# Maths and Philosophy #2: Plato

Following on from Monday’s post, it is only fitting to talk about Socrates’ student, Plato. Born between 429 and 423 BC, Plato was a Greek mathematician and philosopher, who was a strict follower of Socrates’ ideas and beliefs, adopting almost everything about Socrates including his style, philosophy and manner of debate.

Despite being remembered today as a philosopher, Plato played an important role in encouraging the study of mathematics in ancient Greece. He founded his Academy in Athens in 387 BCE, taking inspiration from Pythagoras, where he taught mathematics as a branch of philosophy. Plato believed that one must study five mathematical disciplines: arithmetic, plane geometry, solid geometry, astronomy and harmonics (as depicted in The Republic).

Plato became known as the ‘maker of mathematics’ as his Academy hosted some of the most prominent mathematicians of the time, including Eudoxus, Theaetetus and Archytas.

Plato demanded his students to give accurate definitions, clearly stated assumptions and logical deductive proof, insisting that geometric proofs be demonstrated with no aids other than a straight edge and a compass. Furthermore, he posed to his students the ‘Three Classical Problems’: squaring the circle, doubling the cube and trisecting the angle. Thus, these problems have become identified with Plato, although he was not the first to ask them.

However, as a mathematician, Plato is most well known for his identification of 5 regular symmetrical 3D shapes, which he thought were the basis for the whole universe. They have become known as the Platonic Solids:

• the tetrahedron: made of 4 regular triangles, represented fire
• the octahedron: made of 8 triangles, represented air
• the icosahedron: made of 20 triangles, represented water
• the cube: made of 6 squares, represented earth
• the dodecahedron: made up of 12 pentagons, represented the Universe

Platonic solids have inspired many mathematicians and geometers for many centuries. For example, in around 1600, Kepler created a system of nested Platonic solids and spheres to approximate the distances of well known planets from the Sun. (However, this was later abandoned when it was shown to be not accurate enough.)

Source: 1 | 2 | 3

Stay tuned for the last post of this series on Friday! M x