Steinhaus-Moser Notation is a notation created by Hugo Steinhaus, and extended by Leo Moser.[1] The formula is:
- Triangle(n) = nn =
- 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.
n in a triangle, triangle(n)
Leo Moser extends this notation with pentagons, hexagons, heptagons, octagons, etc., where n inside a x-gon is equal to n inside n (x - 1)-gons. Of course, circles are no longer used in this version, and are replaced by pentagons.
Matt Hudelson[2] 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, \(f_m(n)\) is equal to n inside an m+3-gon.
n inside an n-gon is roughly \(f_\omega(n)\) in the fast-growing hierarchy.
Contents
Examples
- Square(n) = Trianglen(n) = triangle(triangle(...triangle(n)...)) with n triangle()'s,
- Triangle(triangle(n)) = (nn)(nn) = 2(nn)
- Triangle3(n) = triangle(triangle(triangle(n))) = ((nn)(nn))((nn)(nn))
Pseudocode
function polygon(n, level):
if level == 3:
return nn
r := n
repeat n times:
r := polygon(r, level - 1)
return r
