PLATO: THE ACADEMY  
History
 

1. BACKGROUND TO THE PERIOD  

Aristotle and Plato in the centre of Raphael's painting "The School in Athens". The Vatican Museum.

The Peloponnesian Wars took place in the IVth century B.C. Sparta fought against Athens and behind them other Greek towns followed them into warfare. Sparta called on Persia to help them keep control of the towns they had occupied. Athens and Thebes became allies and together managed to defeat Sparta. King Philip of Macedon took advantage of the situation and became ruler of Greece. His reign lasted from 360 B.C. to 336 B.C. when, upon his death, his son Alexander took the throne. Alexander the Great was responsible for the invasion of the Persian empire, which included Syria, Palestine, Egypt, Mesopotamia and Iran.

This century began with the death of Socrates (399 B.C.) The two great philosophers Aristotle and Plato, one of Socrates students and admirers also belonged to this period along with Archytas. Aristotle was Alexander the Great's private tutor and instilled in him the superiority of the Hellenic culture and encouraged him to go East and extend his empire. Plato managed to bring the greatest thinkers of the time together at his Academy in Athens. His contributions to mathematics include his rigorous method of justifying solutions through logical reasoning, his analytical method of demonstration and the conservation, transmission and development of mathematical knowledge at that time

The most significant mathematicians of the period were:

Plato

He wrote Timaeus, a treatise about regular solids and how they relate to 'cosmic bodies'.

 

A close up of "The School in Athens"

Aristotle (384 B.C. - 322 B.C.)

The first systemiser of Logic

He proved the irrationality of the square roots from 3 to 17 (perfect squares excluded). He appears to have used Aristotle's method for the square root of 2. 

 

Theodorus of Cyrene (390 B.C.)
Theaetetus of Attica

 (414 B.C. - 369 B.C.)

 

 



He was the first to write about the octahedron and the icosahedron. He is attributed the theorem proving the existence of 5 and only 5 regular polyhedra.

He found the ratios of the edges of the regular solids to the radius of the circumscribed sphere.

His definition of proportion was similar that used today. This definition was significant as it could be used with incommensurable quantities. He formulated the axiom which served as the basis for the method of exhaustion. This method was based on the idea of infinitesimals.

 

Eudoxus of Cnidus (355 B.C.)

Menaechmus (350 B.C.) He discovered the ellipse, the hyperbola and the parabola. This discovery allowed the duplication of the cube to be calculated.
Dinostratus (350 B.C.)

He proved the squaring of the circle by using the trisectrix of Hippias.

This curve became known as the quadratrix.

Autolycus of Pitane (330 B.C.)

His treatise On the Moving Sphere is the oldest written work to survive until the present day. 

Archaeological Museum at Pergamon Some of the smaller pieces from excavations of ancient Pitane form part of its collection


       
           
  Rosa Jiménez Iraundegui
 
Spanish Ministry of Education. Year 2001