Albion College

Mathematics and Computer Science

Mathematics and Computer Science

COLLOQUIUM

Relationships between Platonic Solids and Scottish Carved Stone Balls

David A. Reimann

In this talk, we will trace the history of Platonic Solids and Scottish carved stone balls,
then examine the relationships between these objects.
The first account of the Platonic solids,
namely the regular tetrahedron, cube, octahedron, dodecahedron, and icosahedron, were first given by Plato in about 360 BCE.
However, most scholars contend that these objects were known to others before Plato.
Over 425 Neolithic stone balls with carved knobs have been found in northern Scotland and date to about 2000 BCE.
There is no recorded use of these objects, which has resulted in much speculation about their purpose.
A theory that these were models of Platonic solids was advanced in 1979.
Yet these objects are clearly not polyhedra and thus do not represent examples of Platonic solids, despite recent claims to that effect.
In some cases, the symmetry of the knob placements is consistent with the symmetries associated with Platonic solids.
The symmetric form contributes to the aesthetic appeal of many carved stone balls, thus they can be considered very early examples of mathematical art.
Examples are shown along with pictures of modern art that they have inspired.
Could knowledge of these objects have traveled to from Scotland to Greece and helped develop the
Greek theory of Platonic solids?