The MacPlatonic Solids

Tony Mann

University of Greenwich

“Early Mathematics”

• How can we approach the mathematics of the past without viewing it through the distorting lens of our own mathematical culture?

• Early music

• We can listen to original instruments of the composer’s time but we don’t have original ears!

Neolithic carved stone balls

(British Museum)

Neolithic carved stone balls

Towie, Aberdeenshire (Wikimedia Commons)

Neolithic carved stone balls

Golspie, Aberdeenshire (Dr James B Simpson, via

Wikimedia Commons)

Ayrshire (Wikimedia Commons)

Neolithic carved stone balls

The Platonic Solids• Five regular convex polyhedra

exist

• Tetrahedron, cube, octahedron, dodecahedron, icosahedron

• Attributed to Thaetetus

• Described in Plato’s Timaeus © Marie-Lan Nguyen / Wikimedia Commons

The MacPlatonic Solids

A petrosphere

Thanks to John Sharp

Inspiration?

Thanks to John Sharp

Uses?

• Bolas?

• Weights or measures?

• Ball games?

• Sink stones?

• Rollers for megaliths?

• Oracles / dice?

• Denoting “the right to speak”?

Egyptian dice

Myers Collection, Eton College

Currently on display, Barber Institute

Postcard (I)

Postcard (II)

Contemporary art

Red Fruit

Peter Randall-Page

Contemporary public art

First Conundrum (2000)Remco de Fouw

Edinburgh

First Conundrum

Palaeolithic Hand-axes

Kentish hand-axes (Wikimedia Commons)

Hand-axes

• Found in large numbers in Europe, Africa, North Asia

• Made by knapping

• For butchery? (Effective)

• Killer frisbees?

• But most specimens show no signs of use

• Made to attract women?

Celts

Behold the mysterious celt,

with a property that amuses.

One way it will spin,

the other way it refuses.

Andy Titcomb, Wikimedia Commons

Mathematics of rattlebacks

• Worked out in the 1980s by

Sir Hermann Bondi (Cambridge)

Mont Hubbard (Univ of California)

Rattleback

(Hugh Hunt)

Conclusion

• We’d like to connect mathematically with our ancestors

• But we can’t have “original ears”