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Path: utzoo!linus!philabs!cmcl2!seismo!rochester!ritcv!waf0116
From: waf0116@ritcv.UUCP (rn)
Newsgroups: net.math
Subject: solution (maybe) to circles
Message-ID: <8987@ritcv.UUCP>
Date: Thu, 31-Oct-85 22:57:56 EST
Article-I.D.: ritcv.8987
Posted: Thu Oct 31 22:57:56 1985
Date-Received: Tue, 5-Nov-85 04:50:25 EST
Reply-To: waf0116@ritcv.UUCP (William A. Fuss)
Organization: Rochester Institute of Technology, Rochester, NY
Lines: 60

I tried sending this e-mail but it FAILED!!! so........

Charlie-

I don't know if I'm late or what, but I have a possible
solution to your problem.

It takes a while to do by hand, but if you can think
through an algorithm(which seems to work), it can be written, right?!?!

anyway my guess:


	you have 2 circles:		A and B
	find the centers of each:	Ca and Cb
	find the distance between
	   centers:			D
	** Use Pythogrean Theorem to find D**

I am **assuming** that you consider the shortest distance between
a small circle within a larger circle to be zero because
they intersect at their centers.

Now, take circle A as the reference circle, find
the distance between Ca and all points that comprise
circle B and compare each of these individual distances
with D.  When you find a shorter distance, remember this
distance and the coordinates of the point.  Continue selecting
points along the circumference (sp) of B until either you find
a new short distance or you finish traversing the circumference.
Label the point of shortest distance Pb.

Now make circle B your reference circle with reference point
Pb.  Traverse the circumference of A in the similar fashion
As you did with circle B.  When you find the new shortest point
from circle A to Pb , label that point Pa.

Now the shortest distance between the 2 circles is:

	D = square root[ (Xa - Xb)^2 + (Ya - Yb)^2 + (Za - Zb)^2 ]

	where
		Xa,Ya,Za are the coorinates of Pa
	and
		Xb,Yb,Zb are the coorinates of Pb

Kinda long, but it seems to work on paper.....
If you don't see how this works (if it really does work)
let me know!!!!!

Thanks!!!


dr. billfuss

--------------------------------------------
"Smile, the world may never know!"

		. .
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