Originally Posted by
John Forester
Your attitude is equivalent to that of some Mid-Western legislatures who declared that in their state pi=3.0. No matter what the statute says, it cannot be carried out....
Originally Posted by
jputnam
... I don't know what the value of pi is in your world, but it must be phenomenally large.
You guys got me thinking. Your fight about pi makes me think maybe we really do need to re-think our assumptions of bikeways right from the basic principles.
Forester is only partly right about pi, and you were facetious but perhaps closer to right? Let me explain ... you said "in your world". Well, when we draw circles on the world we're drawing on the surface, and the radius is also measured on the surface. How else are you gonna do it, drill a tunnel? So it hit me: a circle around the equator has pi=2, since in "2 pi R" the "R" is one quarter of the Earth's circumference. Visualize the radius drawn from the north pole down to the equator on the surface. On the other hand a small circle drawn at latitude 89.9999°, where the surface is flat for all practical purposes, would have the familiar value for pi. So a circle around each Latitude will have a different value of Pi, ranging from 2.0 to 3.1415926 .... if you're measuring a circle around the earth at that latitude.
I don't know about you, but I couldn't rest until I figured out what Pi really is in Indiana (it was the Indiana legislature that tried to make pi=3), and if it wasn't 3 there, where in the world is it 3? So I broke out the rusty Trig, and less head-scratching than I expected, and I think that Pi in Indiana at Latitude 40° is 2.7577. Not 3. So they missed after all. From there it's easy to figure that Pi is exactly 3 at a latitude of 60°, which is in Alaska, not Indiana. Had it been an Alaska legislature they might have gotten away with it.
btw, I get Pi(latitude L) is [180/(90-L)]cos(L)
So if Pi varies on where you draw the circle, then maybe the best cycling infrastructure will also vary.