Using Streams to Implement Mathematical Functions

Streams, and especially IntStreams, are an elegant way of implementing summation terms (∑). The ranges of the Stream can be used as the bounds of the summation.

E.g., Madhava’s approximation of Pi is given by the formula (Source: wikipedia):

This can be calculated with an arbitrary precision. E.g., for 101 terms:

double pi = Math.sqrt(12) * 
            IntStream.rangeClosed(0, 100)
                     .mapToDouble(k -> Math.pow(-3, -1 * k) / (2 * k + 1))
                     .sum();

Note: With double‘s precision, selecting an upper bound of 29 is sufficient to get a result that’s indistinguishable from Math.Pi.