Before there was floating point, or a way to write zero, or algebraic notation, Archimedes bounded the value of pi by estimating the perimeter of regular polygons inside and outside the circle. His computation is repeated and explained here using MATLAB.
Am I the only one? but this code is failing.
error= Assignment between unlike types is not allowed.
Error in ComputationOfPiByArchimedes (line 222)
cf(end+1) = r;
I am running in "run and advance" mode.
The reason is that cf is vpi and r is a vpi (by propagation). But on the 15th or 16th iteration r is assigned 1 (r=1).
So I changed to r= vpi(1) and it corrected the problem.
Still I wonder. After all, this is a pick of the week, so it was working.
When did it break?
This is a lovely piece of work and is a credit to the author Bill McKeeman. This is a great example to use when explaining successive approximations and the difference between rational and floating point numbers.
With reference to Bill's and John D'Errico's comments I would like to make two points:
Unfortunately Mathworks's websites are so far behind the times that it makes publishing anything that includes mathematics very difficult, and anything such as Bill's work, nearly impossible, as he notes in his 20 Jun 2011 comment.
Mathworks should look at how Stack Exchange handles typesetting text, mathematics, code, and diagrams. Here are examples of my posts to Math Stack Exchange:
so you can can switch from Stack Exchange to Mathworks and back, to see the stark contrast.
I agree with John's two uses of FEX, but I would add a third: to see BAD code. As John knows well, such code can lead to very lively discussions indeed. These discussions can be very fruitful for all concerned, except perhaps the writer of the code.
It is for this third reason that I deplore Mathworks's policy of allowing code submissions and the discussion surrounding the submission, to be deleted by the author of the code. If authors knew that they could not delete their code, then they might be more careful about what they submit.
There are two uses for the File Exchange that I love. One is to provide high quality code. The second is to teach others about some interesting part of mathematics and hopefully, write it using well written MATLAB code. This submission eminently qualifies. You can read it and learn something from what Bill has done.
24 Nov 2010
Typo in title page
26 Nov 2010
Rewrote some of the descriptive material.
27 Nov 2010
01 Dec 2010
Minor fixes, sent wrong file last submission.
03 Dec 2010
Apologies for many updates. Wordsmithing again.
18 Feb 2012
Fixed type in Greek integer
26 Feb 2012
Still trying to change typo in Greek number
29 Feb 2012
Previous version did not have vpi or fr on the MATLAB path -- caused errors.
16 Mar 2012
The submitted zip file still did not have the right contents. Trying again.