# Person: Archytas Of Tarentum

Archytas was a Greek mathematician, statesman and philosopher who worked on the harmonic mean and the problem of duplicating the cube.

### Mathematical Profile (Excerpt):

• Archytas led the Pythagoreans in Tarentum and tried to unite the Greek towns in the area to form an alliance against their non-Greek neighbours.
• Plato wrote to Archytas who sent a ship to rescue him.
• This is done, however, because of the style of Archytas's philosophy rather than the strict chronology.
• Archytas was a pupil of Philolaus and so was a firm supporter of the philosophy of Pythagoras believing that mathematics provided the path to the understanding of all things.
• Although Archytas studied many topics, since he was a Pythagorean, mathematics was his main subject and all other disciplines were seen as dependent on mathematics.
• Archytas worked on the harmonic mean and gave it that name (it had been called sub-contrary in earlier times).
• Archytas solved the problem with a remarkable geometric solution (not of course a ruler and compass construction).
• One interesting innovation which Archytas brought into his solution of finding two mean proportionals between two line segments was to introduce movement into geometry.
• We know of Archytas's solution to the problem of duplicating the cube through the writings of Eutocius of Ascalon.
• Another interesting mathematical discovery due to Archytas is that there can be no number which is a geometric mean between two numbers in the ratio (n+1):n(n+1) : n(n+1):n.
• Archytas built on this earlier work and his discoveries are then largely those presented by Euclid in the Elements Book VIII.
• Archytas is sometimes called the founder of mechanics and he is said to have invented two mechanical devices.
• Finally we quote again from the writings of Archytas about his theory of how to learn.

Born about 428 BC, Tarentum, Magna Graecia (now Taranto, Italy). Died about 350 BC.

View full biography at MacTutor

Ancient Greek, Geometry, Origin Italy

Epochs: 1

Thank you to the contributors under CC BY-SA 4.0!

Github:

non-Github:
@J-J-O'Connor
@E-F-Robertson

### References

#### Adapted from other CC BY-SA 4.0 Sources:

1. Oâ€™Connor, John J; Robertson, Edmund F: MacTutor History of Mathematics Archive