Carved stone balls
The megalithic people migrated from the South,
one branch to Scandinavia, another to Brittany and Britain.
The megaliths of Britain date from 3000 BC to 1500 BC.
The largest circles in Britain are Avebury (SW of London)
and Callanish (on the island of Lewis in the Outer
Hebrides.) Both of these figure prominantly in the
work of Alexander Thom.
Euclid's Elements ends (Book XIII) with the
construction of the five Platonic solids:
and they proof there are no others.
- Tetrahedron (pyramid, 4 triangles)
- Cube (6 squares)
- Octahedron (two pyramids on a square base, 8 triangles)
- Icosahedron (20 triangles)
- Dodecahedron (12 pentagons)
The first three are generally regarded as
Pythagorean and known to the ancient Egyptians.
The latter two are usually thought to be discoveries
at Plato's Academy.
However, it seems they were
known to the megalithic people of Scotland,
from whom the carved stone balls
have come down to us. Some 387 are catalogued
by the National Museum of Antiquities of Scotland.
Cf. Dorothy N. Marshall, Carved stone balls, Proc. Soc. Antiquaries
Scotland, v. 108 (1976-77) pp. 40-72.
About the use of these balls: nobody knows. Among the speculations:
weights and measures, money or trade objects, ball games,
models for the celestial sphere.
Ralph H. Abraham, 25 April 1996.