ancient mathematics

stoneBalls.jpg

Hundreds of approximately 3 inch stoneballs have been found in Scotland.

They are believed to date about 200BC and many of them (at least roughly) resemble circle packings of the sphere. even more intriguig: The combinatorics of all five platonic solids occur — see above image (well to be precise the two carvings in the center and right to it have the same combinatorics of their knobs but a ball having the 20 knobs for a icosahedron can be seen here). Their use is completely unknown.
A big collection can be found at the Hunterian (see here and a particular nice decorated one here)
The balls are well documented in
Dorothy N. Marshall, “Carved Stone Balls,” Proceedings of the Society of Antiquaries of Scotland 108, pp. 40-72, 1976/77. The reference is online at the Scociety of Antiquaries of Scotland pages
(goto this page and browse for the Proceedings of the Society of Antiquaries of Scotland).
The above image is from here and there cited as a scan from a book of Critchlow and Lawlor.

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