To understand the history of the platonic solids in ancient Greek culture, I wish to take a look at a timeline of selected mathematicians. One of the earliest was Bailey’s, who is said to be one of the teachers of Pythagoras. Next on the timeline is Plato. But note that Pythagoras died in 495 bc and Plato does not appear until 427 BC. So according to these approximate dates, Plato and Protagoras never met no Did Plato ever make Euclid who does not appear on our timeline until 325 BC, over 20 years after Plato’s death. To round off our timeline, we have Archimedes. This is interesting if we study a famous Renaissance painting a fresco, in one of the chapels in the Vatican in Rome, called the School of Athens, which depicts many famous men of learning from the ancient Greek period, all in one room, so to speak. Here is Socrates, Plato, and Aristotle. Here’s a cropped image of Euclid, with a compass and Pythagoras writing in a book The School of Athens refers to the Academy, which Plato founded in Athens in 387 BC. Plato had been inspired by Pythagoras and the pythagoreans. The Academy remained a center of learning for 300 years, before being destroyed by the Romans in 86 BC. Legend has it that on the doorstep was written, let no one ignorant of geometry enter here. Such was the importance the Greeks placed on the understanding of mathematics. Many of the figures pictured did attend the academy like Euclid, but they did so at different times over that 300 year period. And some others never did. Like Pythagoras, who was dead and gone 100 years before the Academy was established. Going back to Pythagoras. He was born on the Greek island of Samos. As a young man, he had been educated. But it wasn’t until middle age and he traveled firstly to Egypt, and then to Babylon, where he learned more mathematics from those cultures. Returning to Greece, he founded a commune in southern Italy, at Croton, then part of the Greek sphere and attracted many followers. Here is a painting called Pythagoras in celebrate sunrise. The commune came to be regarded as a cult, with many cult like practices, like taking off your right shoe before your left, but washing your left foot before you’re ready They did not eat fish, no beans. The cult gained enemies who persecuted it. Nevertheless, the Pythagorean survived and their influence spread far and wide throughout Ancient Greece. In mathematics, the pythagoreans believed all his number. Everything they thought could be expressed in terms of rational numbers. They made discoveries about mathematical relationships, for instance, in music, and they knew most, if not all of the regular solids. Fill Elias a Pythagorean link the solids with the four classical elements earth, water, fire and air. Earth it Solid things, water, liquid things, for things that destroy an air, things that moved in his dialogue cumulus in 360 BC, Plato linked the ether or the universe to the fifth regular solid. So we end up with what’s known as the platonic solids. And finally, here they are. Fire is represented by the tetrahedron air, by the octahedron. Water by the icosahedron. Earth by the cube and the universe by the dodecahedron The idea that the platonic solids somehow explain the world persisted right up to the Renaissance, when the German mathematician Kepler proposed that the Botanic solids, explained the orbits of the planets around the sun, and that maybe this was God’s plan, even build a model in metal to show this. It wasn’t until later on, when he worked out the orbits of some of the other planets that he dropped this theory. So that’s a bit about the history of tonic solids. Next time we’ll look at a definition, and we’ll compare the platonic solids with the archimedean solids. I’ll see you then.