Subject: Re: gabriel's horn
From: Paul Hertzel (hertzpau@niacc.cc.ia.us)
Date: Fri Feb 25 2000 - 13:33:55 EST
RayM wrote,
> Once the
>coating thickness is specified, it is trivial to calculate the area that a
>given volume will cover _to that thickness._ The comparison to 1/x is
>that filling volume allows the "coating" thickness to thin out away from
>the origin. Actually painting the surface requires the volume between the
>surfaces generated by 1/x and 1/x+(coating_thickness), i.e. an infinite
>slab.
If I'm understanding this correctly, then you're concluding an infinite volume
of paint is needed to paint the outside surface. But this is false. You vary
the thickness as you paint to the right, and there's more than enough to go
around. Make the thickness a function of the radius at a given point, and you
can paint the surface with an eyedropper of paint.
You just can't paint it with a 2-d liquid, whatever that is. It's the
ability to vary
the 3rd dimension that is missing from the 2-d reality.
Paul Hertzel
NIACC
Mason City
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