JT
Posts:
1,299
Registered:
4/7/12


Re: the surfer's value of the ratio of the diameter to the area of sphere
Posted:
May 8, 2013 6:31 PM


On 9 Maj, 00:27, JT <jonas.thornv...@gmail.com> wrote: > On 8 Maj, 17:18, 1treePetrifiedForestLane <Space...@hotmail.com> > wrote: > > > > > > > > > > > the intersting thing is that, dimensionally, > > the units of area/diameter are different > > from circumference/diameter; the latter is dimensionless. > > > > pi is used "symbolically;" > > > the most important thing is that the area > > > of the great circle is a fourth of the whole surface. > > > > if you investigate the edgestangenttosphere duals > > > of hexahedra & octahedra, you'll see where three fourths is. > > Yes indeed it is, therefore the relation should be described in > fraction of a hexagon slice side (from center to vertice), because > that is to become the radius as you scale it up to a circle.
And that fraction will not be a approximation, it will in fact be exact relative the sought smoothness, you can of course save these fractions as you refine the circle exactly as you save your approximated Pi values.

