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![[parent]](http://images.planetmath.org:8080/images/uparrow.png) Viewing Message
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| ``Remarks on notation and other stuff''
by NeuRet on 2002-08-07 15:05:58 |
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| 1) The elements of a Cartesian product X \times Y are ordered pairs, most commonly denoted by (x,y), not x \times y. It is a bit confusing to think about 0 \times 1, for it feels as if you were referring to 0 and 1 as sets (which they are, but only if we're talking about set theory and ordinals). Why not call it (0,1) instead?
2) It is not clear to me how this torus differs from a Klein bottle (but maybe I'm just being purposely dense). The orientation of opposite edges is important. E.g.
+-<-+
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^ ^ <---- This is a torus
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+-<-+
+-<-+
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^ ^ <----- This is a Klein bottle
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+->-+
3) If you follow akrowne's advice and get a little more explicit, why not give your torus a definite shape, i.e. a parametrization? I particularly like
(cos(s)*(R + r*cos(t)), sin(s)*(R + r*cos(t)), r*sin(t))
for 0 <= s,t <= 2pi. |
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