THE PLATONIC SOLIDS

The properties of solid figures have kept mathematicians occupied for centuries. Regular polyhedra are formed from regular polygons such as squares or triangles and mathematicians have failed to find any more than five of them.

Although they were defined by Pythagoras two hundred years before Plato was born, they are known collectively as the platonic solids, named in honour of PLATO by the geometer Euclid.

“THE PLATONIC SOLIDS – The regular polyhedron is defined as a three-dimensional solid comprising regular polygons for its surfaces – and with all its surfaces, edges and vertices identical. The five regular polyhedra are the tetrahedron (four triangular faces), the cube (six square faces), the octahedron (eight triangular faces), the dodecahedron (twelve pentagonal faces) and the icosahedron (twenty triangular faces).”

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DEMOCRITUS of ABDERA (c.460 – c.370 BCE)

DEMOCRITUS

Fifth century BCE – Greece

‘Matter is made up of empty-space and an infinite number of tiny invisible particles called atomos or atoms’

Democritus’ atomic theory was probably based on previous ideas of other Greek philosophers. It was the first scientific attempt to explain the nature of matter; however, many of Democritus’ assumptions have now been proved wrong.

Democritus left no written record of his work and little is known about his life, but we know about his atomic theory from the second century CE Greek cynic and biographer Diogenes Laertius’ book ‘Lives of Eminent Philosophers’.

Democritus reasoned that, if he were to attempt to cut an object in half over and over, he would eventually reach a tiny grain of matter that could not be cut in half. Democritus called these hypothetical building blocks of matter “atoms”, after the Greek atomos, ‘uncuttable’ – suggesting that atoms could not be divided indefinitely into smaller parts and that it is impossible to create new matter. All that you can see is a product of packing together a myriad of miniscule atoms.
He said that atoms were always in motion and as they moved about they collided with other atoms; sometimes they interlocked and held together, sometimes they rebounded from collisions. The Roman poet Lucretius (c.94 – c.55 BCE) imagined Democritus’ atoms with hooks that fastened them together.

His remains one of the earliest attempts to explain the universe with a few simple physical and mathematical laws. For Democritus, there were only two things, space and atoms. Both had always existed and always would exist because de nihilo nihil ‘nothing could come from nothing’. Balancing the idea that the atom is the only unit of being, the Void is the single kind of not being. The higher the atom-to-void ratio, the denser the material. Atoms simply combined with other atoms in the Void; solid, impenetrable, indivisible blocks which never change; they combine to form different things, from rocks to plants to animals. When these things died or fell apart the structure disintegrated and the atoms were free to form new things by combining again in a different shape with other atoms.

Democritus reasoned that the method by which the atoms could combine was through their different shapes. While all the atoms were the same in substance, liquids were thought to have smooth round edges so they could fall over each other, while those that made up solids had toothed rough edges, which could hook on to each other.
Atoms of fire had tetragonal shape; atoms of earth, cubic; atoms of air, octahedral; and those of water were icosahedral.

Democritus’ thesis completely rejects the notion of the spiritual or the religious. The soul was explainable through a fast-moving group of atoms brought together by encasement in the body. The motion produced sensations that interacted with the mind (itself a collection of atoms) to produce thoughts and feelings. Once dead, the object that held the fast-moving atoms disintegrated and thus released they could separate and interact with other atoms to form new things. Leaving no place for abstract notions of the supernatural or an afterlife, this marked the arrival of materialism.

THE PLATONIC SOLIDS

As with physical form, Democritus argued that other perceived differences in things, such as their taste, could be explained by the edges of the atoms. Likewise the colour of things was explained by the position of the atoms within a compound, which would result in darker or lighter shades.

Democritus had envisaged free atoms as flying about ceaselessly through empty space. What was needed therefore, was a precise picture of how atoms moved through space. Such a picture required knowledge of the laws that governed all motion.

DEMOCRITUS CRATER

The Greek philosopher ARISTOTLE rejected Democritus’ idea of the atom and said that matter was completely uniform and continuous. The influence of Aristotle was extraordinary. His concept of matter was at variance with modern thinking, but it was accepted for around 20 centuries until it was replaced by DALTON‘s atomic theory in 1808.

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