Love this one...

Some partial backups of posts from the past (Feb, 2004)
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Canadian Zoetrope
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Joined: Thu Jan 15, 2004 1:54 am

Love this one...

Post by Canadian Zoetrope » Thu Jan 15, 2004 1:54 am

The Infinite Circle

Nicholas of Cusa (1401-1464) made the following interesting point regarding the shape of an infinite circle. The curvature of a circle's circumference decreases as the size of the circle increases. For example, the curvature of the earth's surface is so negligible that it appears flat. The limit of decrease in curvature is a straight line.

An infinite circle is therefore... a straight line!
Edited by: Canadian Zoetrope at: 1/14/04 9:17 am

voce io
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Joined: Wed Oct 29, 2003 12:05 am

...

Post by voce io » Thu Jan 15, 2004 3:47 am

Abstractly, theoretically, merely the appearance of a straight line.

Thomas Knierim
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Joined: Wed Jul 17, 2002 6:20 pm

Re: Love this one...

Post by Thomas Knierim » Fri Jan 16, 2004 12:31 pm

<span style="color:white;">Zoetrope: An infinite circle is therefore... a straight line!</span>

Unfortunately the conclusion is wrong. You said earlier:

<span style="color:white;">The curvature of a circle's circumference decreases as the size of the circle increases. For example, the curvature of the earth's surface is so negligible that it appears flat. The limit of decrease in curvature is a straight line.</span>

Yet it never reaches that limit. The Cusan circle is simply a spiral.

Thomas

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Dave Toast
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Joined: Fri Mar 07, 2003 6:22 pm

Re: Love this one...

Post by Dave Toast » Sat Jan 17, 2004 4:09 am

The transfinite is not the infinite.

An infinite circle is an impossibility, as is an infinite anything.

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