Talk:Square pyramidal number: Difference between revisions

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{{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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==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|<fontspan colorstyle="color:black;">Little</fontspan>]][[User talk:Little Mountain 5|<fontspan colorstyle="color:red;">Mountain</fontspan>]][[Special:Contribs/Little Mountain 5|<fontspan colorstyle="color:#00008B;">5</fontspan>]]</b>'' 22:35, 30 December 2013 (UTC)

== Simplification of the current proof ==

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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)

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==Did you know nomination==

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