Revision as of 14:52, 6 October 2013 edit Ancora Luciano (talk \| contribs) 318 edits →Sum of the first n squares (geometrical proof) ← Previous edit		Revision as of 08:03, 7 October 2013 edit undo Ancora Luciano (talk \| contribs) 318 edits →Sum of the first n squares (geometrical proof) Next edit →
Line 84: == Sum of the first ''n'' squares (geometrical proof) == See ~~the animation~~ at: https://sites.google.com/site/leggendoarchimede <small><span class="autosigned">— Preceding [[Wikipedia:Signatures\|unsigned]] comment added by [[User:Ancora Luciano\|Ancora Luciano]] ([[User talk:Ancora Luciano\|talk]] • [[Special:Contributions/Ancora Luciano\|contribs]]) 13:06, 27 June 2013 (UTC)</span></small><!-- Template:Unsigned --> <!--Autosigned by SineBot--> [[File:Pyram.jpg\|thumb\|tridimensional model]] We represent the square pyramidal number P<sub>6</sub> = 91 with cubes of unit volume, as shown, and inscribe in building a pyramid (in red). Let V<sub>6</sub> the volume of the inscribed pyramid. To obtain P<sub>6</sub> you may add to V<sub>6</sub> the excess external volume to the red pyramid. Such excess is: 2/3 for each cube placed on the central edge, and 1/2 for the cubes forming the steps of the building (enlarge for a better look of highlighted part). Then, calculating one has:

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