The Amazing Mathematics of the Golden Ratio

Let me show you some awesome numerical patterns within "the golden ratio", beginning with a story about this number from my childhood, and building to a whole web of connections it has with the "Fibonacci sequence", the "Lucas numbers", and more!

Many people associate this number/ratio with geometry and shapes, but there are tons of numerical traits that make it special too! This episode covers some of my favorite numerical aspects and doesn't cover the geometric aspects, which I will cover at another point in the future. The golden ratio will also play a key role in a future episode about irrational numbers. And in another future episode, we will meet some other "metallic" numbers such as the "silver ratio" and "bronze ratio"!

By the way, the symbol I am using for the golden ratio is the greek letter "phi", which is used for a few things in math, one of which is this number. "Phi" is pronounced more like "fee" according to the sources I've read, although you'll hear some people pronounce it like "fye".

Here's links to two previous episodes that include the Golden Ratio:
   • How to Count in Fractional and Irrati...  
   • Capturing Infinity With Fractions  
(doesn't matter if you watch these before or after this video)

Special thanks to Evan Clark and to all of my Patreon supporters:
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(To join that list of people supporting this channel, and get cool bonus content, check out the Combo Class Patreon at   / comboclass  )

Make sure you're also tuned in to my ‪@Domotro‬ channel for my bonus videos and livestreams and other content!

By the way, I've started putting shorts on this channel but they typically won't go to notifications or subscription feeds (they typically have been on my ‪@Domotro‬ channel and did so well for that channel that I want more people on that shorts page to find this channel too). They will be available on the "shorts" tab on this channel, and I will link the recent ones in video descriptions like this. Here are the ones I've put on this channel so far:
   • Shorts  
   • Shorts  
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   • Shorts  

If you want to mail me anything (such as any clocks/dice/etc. that you'd like to see in the background of Grade -2), here's my private mailbox address (not my home address). If you're going to send anything, please watch this short video first:    • You Can Now Mail Me Things to Put in ...  
Domotro
1442 A Walnut Street, Box # 401
Berkeley, CA 94709

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If you want to try to help with Combo Class in some way, or collaborate in some form, reach out at combouniversity(at)gmail(dot)com

In case people search any of these words, some topics mentioned in this video are: the golden ratio (phi), square numbers, cube numbers, other integer powers, the fibonacci sequence, the lucas numbers, infinite continued fractions, infinite square roots, and more!

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DISCLAIMER: Do not copy any uses of fire, sharp items, or other dangerous tools or activities you may see in this series. These videos are for educational (and entertainment) purposes.