Genius at Play
The last time I visited John Horton Conway, he showed me a book, Genius At Play: The Curious Mind of John Horton Conway
He just wanted to show me a picture from the book. While he was browsing this book about himself, I took a photo of him (featured on the left). The picture he was looking for was on page 314. I am reproducing it here (Photo by Michael A. Stecker, courtesy of Stephen D. Miller).
When we finally found the picture, he asked me how many tennis balls were in it. I smelled a trick question right away and didn’t bite. I shrugged. It appears that one of the balls at the far corner at the base of the pyramid had rolled away. So there was one less ball than I would have calculated. So, how many balls are there?
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tomislater:
1662?
28 July 2015, 5:14 pmNaveen Dankal:
down vote accepted
There are two different kinds of layers here, as it alternates between centered hexagonal numbers (e.g. the top layer is the first centered hexagonal number, i.e. 1, the third layer from the top is the second centered hexagonal number, i.e. 7, etc.), and layers where the sides alternate between lengths n and n+1 (e.g. the second layer from the top of the pyramid is a ‘hexagon’ with sides 1 and 2, the fourth layer is a hexagon with sides 2 and 3, etc.
So, the numbers of tennis balls in all the odd layers of this pyramid is 9^3=729
For the other layers: The formula for the figure with sides n and n+1 is 3n^2.
Since you have 8 of those layers, you have 3 times the sum of the first 8 square numbers, and the general sum of the first n square numbers is n(n+1)(2n+1)/6, so that gives you 3⋅8(8+1)(2⋅8+1)/6=612 more tennis balls, for a total of 729+612=1341
18 January 2018, 11:15 pm魔大农:
Hi Tanya,
I was wondering if you’d be willing to contribute your photo(s) of John Conway to the public domain, by assigning a creative commons license. If you could upload them to commons.wikimedia.org yourself, that would be perfect, but I would also be happy to do that. The latest photos of JHC now available in this way are from 2005.
Kind regards,
31 May 2020, 5:30 pmFrode 魔大农 Lindeijer
tanyakh:
I tried to upload this picture to wiki. I am not sure it worked. Also, there is a typo in the title. I can’t fix it. It would be great if someone can remove the text after the period.
9 July 2020, 9:21 pm魔大农:
Ah, great! Only just saw you did. 🙂
I did some retouching right away, uploaded the result under a different name and added it to his Dutch Wikipedia page.
https://commons.wikimedia.org/wiki/File:John_Conway_browses_Genius_at_Play.jpg
https://nl.wikipedia.org/wiki/John_Conway
Thanks!
17 April 2022, 4:24 pmTanya Khovanova's Math Blog » Blog Archive » Retouched Picture of John Conway:
[…] posts about John Conway has a picture I took of him in 2015, leafing through a book about himself, Genius at Play. I allowed Wikipedia to use this image, and they did. They also retouched it for their article on […]
28 April 2022, 2:17 pm