Symmetry from the Greek words “syn” and “metros”

The five regular polyhedra (tetrahedron, hexahedron or cube, octahedron, dodecahedron and icosahedron) are often cited as an expression of perfect symmetry. These polyhedra are today called Platonic solids after the Greek Philosopher Plato. He thought they were so fundamental that they must be the basic building units shaping the material world. The word symmetry began shaping at around the same time, when Plato founded his science and philosophy institution in Athens in 387 BC. In his book about symmetry [1], Marcus du Sautoy explains how the word symmetry made its way into the English language, from Greek via Latin:

It is the Greek language that assigned a name to the common trait that bound Plato's five objects [Platonic solids] together: symmetros. In the first century AD the Roman author Pliny the Elder bemoaned Latin's lack of a word for symmetry. Symmetros combines the Greek words syn, meaning ‘same’, and metros, meaning ‘measure’. Together they describe something ‘ with equal measure’. Symmetry for the Greeks was reserved for describing an object in which some of the internal physical dimensions were the same across the shape. In symmetrical solids the edges were all the same length, the faces all had the same area, and the angles between adjacent faces were all equal. Symmetry is about measurement and geometry. It would take some time for symmetry to become recognized as a mathematical property that goes beyond simple measurement, although the Greek philosophers were beginning to explore the idea of symmetry as a powerful image beyond physical shapes.

Keywords: geometry, mathematics, etymology, history, Greek, Latin

Reference
[1] Marcus du Sautoy: Symmetry. A Journey into the Patterns of Nature. First Harper Perennial Edition, Harper Collins Publishers, New York, 2009.