Another Casual Coder

Srinivasa Ramanujan is one of my heroes. A brilliant mind from Southern India (Chennai) who had an incredible talent for numbers and unfortunately a very tragic and brief life. If you want to learn more about him I recommend reading The Man Who Knew Infinity instead of watching the movie. In the movie there is no, zero, mathematics. And if you learn about Ramanujan without appreciating his work in math it is as if you were learning about Einstein without appreciating his work in Physics.

In the book you'll find one of the very first problems proposed by Ramanujan when he was still a kid. It was an infinite series (95% of his work revolved around infinity) where he asked all the top mathematicians in the world if they could solve it. Simply stated, here it is:


What's the value of X? Top mathematicians all over the world jumped into this problem but with no success. They worked on it for months and months until they all, one by one, gave up. Finally Ramanujan gave away the solution. X = 3.

The mathematics behind the proof are pretty advanced. Only if the mathematicians 100+ years ago had access to a Surface Laptop with Visual Studio installed....

Writing a simple code to converge the series above is relatively easy. The equation is very suitable for a recursive solution, and hopefully the convergence will happen quick enough that the stack won't blow up. In my 2-lines recursive function I use a max seed to stop the recursion (remember, this is an infinite sum). Running the code for, say, 70 iterations quickly shows where it is converging towards. Code is below, output down below, cheers, Marcelo.

class Program
{
static void Main(string[] args)
{
int max = 70;
for (int i = 0; i <= max; i++)
{
Console.WriteLine("For terms = {0}, RFP = {1}", i, RamanujanFirstProblem(2, i));
}
}
static double RamanujanFirstProblem(int currentSeed, int maxSeed)
{
if (currentSeed >= maxSeed) return 0.0;
return Math.Sqrt(1 + currentSeed * RamanujanFirstProblem(currentSeed + 1, maxSeed));
}
}