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| These reference pages describe some of the fascinating properties of The Golden Ratio and some related math problems. |
About The Golden RatioWhen I was in high school, I became quite fascinated with the number known as The Golden Ratio, which is approximately 1.618, and is represented by the Greek letter phi (φ).The number shows up in a variety of places, and its appearance always surprised me. As a competitor in various high school math competitions, I made a policy for myself: If I'm ever doing a sequences-and-series problem, and I don't know the answer, I will ALWAYS guess The Golden Ratio, if it seems to be "reasonable" in the context of the problem. Surprisingly, that policy worked to my advantage in at least a couple cases; I got the correct answer to problems I had no idea how to solve. Of course, I shared this policy with my teammates, which resulted in a bit of consternation on the part of the competition graders, who thought everyone was cheating, because they kept guessing the same wrong answer! But even though The Golden Ratio does have the capability of getting you in trouble if you're not careful, it's still a very fun number, and I created these pages as a way of exploring some of the fun things this number does. Teachers: if you have students who are curious about "special" numbers, and want a little bit of enrichment activity, set them loose on these pages. The pages are written in a way that should be entertaining to read, and only uses high school level concepts, so most students with even a modicum of curiosity should enjoy exploring these pages. I hope you enjoy this little mathematical journey!
"The Golden Ratio" is written by Douglas Twitchell, and hosted at The Problem Site. Contents copyright 2008 by Douglas Twitchell. Contents of this page may not be reproduced without permission of the author.
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