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{{GA|00:24, 25 December 2021 (UTC)|subtopic=Mathematics and mathematicians|page=1|oldid=1061933655}}
{{DYK talk|14 January|2022|image=Rye Castle, Rye, East Sussex, England-6April2011 (1) (cropped).jpg|entry=... that the '''[[square pyramidal number|number of cannonballs in a square pyramid]]''' ''(pictured)'' with <math>n</math> cannonballs along each edge is <math>\frac{n(n+1)(2n+1)}{6}</math>?|nompage=Template:Did you know nominations/Square pyramidal number}}
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{{WikiProject Mathematics|priority=low}}
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==Untitled==
In all articles found the formula for the square pyramidal number is proofed by using the inductive methode. Isn't there a direct proof?
Jon van den Helder
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[[User:Bill01568|Bill01568]] ([[User talk:Bill01568|talk]]) 16:29, 30 December 2013 (UTC)
:Seems reasonable, [[File:Yes check.svg|20px|link=|alt=]] '''Done'''<!-- Template:ESp -->. ''<b style="font-variant:small-caps;">[[User:Little Mountain 5|<
== Simplification of the current proof ==
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::The proof by induction is indeed not that hard, but you need to know the formula in the first place. This way you get the formula automatically, and the proof isn't long at all (it can be done with one picture, http://forumbgz.ru/user/upload/file580638.jpg (with some unimportant text in russian)). But I'm not sure if some random picture on the internet is considered a source. [[User:MYXOMOPbI4|MYXOMOPbI4]] ([[User talk:MYXOMOPbI4|talk]]) 22:53, 7 September 2017 (UTC)
:::It's more or less obvious that the formula is a cubic polynomial and from that and the first four values you can immediately derive it by finite differences. And no, random pictures on the internet, especially from a site whose address syntax suggests that it's an open wiki, are not reliable sources. —[[User:David Eppstein|David Eppstein]] ([[User talk:David Eppstein|talk]]) 00:27, 8 September 2017 (UTC)
== Link addition ==
A link to Lucas Numbers should be provided for completeness. [[Special:Contributions/199.209.255.246|199.209.255.246]] ([[User talk:199.209.255.246|talk]]) 14:40, 10 September 2018 (UTC)
:Only if the connection can be sourced. Otherwise the unsourced paragraph mentioning Lucas should be removed. —[[User:David Eppstein|David Eppstein]] ([[User talk:David Eppstein|talk]]) 16:33, 10 September 2018 (UTC)
== Archimedes ==
I don't see any mention of Archimedes, who probably gave the first formula for the sum of squares of the first n natural numbers in his book 'On Spirals'. It doesn't at first sight look like the modern formula, and the derivation is horribly complicated, but it is there after all. See the discussion in Heath's edition of Archimedes, especially on page 109 in the Dover edition.[[Special:Contributions/2A00:23C8:7906:1301:A453:48F9:36D5:B594|2A00:23C8:7906:1301:A453:48F9:36D5:B594]] ([[User talk:2A00:23C8:7906:1301:A453:48F9:36D5:B594|talk]]) 21:23, 7 March 2021 (UTC)
:Added. I used the 1897 edition rather than the Dover edition, but the pagination is the same. —[[User:David Eppstein|David Eppstein]] ([[User talk:David Eppstein|talk]]) 00:43, 8 March 2021 (UTC)
{{Talk:Square pyramidal number/GA1}}
==Did you know nomination==
{{Template:Did you know nominations/Square pyramidal number}}
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