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::::That website helped '''''a lot'''''. There is so much information on there about what I was looking for that it gave me a slight inferiority complex because of how many ''hours'' and ''hours'' I spent working on this stuff when it took me under a second to get a full sequence along with formulas. To my relief though, there was a few things that it didn't know, so I don't feel as bad, but it knows enough to give a good resorce. Be prepared for a new article on the subject, but there are two more things. First, I don't know what I should title it; I've recently been refering to the topic as tessellation conglomerates for lack of a better term, but that name is completely made up by me. Also, when I finish, it might be good to move "Squares in a square" to the page. (I realize what I've been typing takes up a lot of room. I won't be offended if you delete my previous entries.) [[User:Frivolous Consultant|Frivolous Consultant]] ([[User talk:Frivolous Consultant|talk]]) 23:21, 25 October 2012 (UTC)
== Quadrature of the parabola ==
I found that the "square pyramidal number" can be used to prove the theorem of Archimedes on the area of parabolic segment. The proof, carried out without the use of "mathematical analysis", is on the site "Leggendo Archimede" on page 02, at the following web address:
https:
:https://sites.google.com/site/leggendoarchimede/
::On page 07 of that site, in the article "Numeri e geometria", is exposed an ingenious method to derive the first formula of this article, and others of the same type, using geometric patterns in the spaces of 2 and 3 dimensions.
Luciano Ancora - 11:22, 5 mag 2013
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