stefan Intermediate

I manage to get Latex output in the blog engine I use, not perfect yet but acceptable. Check out:

http://www.c-lambda.se/a-deep-question.html

Thanks all I managed to find one good answer to the question. The discussion hear led me to it. Thanks!

(Quote from Eric Walker)

Yes I should nuke the point to the upper part, that's the optimal version

(Quote from Eric Walker)

f is an assumed density of mu, every function on the sphere can be written as an even blus and odd function f(p) = (f(p) + f(-p))/2 + ((f(p) - f(-p))/2, then a even id a(-p)=p and odd if a(-p)=-a(p). The uniform density is even.…

Then consider:

https://en.wikipedia.org/wiki/Funk_transform

If \mu has a density f, then being in G is the same as integrating f along a great circle is always 1/4 pi

no?

(Quote from THHuxleynew)

So what do you like my added retake of the problem ?

(Quote from Eric Walker)

Eric I still think I motivated why I would like to include the definition as is, but i also see a value to add what I think THHuxleynew's is indicating. I'm still not convinced that his suggestion can precisely lead to the…

(Quote from THHuxleynew)

I will add a formulation in the discussion section that I think will be more to the point.

(Quote from Eric Walker)

I will add this information

(Quote from Eric Walker)

No that's not correct. Take the set [a,b] then for each x,y in [a,b] a point p in between x,y also is located in [a,b] hence adding middle numbers does not incrase the set. However if you take the union of [1,2] and [4,5] you can…

(Quote from THHuxleynew)


Somtimes a more general problem is easier to prove so I will add that as a comment. I'll add your suggestion as an reformulation tag. Also note that if you have amoving measure of charge on a great circle that does not radiate…

(Quote from THHuxleynew)


Maybe you are right it complicates things, I would just as well define a measure on S2. But in order to define the density of the covering I need to, for each point in the sphere, match that to a point in a specific great…

(Quote from Eric Walker)

A measur can put the weight zero on a specific great circel with a specific normal. My mapping (my map M) the set of great circles maps to the upper half sphere the induced meassure on the image
will essentially put zero weight…

(Quote from Eric Walker)

So what you are saying is equivalent to if I give you the set of real numbers you can find new numbers between them which is not real number. This is of cause wrong.

teh example works by M such that of O is such that O z points into the downward sphere it maps O onto Flip O, where Flip just result in the same great circle
as the original but the resulting normal points to the upper sphere. You don't change the…

(Quote from Eric Walker)


I think the example is correct so each great circle can have two normal if it is pointing towards the lower sphere you can change the normal by mirroring it to the upper sphere keeping the actual great circle the same. So no you…

I added a commentary to help you dig out from the Underland dungeon. I added an explanation section at the bottom of the page and changed
geodesics, which I thought was great circles e.g. straight lines in a spherical geometry. I referred to the…

I discovered a very simple example that is extreme and is a nontrivial example with nonzero total(G) and where one see that the extreme
value for this special case is the maximum modulo all loop flippings.

(Quote from THHuxleynew)

Should I use matehmatical nomeclature on a mathematical site the things stays short and tidy. I can add explanation for all the notions in the question but then the question will be very long.
What I will do add a explanation…