# Steinhaus-Moser Notation

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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.

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[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, $$f_{m - 3}(n)$$ is equal to n inside an m-gon.

n inside an n-gon is roughly $$f_\omega(n)$$ in the fast-growing hierarchy.

### ExamplesEdit

• 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 Edit

function polygon(n, level):
if level == 3:
return nn
r := n
repeat n times:
r := polygon(r, level - 1)
return r