Infinite series

Comment

Comment by David Rutten on June 2, 2015 at 1:50am

Either it's an intrinsic property, i.e. Phi is 'closer' to a rational number than pi is (which makes sense, phi is algebraic whereas pi is transcendental), or the series is just better designed.

Comment by Alex on June 1, 2015 at 10:31am

Thanks David :) I wonder what caused the speed of convergence Phi?

Comment by David Rutten on June 1, 2015 at 9:21am

Turns out this series for Phi converges very quickly.

Comment by Alex on June 1, 2015 at 5:43am

You can look at how it looks with the golden section?

Comment by David Rutten on May 30, 2015 at 12:40pm

In this case it has nothing to do with Grasshopper. I'm just studying some basic number theory and wanted to get a better feel for this approach to transcendental numbers. Most series very quickly require very big numbers*, making them impractical for the kind of number-crunching available in GH (I'd need to use Mathematica for those, but I'm not fluent enough in that environment to code this up).

* Typically because they involve increasing powers or factorials.

Comment by William Carroll on May 30, 2015 at 12:26pm

Very nice, David. This may be my thickness speaking here, but what is the purpose of this experiment? Stress-testing GH? Or are there certain implications of this experiment that I am failing to realize? In other words -- and I hope this doesn't come off as rude -- why are you interested in convergence behavior? As a side-note: I am always impressed by the succinctness of your definitions. A true master!

Thank you for all of your hard work.