Content deleted Content added
Line 14:
[[User:CRGreathouse|CRGreathouse]]<small> ([[User talk:CRGreathouse|t]] | [[Special:Contributions/CRGreathouse|c]])</small> 18:22, 31 August 2009 (UTC)
::Nicomachus observes it but doesn't offer a proof. I haven't looked up Aryabhata's discussion, but the general style of the early Indian mathematicians was to state results without proof. In fact this was also common in European algebra down to the 17th century. For example, Descartes stated his 'rule of signs' without anything resembling a proof. I think this was partly because mathematicians often regarded their methods as 'trade secrets', which they could use to solve challenge problems, but also because until the principle of mathematical induction was understood, a lot of problems were difficult to prove rigorously with the available methods.[[Special:Contributions/2A00:23C8:7907:4B01:B180:FF9C:33B1:1040|2A00:23C8:7907:4B01:B180:FF9C:33B1:1040]] ([[User talk:2A00:23C8:7907:4B01:B180:FF9C:33B1:1040|talk]]) 21:29, 9 November 2021 (UTC)Added by same commenter: the passage in Nicomachus is in Chapter 20 of Book 2 of his 'Arithmetic', not in Chapter 20 of the whole work, which would be in Book 1.[[Special:Contributions/2A00:23C8:7907:4B01:5064:8DD0:F21C:FD4B|2A00:23C8:7907:4B01:5064:8DD0:F21C:FD4B]] ([[User talk:2A00:23C8:7907:4B01:5064:8DD0:F21C:FD4B|talk]]) 15:38, 17 November 2021 (UTC)
== Sum of the first "n" cubes - even cubes - odd cubes (geometrical proofs) ==
| |||