The MacPlatonic Solids Tony Mann University of Greenwich.
-
Upload
carmel-stone -
Category
Documents
-
view
218 -
download
3
Transcript of The MacPlatonic Solids Tony Mann University of Greenwich.
![Page 1: The MacPlatonic Solids Tony Mann University of Greenwich.](https://reader035.fdocuments.net/reader035/viewer/2022070403/56649f325503460f94c4ee36/html5/thumbnails/1.jpg)
The MacPlatonic Solids
Tony Mann
University of Greenwich
![Page 2: The MacPlatonic Solids Tony Mann University of Greenwich.](https://reader035.fdocuments.net/reader035/viewer/2022070403/56649f325503460f94c4ee36/html5/thumbnails/2.jpg)
“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!
![Page 3: The MacPlatonic Solids Tony Mann University of Greenwich.](https://reader035.fdocuments.net/reader035/viewer/2022070403/56649f325503460f94c4ee36/html5/thumbnails/3.jpg)
Neolithic carved stone balls
(British Museum)
![Page 4: The MacPlatonic Solids Tony Mann University of Greenwich.](https://reader035.fdocuments.net/reader035/viewer/2022070403/56649f325503460f94c4ee36/html5/thumbnails/4.jpg)
Neolithic carved stone balls
Towie, Aberdeenshire (Wikimedia Commons)
![Page 5: The MacPlatonic Solids Tony Mann University of Greenwich.](https://reader035.fdocuments.net/reader035/viewer/2022070403/56649f325503460f94c4ee36/html5/thumbnails/5.jpg)
Neolithic carved stone balls
Golspie, Aberdeenshire (Dr James B Simpson, via
Wikimedia Commons)
Ayrshire (Wikimedia Commons)
![Page 6: The MacPlatonic Solids Tony Mann University of Greenwich.](https://reader035.fdocuments.net/reader035/viewer/2022070403/56649f325503460f94c4ee36/html5/thumbnails/6.jpg)
Neolithic carved stone balls
![Page 7: The MacPlatonic Solids Tony Mann University of Greenwich.](https://reader035.fdocuments.net/reader035/viewer/2022070403/56649f325503460f94c4ee36/html5/thumbnails/7.jpg)
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
![Page 8: The MacPlatonic Solids Tony Mann University of Greenwich.](https://reader035.fdocuments.net/reader035/viewer/2022070403/56649f325503460f94c4ee36/html5/thumbnails/8.jpg)
The MacPlatonic Solids
![Page 9: The MacPlatonic Solids Tony Mann University of Greenwich.](https://reader035.fdocuments.net/reader035/viewer/2022070403/56649f325503460f94c4ee36/html5/thumbnails/9.jpg)
A petrosphere
Thanks to John Sharp
![Page 10: The MacPlatonic Solids Tony Mann University of Greenwich.](https://reader035.fdocuments.net/reader035/viewer/2022070403/56649f325503460f94c4ee36/html5/thumbnails/10.jpg)
Inspiration?
Thanks to John Sharp
![Page 11: The MacPlatonic Solids Tony Mann University of Greenwich.](https://reader035.fdocuments.net/reader035/viewer/2022070403/56649f325503460f94c4ee36/html5/thumbnails/11.jpg)
Uses?
• Bolas?
• Weights or measures?
• Ball games?
• Sink stones?
• Rollers for megaliths?
• Oracles / dice?
• Denoting “the right to speak”?
![Page 12: The MacPlatonic Solids Tony Mann University of Greenwich.](https://reader035.fdocuments.net/reader035/viewer/2022070403/56649f325503460f94c4ee36/html5/thumbnails/12.jpg)
Egyptian dice
Myers Collection, Eton College
Currently on display, Barber Institute
![Page 13: The MacPlatonic Solids Tony Mann University of Greenwich.](https://reader035.fdocuments.net/reader035/viewer/2022070403/56649f325503460f94c4ee36/html5/thumbnails/13.jpg)
Postcard (I)
![Page 14: The MacPlatonic Solids Tony Mann University of Greenwich.](https://reader035.fdocuments.net/reader035/viewer/2022070403/56649f325503460f94c4ee36/html5/thumbnails/14.jpg)
Postcard (II)
![Page 15: The MacPlatonic Solids Tony Mann University of Greenwich.](https://reader035.fdocuments.net/reader035/viewer/2022070403/56649f325503460f94c4ee36/html5/thumbnails/15.jpg)
Contemporary art
Red Fruit
Peter Randall-Page
![Page 16: The MacPlatonic Solids Tony Mann University of Greenwich.](https://reader035.fdocuments.net/reader035/viewer/2022070403/56649f325503460f94c4ee36/html5/thumbnails/16.jpg)
Contemporary public art
First Conundrum (2000)Remco de Fouw
Edinburgh
![Page 17: The MacPlatonic Solids Tony Mann University of Greenwich.](https://reader035.fdocuments.net/reader035/viewer/2022070403/56649f325503460f94c4ee36/html5/thumbnails/17.jpg)
First Conundrum
![Page 18: The MacPlatonic Solids Tony Mann University of Greenwich.](https://reader035.fdocuments.net/reader035/viewer/2022070403/56649f325503460f94c4ee36/html5/thumbnails/18.jpg)
Palaeolithic Hand-axes
Kentish hand-axes (Wikimedia Commons)
![Page 19: The MacPlatonic Solids Tony Mann University of Greenwich.](https://reader035.fdocuments.net/reader035/viewer/2022070403/56649f325503460f94c4ee36/html5/thumbnails/19.jpg)
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?
![Page 20: The MacPlatonic Solids Tony Mann University of Greenwich.](https://reader035.fdocuments.net/reader035/viewer/2022070403/56649f325503460f94c4ee36/html5/thumbnails/20.jpg)
![Page 21: The MacPlatonic Solids Tony Mann University of Greenwich.](https://reader035.fdocuments.net/reader035/viewer/2022070403/56649f325503460f94c4ee36/html5/thumbnails/21.jpg)
Celts
Behold the mysterious celt,
with a property that amuses.
One way it will spin,
the other way it refuses.
Andy Titcomb, Wikimedia Commons
![Page 22: The MacPlatonic Solids Tony Mann University of Greenwich.](https://reader035.fdocuments.net/reader035/viewer/2022070403/56649f325503460f94c4ee36/html5/thumbnails/22.jpg)
Mathematics of rattlebacks
• Worked out in the 1980s by
Sir Hermann Bondi (Cambridge)
Mont Hubbard (Univ of California)
![Page 23: The MacPlatonic Solids Tony Mann University of Greenwich.](https://reader035.fdocuments.net/reader035/viewer/2022070403/56649f325503460f94c4ee36/html5/thumbnails/23.jpg)
Rattleback
(Hugh Hunt)
![Page 24: The MacPlatonic Solids Tony Mann University of Greenwich.](https://reader035.fdocuments.net/reader035/viewer/2022070403/56649f325503460f94c4ee36/html5/thumbnails/24.jpg)
Conclusion
• We’d like to connect mathematically with our ancestors
• But we can’t have “original ears”