8/2/2019 Strictly Platonic (On The Platonic Solids)

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Ken Earley

Dr. McGinnis

09-12-11

Hon 3010

Strictly Platonic

Many of the ideas and thought processes that were brought to light in AncientGreece, are still around today. They work together in complex matrix that works towards

explaining the universe. Various philosophers set out to explain parts of the cosmos;

their ideas were then either discounted or expanded upon. Two philosophers still talked

about eons later, Pythagoras and Plato, had philosophies that intertwine to explain more

of our universe.

The basis of Pythagoreanism lies in two separate values, on which lifestyles were

built, metempsychosis and structure. Pythagoras emphasis on structure resulted in a

self-imposed lifestyle that ritualized diet and religion. His search for structure throughout

his life and the universe resulted in a lot of what he is remembered for. This search

yielded advances in mathematical structures like numerical classification and geometry.

Pythagoras had a large impact in advancing mathematics and science, his impact canalso be seen through the transparent lives of many other philosophers. Plato is another

philosopher who valued structure, and searched for it.

Among the many things that Plato influenced over his years on the earth,

Platonic Solids is one of the most interesting. There are five basic elements to the

Ancient Greek world, to each are assigned a different Platonic solid. These five figures

consist ofthe cube, dodecahedron, icosahedron, octahedron, and tetrahedron. Plato

associated each figure with a basic element. The associations werent made haphazardly;they are easily relatable, keeping in mind each element and the physical representations

of each solid. Looking at a cube, the corners seem to be fairly sharp, until you look at the

other Platonic solids, which have much more drastic angles. The cube represents earth,

simply illustrated by dirt. Dirts crumblingflow, isnt as smooth or fine as the flow of a

liquid, which has a more complex structure, of the five solids. This chunk-like structure

of the cube causes a jagged, or rough flow, like sifting dirt through your hands. Liquid,

or water, is represented by the icosahedron, the most spherical appearing solid, as such

water flows smoothly, as if youre rolling microscopic balls out of your hand. Air, the

octahedron of the group, has molecules that are smooth and fine enough that we barely

feel them most of the time. Fire is represented by the tetrahedron, a very sharp,pointy,

polyhedron that represents the stabbing heat of fire.

The understanding of these four basic Greek elements is fairly simple, though the

math behind them can become rather complex. There are five of these solids, each are

mathematically perfectly symmetrical polyhedra. Each of the five figures have many

shared characteristics that help classify them as Platonic solids. Each figure has

corresponding numbers of faces and vertices, arranged so that each vertex has a sum of

angles that are less than 360 degrees and have at least three faces that form the corner. If

these conditions arent met the figure formed wont be a truly three-dimensional,

symmetrical figure. Also, each figure can be linearly represented, as the number of faces

plus the number of vertices is equal to the number of edges, plus two. (# of faces + # of

vertices = # of edges + 2). All of the math behind the justification for the existance of

only five Platonic solids falls in line with the basis Pythagorean mathematics.

http://mathworld.wolfram.com/Cube.htmlhttp://mathworld.wolfram.com/Dodecahedron.htmlhttp://mathworld.wolfram.com/Icosahedron.htmlhttp://mathworld.wolfram.com/Octahedron.htmlhttp://mathworld.wolfram.com/Tetrahedron.htmlhttp://mathworld.wolfram.com/Tetrahedron.htmlhttp://mathworld.wolfram.com/Octahedron.htmlhttp://mathworld.wolfram.com/Icosahedron.htmlhttp://mathworld.wolfram.com/Dodecahedron.htmlhttp://mathworld.wolfram.com/Cube.html

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