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To: rlpowell@digitalkingdom.org
From: xah lee <xah@xahlee.org>
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Date: Tue, 2 Nov 2004 15:03:19 -0800
Subject: [lojban] Re: how to say manifold
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hi Robin,

http://en.wikipedia.org/wiki/Manifold

an informal explanation can be found in this harangue:
http://www.xahlee.org/Writ_dir/comp_lang_lisp/153.txt

excerpt:
Manifold, like polytope, is a generic name for certain concept of
arbitrary dimensions. In 2-D, we have curves. For example, most of you
know that the graph of y=x^2 is a parabola, and y=x is a line. These
things are called plane curves. The curves themselves are of
1-dimension, but they sits in a 2-dimensional plane. Now, in
3-dimensions, we can also plot functions to form space curves or
surfaces. For example, z=x+y is a plane, and z=x*y is a saddle shaped
surface. Restricting the values of y to a constant then we have curves
in space. Here, the idea is that in 3-D we can have 1-D objects like
curves, or 2-D objects like surfaces. As with regular solids of higher
dimensions, mathematician's imagination faculties thought about curves
and surfaces in higher dimensions. Basically, in n-dimension you can
have "curves/surfaces" that has dimensions less then n. For example,
in 3-D we can have the 2-D surfaces or the 1-D curves, and in 2-D
plane we can have 1-D curves or 0-D dots. Therefore, in 4-dimensional
space, we can have not only 0-D dots or 1-D curves or 2-D surfaces,
but we can also have "curve/surface-like" objects that's 3-D, sitting
in 4-D space. The general name for these curve/surface-like objects in
arbitrary dimensions is called _MANIFOLD_. Thus, a curve is just a
1-dimensional manifold. A surface is a 2-dimensional manifold. How
fantastically fascinating.

Thanks.

  Xah
  xah@xahlee.org
  http://xahlee.org/PageTwo_dir/more.html


On Aug 9, 2004, at 11:58 AM, Robin Lee Powell wrote:

On Mon, Aug 02, 2004 at 08:25:53PM -0400, xahlee.org wrote:
> how to say manifold?
>
> in particular, curves and surfaces?

Can you give me a link to the definition of manifold that you are
thinking about?

-Robin

-- 
http://www.digitalkingdom.org/~rlpowell/ *** http://www.lojban.org/
Reason #237 To Learn Lojban: "Homonyms: Their Grate!"


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