[Phys-L] Fermi question on state borders
> Chuck Britton
> Tue, Nov 28 at 8:32 AM
> Not all Random ‘Location’ Generators are created equal.
> Polar versus Cartesian can make a difference?
Hmmm - not the first time this has been mentioned.It seems to me that a
randomly spaced point at a line location at a random angle from a zero point
point leads to an inverse square kind of spatial distribution of points.This
is, after all, the primitive description of the field around a point source.
What the question proposes is a random distribution on the plane. so in Polar
form, the distribution of points should be be chosen as the square root of
displacement from the zero point.
In a similar way, if we are to provide a locus of equal probability to the
perimeter of a square, that locus can not be a smaller square whose dimensions
are half as longas the outer square, because that locus encloses merely one
quarter of the possible positions available. Instead a side length of 1 /
sqrt(2) times the outer square side length is needed.