[net.math] solution

roderick (02/24/83)

The problem is that the definition of  i  is not  i = sqrt(-1),
but that  i**2 = -1.  These are two completely different things,
despite the tempting intuitiveness of the former.  Any experience
with abstract algebra (especially extension fields; C is R extended
with a symbol  i  defined by  i**2 = -1) and you will understand
why things like this are done.  (For one thing, they don't lead
to contradictions like the one you gave.)  Finally note that
square root is defined as a value which squared gives the original
number; in the strictest sense, it is not even a function.

Rod Glover
U of T
..!utzoo!utcsrgv!roderick

msb@lsuc.UUCP (Mark Brader) (02/18/85)

Guvf vf rnfl, naq lbh qba'g arrq pnyphyhf.  (Ng yrnfg, lbh qba'g arrq gb
gnxr qrevingvirf naq gur yvxr.  Jung haqreyvrf gur fbyhgvba vf nabgure znggre.)

Yrg gur zvahgr unaq or BZ naq gur ubhe unaq BU.  Gura BZ=4, BU=3, naq obgu
cbvagf Z naq U ner eribyivat, rnpu ng n havsbez fcrrq, nobhg gur pragre B.
Abj fjvgpu gb n havsbezyl ebgngvat senzr bs ersrerapr fb gung BZ vf svkrq.
Va guvf senzr, U jvyy fgvyy or havsbezyl eribyivat nobhg B, gubhtu ng n
qvssrerag fcrrq.

Fvapr U vf zbivat ng n pbafgnag fcrrq, vgf qvfgnapr sebz Z zhfg or vapernfvat
zbfg encvqyl jura vg vf zbivat qverpgyl njnl sebz Z, vs guvf rire unccraf;
naq vg qbrf, ba nygreangr bppnfvbaf jura natyr BUZ vf n evtug natyr.
Jr gura fvzcyl nccyl Clguntbenf gb ernpu gur nafjre ZU = fdeg(7).

Znex Oenqre

waf0116@ritcv.UUCP (rn) (11/01/85)

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!"

		. .
		\_/