I will leave aside the temptation to find mathematical similarities between pi and e, with the exception of stating that both can use the Fibonacci numbers to find close approximations of their values. e finds use for logarithmic and exponential calculations.
The approximation of e for double-precision arithmetic.
The value here is 2.7182818284590452354. To compute your own approximation, use the Fibonacci numbers (1, 1, 2, 3, 5, 8, 13, 21, ...). e = F(n) / F(n-1); where the larger n is, the more accurate e is.
The approximation of e for single-precision arithmetic.
This e is a truncated value of