View Single Post
  #20   Spotlight this post!  
Unread 15-12-2012, 01:15
Ether's Avatar
Ether Ether is offline
systems engineer (retired)
no team
 
Join Date: Nov 2009
Rookie Year: 1969
Location: US
Posts: 8,128
Ether has a reputation beyond reputeEther has a reputation beyond reputeEther has a reputation beyond reputeEther has a reputation beyond reputeEther has a reputation beyond reputeEther has a reputation beyond reputeEther has a reputation beyond reputeEther has a reputation beyond reputeEther has a reputation beyond reputeEther has a reputation beyond reputeEther has a reputation beyond repute
Re: numerical computation contest

Quote:
Originally Posted by DampRobot View Post
Was the "challenge" to write a program that found the solutions of these functions through guess and check?
There is no explicit solution so you have to use iteration.

For folks like Christopher149 who know how to use modern math tools like Mathematica this is very simple to do, and you can get answers of arbitrary precision.

Mathematica is very expensive, but there are free CAS (Computer Algebra System) tools like Maxima which anybody can download and install for free. Maxima can also solve this problem with arbitrary precision (see my earlier post where I used Maxima to get 600 digits).

Attached are:

- The derivation of the equations

- A simple Delphi console app code which uses a binary search to find theta


If you replace sin(theta)/theta - 5280/5281 with a 12th degree Taylor expansion (see Richard's earlier post about Taylor expansion), you can squeeze out 16 decimal digits of accuracy with this simple code using Intel's X86 Extended Precision floats


Attached Thumbnails
Click image for larger version

Name:	equations.png
Views:	28
Size:	13.8 KB
ID:	13298  Click image for larger version

Name:	Taylor.png
Views:	18
Size:	4.2 KB
ID:	13302  
Attached Files
File Type: pdf code.pdf (25.7 KB, 10 views)

Last edited by Ether : 15-12-2012 at 01:51.