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For example, the gnomon of the square number is the odd number, of the general > form 2n + 1, n = 1, 2, 3, ... . The square of size 8 composed of gnomons looks > like this:

This definition from Wikipedia, shows a square filled with increasing by one, Natural numbers, following the L shape growing from a corner of the square.

Are there infinite gnomons? What are other gnomons? I'm thinking like Pascal's Triangle, not Geometry of Euclid here.

prog9910
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  • Can Pascal's Triangle be turned into a gnomon? – prog9910 Jul 01 '24 at 22:55
  • See here for a telescopy viewpoint. $ \ $ – Bill Dubuque Jul 01 '24 at 23:00
  • My comment was on your question, not a reply to your earlier comment on Pascal's trinagle. $\ \ $ – Bill Dubuque Jul 01 '24 at 23:43
  • Thanks to your help, @BillDubuque The key is Gnomons are built around Figurate numbers, and Figurate numbers come from Figures (Geometry) - such as Centers of Squares, Pentagons, Hexagons, and such. See: JSTOR: Figurate numbers, supermarkets pascal's triangle by Arnall Richards – prog9910 Jul 02 '24 at 00:53

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