Comments on: More on the Golden Solid angle

By: Greg

Greg — Fri, 29 Jan 2010 18:24:19 +0000

I think that is why I am asking for examples of the Golden Solid angle in the Natural World – this was the question being asked in the first place. Phi is not only the solution of a quadratic of course.

By: Ray Girvan

Ray Girvan — Fri, 29 Jan 2010 04:56:58 +0000

All I’m saying is that if there’s some geometrical property of interest/significance in x dimensions, there’s no guarantee that its analogue will do the same in y dimensions. Phi, being a solution of a quadratic, is solidly rooted in 2D geometry.

By: Greg

Greg — Wed, 27 Jan 2010 10:33:43 +0000

I sent the reply using the comment reply box on your site. Never mind. I am not sure what you mean by “where we know it works” – where we know what works? That there are natural world examples of the Golden angle?

I don’t believe that the inability to decompose a rectangular cuboid in a similar manner to a Golden Rectangle has any bearing on the question or the problem.

The Golden Solid angle was arrived at by going from the case of dividing a line into the Golden Ratio, moving up one dimension by curling the line round on itself to give us the Golden angle, and finally rotating the circle about its diameter to give us a sphere and the associated Golden solid angle.

It seems you are happy with the Golden angle, but likewise there is now way of chopping off a part of the circle and getting a smaller version of the original in that manner either, so I don’t really understand what you’re implying.

By: Ray Girvan

Ray Girvan — Wed, 27 Jan 2010 04:27:21 +0000

“Unfortunately this is quite incorrect! Go down one dimension …”

… where we know it works, but there’s no reason to assume that it’ll generalise to 3D. As an example, take the Golden Rectangle: chop off a square, and you get a smaller Golden Rectangle, and so on. But there’s no possible cuboid where you can chop off a cube and get a smaller version of the original in that manner.

“I have written a correcting comment to Ray but he has not posted it on his site yet”

How did you send it? Comments are enabled; there’s no sign of yours having been posted.