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)
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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!" . . \_/