Talk:Pentagonal number

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[edit] Generalized

I don't know what is the point of generalized pentagonal numbers, as opposed to regular pentagonal numbers, so if someone knows, it would be appreciated if they added it to the article. PrimeFan 21:17, 4 Mar 2004 (UTC)

There's a point to the regular ones? The generalized ones are the scrunty little 'pentagons' inside the patterns for the 'regular' ones. Personally, I can't see why a ten-dot pentagon with two dots in the middle is any more regular than the two dots on their own. Grant 18:37, 25 November 2006 (UTC)

[edit] Represents a pentagon

The article should explain what "represents a pentagon" means. 84.139.0.238 17:38, 7 February 2006 (UTC)

You're absolutely right. This is one of those things that need to be explained precisely because they seem so obvious.

You're having a laugh. It's not remotely obvious. Give that one of the chief features of a regular pentagon is its rotational symmetry, might one not expect a pattern of dots that represents such a figure to have its own rotational symmetry? In fact there is no sense in which the number 12, say, represents a pentagon. Grant 17:33, 25 November 2006 (UTC)

I looked to Mathworld for guidance. Their article on the topic has a graphic of dots arranged in pentagons, but nothing in words. So it's a challenge for us to come up with appropriate words. PrimeFan 21:16, 7 February 2006 (UTC)

[edit] Music to my ears

One can see 1, 5, 12, 22, 35... as pentagonal patterns. One can also see this pattern in human music. 1 from monochords, 5 for 'pentatonic scales, 12 for Western dodecaphonic (12 tone) system in music, and 22 for the 'Sruti' (22-tone) system in Indian music. Some jazz musicians have experimented with 35-tone music. Figurate numbers should find a place along side Pythagoras' "music of the spheres" in the bridging of Math and Music. If you like, we can discuss this more over at my forum: http://forums.delphiforums.com/figurate/start