Centering CirclesDate: 10/05/2002 at 08:15:55 From: Stephen Gross Subject: Circles I have two circles that need to be centered on each other but the circle with the larger diameter has the center cut out. How can you center these two by knowing the diameters? Date: 10/05/2002 at 21:15:24 From: Doctor Ian Subject: Re: Circles Hi Stephen, Are you talking about mathematical circles, or physical circles (e.g., made from paper)? If you're talking about paper circles, an easy way to center them is to fold each circle twice, so that you get quarter-circles. One of them will be missing the corner. Put one under the other, and you should see something like this: | . | . | . . . | . . | | . . |______ .__________ Trace the inner arc on the uncut circle, and you can use it to center the cut circle when you've unfolded them. Does this help? Or have I misunderstood your question? - Doctor Ian, The Math Forum http://mathforum.org/dr.math/ Date: 10/05/2002 at 22:17:44 From: Stephen Gross Subject: Circles I'm sorry; I'm talking two metal objects. Is there a math equation that can be used or is it just manipulating them? Date: 10/06/2002 at 09:42:39 From: Doctor Ian Subject: Re: Circles Hi Stephen, Ah, like a washer and a metal disk? That's trickier. One way to go is to make two paper templates, the same size as the objects, and then use those to center the actual objects. Using equations, it's trivial to do this: You just write an equation for each circle, and center them at the same location, e.g., (x - a)^2 + (y - b)^2 = r^2 (x - a)^2 + (y - b)^2 = R^2 The problem is _finding_ the physical centers so that you can align them. One way to do that is to make a square frame that just fits around an object. (You have to make sure the corners are absolutely square, and you can check this by making sure that the diagonals are the same length.) Then you can measure halfway down the frame on each side, and mark the point next to that on the object. Connecting opposite marks will give you a pair of diameters. The diameters will intersect at the center of the circle. But more important, if you align the diameters of two circular objects, their centers will be aligned as well. Does that sound like a workable solution? - Doctor Ian, The Math Forum http://mathforum.org/dr.math/ |
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