It is an extension (devised by Leo Moser) of Hugo Steinhaus's polygon notation.
: n written in an (m + 1)-sided polygon is equivalent to "the number n inside n nested m-sided polygons".
The number n inside two triangles is equivalent to nn inside one triangle, which is equivalent to nn raised to the power of nn.
Steinhaus defined only the triangle, the square, and the circle , which is equivalent to the pentagon defined above.
Megagon is here the name of a polygon with "mega" sides (not to be confused with the polygon with one million sides).
We have (note the convention that powers are evaluated from right to left): Similarly: etc.
Thus: Rounding more crudely (replacing the 257 at the end by 256), we get mega ≈
(see also approximate arithmetic for very large numbers).
It has been proven that in Conway chained arrow notation, and, in Knuth's up-arrow notation, Therefore, Moser's number, although incomprehensibly large, is vanishingly small compared to Graham's number:[2]