About: Steinhaus-Moser Notation   Sponge Permalink

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Steinhaus-Moser Notation is a notation created by Hugo Steinhaus, and extended by Leo Moser. The formula is: * Triangle(n) = nn = File:Steinhaustriangle.svg * Square(n) = \(\boxed{n}\) = n inside n triangles * Circle(n) = ⓝ = n inside n squares Triangle(n) would be graphically displayed by n inside a triangle, and the same for Square and Circle. Leo Moser extends this notation with pentagons, hexagons, heptagons, octagons, etc., where n inside a x-gon is equal to x inside n (x - 1)-gons. Of course, circles are no longer used in this version, and are replaced by pentagons.

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rdf:type
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  • Steinhaus-Moser Notation
rdfs:comment
  • Steinhaus-Moser Notation is a notation created by Hugo Steinhaus, and extended by Leo Moser. The formula is: * Triangle(n) = nn = File:Steinhaustriangle.svg * Square(n) = \(\boxed{n}\) = n inside n triangles * Circle(n) = ⓝ = n inside n squares Triangle(n) would be graphically displayed by n inside a triangle, and the same for Square and Circle. Leo Moser extends this notation with pentagons, hexagons, heptagons, octagons, etc., where n inside a x-gon is equal to x inside n (x - 1)-gons. Of course, circles are no longer used in this version, and are replaced by pentagons.
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dbkwik:googology/p...iPageUsesTemplate
Author
  • Hugo Steinhaus, Leo Moser
Year
  • 1950(xsd:integer)
growthrate
  • n inside an n-gon >* PRA
abstract
  • Steinhaus-Moser Notation is a notation created by Hugo Steinhaus, and extended by Leo Moser. The formula is: * Triangle(n) = nn = File:Steinhaustriangle.svg * Square(n) = \(\boxed{n}\) = n inside n triangles * Circle(n) = ⓝ = n inside n squares Triangle(n) would be graphically displayed by n inside a triangle, and the same for Square and Circle. Leo Moser extends this notation with pentagons, hexagons, heptagons, octagons, etc., where n inside a x-gon is equal to x inside n (x - 1)-gons. Of course, circles are no longer used in this version, and are replaced by pentagons. Matt Hudelson defines a similar version like so: * n| = Line(n) = nn * n< = Wedge(n) = n followed by n lines * Triangle(n) = n followed by n wedges * Square(n) = n inside n triangles * etc. Steinhaus-Moser notation is technically a fast iteration hierarchy with \(f_0(n) = n^n\). With this initial rule, \(f_{m - 3}(n)\) is equal to n inside an m-gon. n inside an n-gon is roughly \(f_\omega(n)\) in the fast-growing hierarchy.
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