[math-fun] exp(Pi)- Pi and then ?

5 Dec 2015

      Hello funsters,

  as you may know, there is one funny approximation
of 20 with exp(Pi) - Pi = 19.999099979...

  but are there others the same ?

  maybe,

  by using high speed guessing and some tables,

  3 - (5*Pi)/6 - 6/(5*Pi) = 0 (the error is 1/29189).

  2*Pi/5 + exp(-2*Pi/5) - 5/3*Pi -log(4*Pi/5) - i*Pi = 22/7 (absolute value)

with 12 digits of precision.

(use fixed fonts) :

   Pi          8 Pi        Pi
---- + exp(- ----) + ln(----) + exp(Pi) + Pi I
  3            5          2

  = 24 + 93/110 , 11 digits precision.

that is : 1/3*Pi+exp(-8/5*Pi)+ln(1/2*Pi)+exp(Pi)+I*Pi, absolute value.

any patterns ? aby clue ?

  have a nice day,

  Simon Plouffe