Question regarding Pi and Phi relationships

I posted this here simply because I don't know where to post it...

I was messing around with numbers (as I like to do) and noticed what I thought was something interesting relationship wise between (Piπ)3.141592 and (PhiΦ) also known as the golden ratio 1.618033

Two separate equations:

(Φ*2) = 3.236066 pretty close to the number (π) 3.141592
The difference between (Φ*2) 3.236066 and (π) 3.141592 is roughly 0.094474


(π/2) = 1.570796 pretty close to the number (Φ) 1.618033
The difference between (Φ) 1.618033 and (π/2) 1.570796 is roughly 0.047237

What I find interesting is that 0.047237*2 is exactly 0.094474

The difference between the ~Pi and the real Pi is exactly 2x more than the difference between the ~Phi and the real Phi...

also

(Φ+Φ = 3.236066) - (π/2 = 1.570796) = 1.66527

1.66527 - Φ = 0.047237


maybe someone more educated in math else can explain to me what/why I am seeing this number relationship.

Thanks