A Formula for the Scaling Factor of a Constantly Decreasing ImageDate: 9/28/95 at 13:10:29 From: Clifford West Subject: math Here's a problem for you: I'm looking at a picture of a person holding a mirror and looking into a mirror. I see that the image is repeated over and over again. The large picture is made of an infinite number of smaller pictures, all of which are proportional. The first image is about 15cm. The second image is about 5.8cm. What is the actual height of the 10th image in the picture? An explanation as well as a solution would be helpful. Thanks................Clif West Date: 10/10/95 at 20:54:30 From: Doctor Jonathan Subject: Re: math Sir, I think that the size of the nth image is given by the expression 15*(5.8/15)^n where the zeroth image is the original. The reason for this is that each time the image is copied, it is scaled by a constant factor of 5.8/15. Thus, if this process is repeated, the total scaling factor is (5.8/15)^n. The reason the scaling factor is constant is that for each iteration, the copied image occupies the same portion of the "parent" image. -Doctor Jonathan, The Geometry Forum |
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