«Let no one ignorant of geometry enter» - this phrase was engraved at the door of Plato's Academy (Ancient Greek philosopher and scientist – 427 – 347 B.C.). Those who did not comprehend music, geometry and astronomy were not taken to Plato’s Academy (fig. 1).
“What are the elements of nature, the elements which provide the foundation for things?” - the question arises in Plato’s philosophy (fig. 2). These are the four elements of nature: Earth, Water, Air, Fire. Plato talks about 4 types of particles, corresponding to the 4 prototypes, fundamental elements. According to Plato, all rocks, ores and other non-melting substances are referred to Earth element solids. All melting substances he refers to Water element; all vapours and gaseous – to Air element and all flammable - to Fire element.
Fire is red and flammable, and Earth is dense, heavy and opaque, but that is how we perceive the natural elements with the help of our body. These properties often do not say anything about what are the Fire and the Earth themselves. To learn the essence of fundamental principles, it is necessary to find out what images and numbers helped the Demiurge to organize these elements, i.e. one needneeds to figure out the mathematical definitions of these elements.
And Plato gets the geometric images of the primary elements on the following basis:
- Four geometric images must represent the basic physical properties (hardness, fusibility, air-likeness, fire-likeness);
- At least 3 types of natural elements (Water, Air, Fire) must transform into each other;
- Archetypes (ideas) of elements must be accurate, aesthetically and mathematically perfect.
During Plato’s life, mathematician, Theaetetus developed the geometry of regular polyhedra. Plato used that mathematical novelty.