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  The Golden Ratio as a Continued RadicalLike the previous page, this page could easily fit in the Slick Math! section of the site, because it has a math problem which, at a glance, look fairly intimidating, but is actually quite simple and elegant to solve.Take a look at the following continuing radical expression.  If you read the previous page, you probably have a good idea how to tackle this problem. We start by setting the expression equal to R. Notice, now that the part of the expression which is circled in red is identical to the entire expression:  From this we conclude that R2 - R - 1 = 0. I sure hope this looks familiar to you, because it is exactly the same quadratic equation that we had on the previous page! And, of course, it still evaluates to The Golden Ratio!
Contents copyright 2008 by Douglas Twitchell. Contents of this page may not be reproduced without permission of the author.
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