# Mathematician:Archimedes of Syracuse

## Contents

## Mathematician

Greek mathematician, physicist, astronomer, engineer and general all-round inventor.

Perfected the method of exhaustion.

Considered by many (with some justification) to be the greatest mathematician, inventor and physicist of the ancient world.

Other achievements:

- Discovered the principle of the lever
- Originated the concept of the center of gravity, and found them for several plane figures
- With his machines, he held off several attacks by the Romans under Marcellus

## Nationality

Greek

## History

- Born: c. 287 BCE in Syracuse in Magna Graecia (in Sicily, now part of Italy)
- Died: c. 212 BCE in the Second Punic War. Supposed to have been by a drunken Roman soldier because either:
- He was contemplating a problem in geometry and was unwilling to be disturbed to answer a summons from the Roman general who had captured the city;
- He was killed trying to surrender to the Romans, and a soldier killed him to plunder his mathematical instruments, which the soldier thought were valuable.

## Theorems and Definitions

- Volume of Sphere
- Quadrature of Parabola
- Area of Circle
- Closed Form for Triangular Numbers
- Sum of Sequence of Squares
- Volume of Displaced Fluid equals Volume of Submerged Object
- Principle of Lever

- Archimedean Spiral (although some sources credit this to Conon of Samos)
- Archimedean Principle, otherwise known as the Archimedean Law
- Archimedes' Principle
- Archimedean Property
- Archimedean Polyhedron

Results named for **Archimedes of Syracuse** can be found here.

Definitions of concepts named for **Archimedes of Syracuse** can be found here.

## Inventions

- Archimedes Screw
- A hydraulic mechanism modelling the solar system against the background of the fixed stars

## Writings

These works of Archimedes have survived in some form:

*On Plane Equilibriums*(2 books)*On the Quadrature of the Parabola**The Method*(which includes the calculation of the volume of a sphere)*On the Sphere and Cylinder*(2 books)*On Conoids and Spheroids**On Spirals**On Floating Bodies*(2 books)*Measurement of a Circle**The Sand-Reckoner*

The following works appear no longer to exist:

*On Sphere-making*, believed to have dealt with the techniques for building his solar system model- A work on semiregular polyhedra, mentioned by Pappus of Alexandria
- A work on the number system proposed in
*The Sand-Reckoner*, mentioned by Archimedes himself *On balances and levers*mentioned by Pappus of Alexandria- A treatise about mirrors, mentioned by Theon of Alexandria

## Notable Quotes

*Give me a place to stand on, and I can move the earth.*

*Eureka, eureka!*

*Do not disturb my circles.*

*I do not want to be thought to have uttered vain words, but equally because I am persuaded that it will be of no little service to mathematics; for I apprehend that some, either of my contemporaries or of my successors, will, by means of the method when once established, be able to discover other theorems in addition, which have not yet occurred to me.*- -- from the preamble to
*The Method*

- -- from the preamble to

## Critical View

*From this day forth Archimedes is to be believed in everything he says.*

*He who understands Archimedes and Apollonius will admire less the achievements of the foremost men of later times.*

*Archimedes will be remembered when Aeschylus is forgotten, because languages die and mathematical ideas do not.*- -- G.H. Hardy

*The death of Archimedes at the hands of a Roman soldier is symbolic of a world change of the first magnitude. The Romans were a great race, but they were cursed by the sterility which waits upon practicality. They were not dreamers enough to arrive at new points of view, which could give more fundamental control over the forces of nature. No Roman lost his life because he was absorbed in the contemplation of a mathematical diagram.*

*The treatises are, without exception, monuments of mathematical exposition; the gradual revelation of the plan of attack, the masterly ordering of the propositions, the stern elimination of everything not immediately relevant to the purpose, the finish of the whole, are so impressive in their perfection as to create a feeling akin to awe in the mind of the reader. ... There is at the same time a certain mystery veiling the way in which he arrived at his results. For it is clear that they were not*discovered*by the steps which lead up to them in the finished treatises.*- -- T.L. Heath:
*A History of Greek Mathematics*

- -- T.L. Heath:

*... only praise is due Archimedes for not appreciating the old-maidishness of Plato's rigidly corseted description of what the muse of geometry should be.*- -- 1937: Eric Temple Bell:
*Men of Mathematics*

- -- 1937: Eric Temple Bell:

## Also known as

Archimedes has been given a number of soubriquets throughout the ages, for example: **the old man**, **the wise one**, **the master**, **the great geometer**.

## Sources

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

- 1937: Eric Temple Bell:
*Men of Mathematics*... (previous) ... (next): Chapter $\text{II}$: Modern Minds in Ancient Bodies - 1992: George F. Simmons:
*Calculus Gems*... (previous) ... (next): Chapter $\text {A}.5$: Archimedes (ca. $287$ – $212$ B.C.) - 1997: David Wells:
*Curious and Interesting Numbers*(2nd ed.) ... (previous) ... (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): $-1$ and $i$ - 2008: Ian Stewart:
*Taming the Infinite*... (previous) ... (next): Chapter $2$: The Logic Of Shape