New Directions For π

  • Stan Wagon


Symbolic computations can lead to unexpected and new formulas for famous constants. The four formulas displayed here (from [AW]) all arose by asking Mathematica to evaluate the abstract expression
$$\sum\limits_{k = 0}^\infty {\left({- 4} \right)^{- k} \left({\frac{{a_1}}{{4k + 1}} + \frac{{a_2}}{{4k + 2}} + \frac{{a_3}}{{4k + 3}} + \frac{{a_4}}{{4k + 4}}} \right)} $$
and finding values of the coefficients causing helpful cancellation.


Fractional Part Symbolic Computation Decimal Digit Undetermined Coefficient Correct Digit 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Copyright information

© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  • Stan Wagon
    • 1
  1. 1.Department of Mathematics and Computer ScienceMacalester CollegeSt. PaulUSA

Personalised recommendations