Re: What shape is this.

On Apr 15, 4:25 pm, "rnor...@xxxxxxxxx" <rnor...@xxxxxxxxx> wrote:
On Apr 15, 7:55 am, John Harshman <jharshman.diespam...@xxxxxxxxxxx>


OK, let's get really technical, here.  A torus is defined as a surface
of genus one.  It is a topological concept and the exact shape is
completely unimportant, except for that one hole.  Most commonly, you
see it as the product of two circles where any planar section is
circular.



I find it confusing that the term *product* is used.

I would define a torus as a "circle looped in a circle".
Where *loop* takes on the connotation of *blowing a bubble*.


But I would not define the (hole in the middle) as a circle.

Quite simply "it isn't".



But it need not be.  A lumpy doughnut or bagel is a torus
without being perfectly circular.  It is quite possible for a torus to
conform in part of its surface to a hyperboloid.


Or a coffe cup, or a dvd, or a toilet, or "homer simpson".




Further, let's continue to get technical here.  When spinny "slices"
the torus, there is no reason to believe that the slice is necessarily
a planar cut.  You can take a knife and "slice" an inner tube or bagel
or doughnut by holding the object horizontally, holding the knife
vertically, and making a circular cut,.  One of the pieces is then the
surface spinny described,.  If the inner tube is somewhat distorted
(and a real inner tube when actually inflated inside an automobile
tire is NOT perfect round) then it could easily be a hyperboloid.



To get really technical.
(which is dumb, as nature favours simpletons Like Y.O.O)


You can fold a sphere inside out, (without breaking the topology)

You can change a "Torus" into any shape you like. (so long as it has a
hole).


A torus could even be a piece of "nominal bore tube".



My point is that a *clever person*, would not describe *every*
topological state.

They would simplify and say "circle", Or, Hyperbolia. Depending upon
the audience.


In fact, a *really, really* clever person, cares *more* about the
audience,
than geometry.



Spinny makes an incredibly large number of statements that truly
deserve ridicule.


I'd like to see one.

 However it is not necessary to attack him on every
word he writes.-

.

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