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Math Forum » Discussions » Math Topics » geometry.pre-college.independent

Topic: RE: Is a spiral 1 dimensional?
Replies: 1   Last Post: Jun 22, 2006 4:53 PM

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Joshua Zucker

Posts: 1,450
Registered: 1/30/05
Re: Is a spiral 1 dimensional?
Posted: Jun 22, 2006 4:53 PM
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On 6/22/06, R Kleinschmidt <kleinschmidt@att.net> wrote:
>
> It seems to me that the word "spiral" implies that it exists in a higher
> dimension space. In 1-space, wouldn't a spiral look exactly like a segment,
> ray, or line depending on end points?
>
> Rich Kleinschmidt

I think the proper way to express what you're saying mathematically is
to say that a spiral is a 1-dimensional object embedded in 2 (or 3)
dimensions.

Similarly knot theory is all about what happens when you have a
1-dimensional closed loop embedded in 3 dimensions.

--Joshua Zucker

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