## -0425 – Plato – bio

Plato was born in Athens, Greece around -425. While he is mostly known today as the father of western philosophy, he also studied and taught mathematics and considered math as a branch of philosophy and an important method of understanding. Plato followed in the footsteps of Pythagoras, was a student of Socrates, and founded a school known as “The Academy” at which Aristotle became a student. The Academy is considered to be the first western institution of higher learning and is credited with leading philosophical thought in Greece for several centuries.

Plato wrote a major manuscript called, “The Republic”, that discusses in a dialogue format the concept of justice and how it should be applied in governance. It also discusses other spiritual and philosophical topics.

Plato was involved in identifying five “regular” solid shapes where each face is the same shape and each corner (vertex) is identical to the others. The five shapes are:

• Tetrahedron – 4 sides with 3 angles in each side
• Hexahedron (cube) – 6 sides with 4 angles in each side
• Octahedron – 8 sides with 3 angles in each side
• Dodecahedron – 12 sides with 5 angles in each side
• Icosahedron – 20 sides with 3 angles in each side

The Five Platonic Solids – [faricy.net]

The simplest of polyhedra, the Platonic Solids are the convex polyhedra made of regular convex polygons. They are all regular polyhedra, meaning all faces are congruent regular polygons and all vertices are identical. (The faces and vertex configurations of regular polyhedra may also be star polygons; the stellations of the dodecahedron are good examples.) There are only five such polyhedra, as at least three polygons must meet at each vertex but their interior angles must sum to less than 360°. They can be described by Schläfli Symbol {p,q}, C&R Symbol pq, or Wythoff Symbol q | 2 p, where q regular p-gons meet at a vertex.

The Platonic Solids are named after Plato (c. 350 BC), although it is now known that he was not the first to discover them. Plato associated the cube, octahedron, icosahedron, tetrahedron and dodecahedron with the elements, earth, wind, water, fire, and the cosmos, respectively.

5 Platonic Solids – Numberphile