Quote:
|
Originally Posted by r6r6r
__________________________________________________ _outer surface of tube
..........* Hi *.....inside the tube.......* Hi *.................
__________________________________________________ outer surface of tube
|
The above tube can at best only have one reference to Pi.
However, if we consider the above tube to come around and meet itself this linear tube becomes a torus.
A torus, in conventional/classical understanding has two great circles ergo two primary considerations of specific Pi associations.
And these two catagories of great circle can be identified as being 90 degrees to each other and further more we assign the words horizontal and vertical as an aid to visualization of 90 degrees to each other;
1}
( ( hole
) ) = horizontal equaltorial bisection of torus can also reveal, outer, inner, top and bottom circles that are not equaltorial,
2}
( left
)( right
) = vertical bisection of can reveal great circle that bisects the tube of the torus, the great circle is left or right of center hole of torus,
See this link for above as XY horizontal plane and Z as vertical bisection plane
3} there is a third kind of great circle, Villenau, that is a diagonal plane bisection of whole torus, that is combination of both vertical and horizontal.
The latter #3 is not part of my concerns, at this time.
So when I present Pi, it has mostly been in regards to an abstract, most generalized Pi, that can be referenced to any abstract sphere, or any of of3 kinds of torus equatorial bisection, also producing a great circle.
If Pi is relevant to specifics I mention above, Ive not yet presented any such findings/discoveries.
With a sphere there is not vertical or horizontal inferred/implied until an abstract axis has been specified/define/located.
With a torus vertical and horizontal is inherent because of two special-case findings of at least two great circles, that are at 90 degrees to each and that is determined by geometry of being a torus shape.
If I become aware of special-case Pi becoming more significant to great circles of a torus, I will happily bring that to others attention. At this time all of my Pi presentation is a an abstract generalization.