{II}$: Modern Minds in Ancient Bodies

*Dedicated when Pythagoras discovered that famous figure to celebrate which he made a grand sacrifice of an ox.*- -- Anonymous: found in The Greek Anthology Book $\text {VII}$. Epigrams: $119$

*Alas! why did Pythagoras reverence beans so much and die together with his pupils? There was a field of beans, and in order to avoid trampling them he let himself be killed on the road by the Agrigentines.*- -- Diogenes Laertius: found in The Greek Anthology Book $\text {VII}$. Epigrams: $122$

## Sources

- John J. O'Connor and Edmund F. Robertson: "Pythagoras of Samos": MacTutor History of Mathematics archive

- 1921: Sir Thomas Heath:
*A History of Greek Mathematics: Volume $\text { I }$*... (previous) ... (next): $\text I$: Introductory: The Greeks and Mathematics - 1929: Herbert Westren Turnbull:
*The Great Mathematicians*: Chapter $1$ - 1937: Eric Temple Bell:
*Men of Mathematics*... (previous) ... (next): Chapter $\text{II}$: Modern Minds in Ancient Bodies - 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*... (next): Introduction - 1986: David Wells:
*Curious and Interesting Numbers*... (previous) ... (next): A List of Mathematicians in Chronological Sequence - 1986: David Wells:
*Curious and Interesting Numbers*... (previous) ... (next): $10$ - 1989: Ephraim J. Borowski and Jonathan M. Borwein:
*Dictionary of Mathematics*... (previous) ... (next):**Pythagoras' theorem** - 1991: David Wells:
*Curious and Interesting Geometry*... (previous) ... (next): A Chronological List Of Mathematicians - 1992: George F. Simmons:
*Calculus Gems*... (previous) ... (next): Chapter $\text {A}.2$: Pythagoras (ca. $\text {580}$ – $\text {500}$ B.C.) - 1993: Richard J. Trudeau:
*Introduction to Graph Theory*... (previous) ... (next): $1$. Pure Mathematics: Why study pure mathematics? - 1997: David Wells:
*Curious and Interesting Numbers*(2nd ed.) ... (next): Introduction - 1997: David Wells:
*Curious and Interesting Numbers*(2nd ed.) ... (previous) ... (next): A List of Mathematicians in Chronological Sequence - 1997: David Wells:
*Curious and Interesting Numbers*(2nd ed.) ... (previous) ... (next): $10$ - 1998: David Nelson:
*The Penguin Dictionary of Mathematics*(2nd ed.) ... (previous) ... (next):**Pythagoras**(6th century bc) - 2008: David Nelson:
*The Penguin Dictionary of Mathematics*(4th ed.) ... (previous) ... (next):**Pythagoras**(6th century bc) - 2008: Ian Stewart:
*Taming the Infinite*... (previous) ... (next): Chapter $2$: The Logic of Shape: Pythagoras - 2014: Christopher Clapham and James Nicholson:
*The Concise Oxford Dictionary of Mathematics*(5th ed.) ... (previous) ... (next):**Pythagoras**(died about 500 bc)

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