Re: [Phys-l] a mathematical curiosity

["Bob Sciamanda" <treborsci@verizon.net>]

I would only remark that these are statements more about the manner in which 
we have chosen to partition the area of a sphere rather than about  the 
intrinsic topological properties of a sphere.  I think that the only 
intrinsic topological content of these “equator –based” statements is simply 
that a great circle (any great circle) is larger (in radius and 
circumference)  than any other circle drawn on the surface of a 3-sphere.

From: John Denker
Sent: Monday, January 09, 2012 1:05 PM
To: Forum for Physics Educators
Subject: Re: [Phys-l] a mathematical curiosity
On 01/09/2012 10:25 AM, Bob Sciamanda wrote:
> Similarly all the surface-area is near the equator. You can see this 
> already
> in D=3, on the earth, where the area of the tropical regions is
> large compared to the area of the arctic regions ... “
>
> I am befuddled.  One could just as arbitrarily choose an equator running
> through a rotational pole.  Without the earth’s spin and/or its 
> orientation
> relative to the sun the choice of an equator is completely arbitrary.

Well, we agree that the tilt-angle of the earth's axis is arbitrary
... but once you settle on an angle, the *same* angle determines
the size of the tropic regions and the size of the arctic regions.
  Tropic regions = 2x 23.5 degrees
  Arctic regions = 2x 23.5 degrees

These regions are the same latitude-wise, but very different area-wise.


Bob Sciamanda
Physics, Edinboro Univ of PA (Em)
treborsci@verizon.net
http://mysite.verizon.net/res12merh/