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### A Formula for the Scaling Factor of a Constantly Decreasing Image

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Date: 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

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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Associated Topics:
Middle School Ratio and Proportion

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