I independently 'discovered' this a few years back, basically on the grounds that there are infinitely many shapes with constant diameter but only one (the circle) with constant radius. It stands to reason that the ratio of a circle's circumference to its diameter contains a spurious factor of 2; it must be that the ratio of circumference to radius is the more fundamental quantity.
This discovery was almost enough to make me want to memorize an embarrassing number of digits of 2π; 6.28 is really pathetic. (What's embarrassing, you say? Try 3.141592653589793238462643383279502884197169399...)
Comments
I independently 'discovered' this a few years back, basically on the grounds that there are infinitely many shapes with constant diameter but only one (the circle) with constant radius. It stands to reason that the ratio of a circle's circumference to its diameter contains a spurious factor of 2; it must be that the ratio of circumference to radius is the more fundamental quantity.
This discovery was almost enough to make me want to memorize an embarrassing number of digits of 2π; 6.28 is really pathetic. (What's embarrassing, you say? Try 3.141592653589793238462643383279502884197169399...)
How are you defining diameter? http://mathworld.wolfram.com/Diameter.html only defines it for circular and spherical objects.
http://en.wikipedia.org/wiki/Curve_of_constant_width