Transcript The MacPlatonic Solids: Mathematics in

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?
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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”