The Golden Ratio (represented by ) is one of the greatest discoveries Math has made with applications in but not limited to Architecture (eg. Parthenon) and designs. We will use for the golden ratio at all times in this note.
To start off, It can be represented in terms of itself and with numerous 's: which makes it slip neatly in the continued fraction and with a set of square roots:
If a sequence follows a Fibonacci sequence structure, The ratio between a set of 2 numbers is closer to .
We can divide it in sets like this (preferably)
The bigger number divided by the smaller number is getting closer to the while the smaller number divided by the bigger number is getting closer to
Try it out yourself!
But we can also RANDOMLY choose 2 numbers to start off with. Say, and
which is near 's ish
Try it out and see if you got it!
Stay tuned for more updates in the future and please see the my other note about !