sphere & pseudosphere maximum Surface area Contact? Is it 10% #392 Correcting Math
in [Physics]
|
Prev: Eddington's interpretation of action may unify mechanics and information theory
Next: sphere & pseudosphere maximum Reverse Concavity. Is it 10% #395 Correcting Math
From: Archimedes Plutonium on 6 Feb 2010 02:20 Alright, I have to retrench somewhat here. Looking at Mathworld's pseudosphere and funnel equations, that the contact nested inside is a line contact and not area. So I have to retrench the model and operation. What I do is cut the sphere into half and then cut a hole into what used to be the poles and slide the two hemispheres down the two spines of the pseudosphere and as I slide it down I keep an eye out as to when I reach a maximum surface area contact between the sphere and pseudosphere. This revised model operation reminds me of bicycle axles and the race cup and the bearings in the race cups. So that the bearings freely move around inside the race and that race is like a pseudosphere. But in that bicycle analogy, the bearings want as little of surface contact as possible. Here I want the opposite of the maximum surface area contact. If my hunch is correct it will have a maximum surface area contact of 18 degrees arc on both hemispheres adding up to a total of 36 degrees arc. I think I am getting closer and closer to the perfect model that easily explains and proves the final answer. Another way of finding the final answer is to manipulate the equations and see where intersections of the sphere with pseudosphere occur. I am not expert on those equations and leave it to those who are very much everday familar with those equations. So is the final answer of a Pseudosphere of radius 1 unit with Sphere of radius 1 unit, of the maximum surface area contact that of 10% of the sphere surface? Archimedes Plutonium www.iw.net/~a_plutonium whole entire Universe is just one big atom where dots of the electron-dot-cloud are galaxies |