Mathematical coincidences

Some mathematical coincidences (formulas that produce an irrational number very close to one or ten) that I found using a Python program:

1/3(e-1/pi)+1/5=~0.999991

(e-1)/pi+e/6=~0.999993

(pi+1)/e-pi/6=~1.000008

pi(pi+1/7)-1/pi=~10.00009


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