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!

]]>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,

Frode 魔大农 Lindeijer

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

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