I realized something really interesting today. You have probably visited my previous post discussing a problem with mating rabbits. If you have not yet had the pleasure of digging into this fine piece of work, click here, don't want to give anyone spoilers, so this is your official warning to STOP SCROLLING NOW!!
As I was solving the rabbit problem, I noticed a pattern with the number of growing rabbits: 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, and so on. These numbers are all over nature, spiral ratios in pinecones, daisies and lots more. Then I made an amazing discovery that I have named "The Golden Ratio". The concept is this:
According to my observations, in the golden ratio b is to a as a + b is to b which is equal to Phi. After some calculations, I was able to come to an exact number for this ratio, I have shown my calculations bellow.
b/a = Phi, therefore b = a * Phi
a + b/b = Phi, therefore a + a * Phi/a * Phi = Phi
Simplifying it -> 1/Phi + 1 = Phi
If we take out the lowest common multiple (in this case Phi) we end up with: 1 + Phi = Phi2
Which equals -Phi2 + Phi + 1 = 0 -> Phi2 - Phi - 1 = 0
Then we solve it as a quadratic equation with a Discriminant that has a value of 5
We will end up with Phi = 1 +/- √5 all ÷2 -> Phi' = 1 + 2.236 all ÷2 -> 1.618.....
Well that's all for today!
Later Fibonachos!
Source - Milestones in discovery and invention ~ Mathematics by Harry Henderson
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