Phi is another irrational number just like pi and e. this is an easy way to approximate phi in case of an emergency.
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Step 1: About Phi
Phi is the basis for the golden ratio. I hope you like analogies. Ok now, phi is the basis of the golden ratio. Things are in golden ratio when the whole is to the larger part as the larger part is to the smaller part. Phi is an infinite non repeating decimal. It starts off as 1.61803.
Step 2: Fibonacci Sequence
Phi is related to the fibonacci sequence. The fibonacci sequence starts off as 1 1 2 3 5 8 13 21 34 and so on. I am sure you will figure out this pattern. If not then here you go. 1+1=2 1+2=3 2+3=5 3+5=8 5+8=13 8+13=21 13+21=34 and so on.
Step 3: Lets Get Approximating!
Ok so to approximate phi you need to understand the fibonacci sequence(last step) Now lets start. Take 1 fibonacci number lets say 13 then add it to the previous number which would be 1 1 2 3 5 8 13 so it is 8. 13+8=21 then take the new number(21) and divide it by the original number(13) 21/13=1.61538 ect. you wont always get the same number for every fibonacci number ex. 8+5=13 13/8=1.625 but it is close enough.