Quote:
Originally Posted by DampRobot
Was the "challenge" to write a program that found the solutions of these functions through guess and check?
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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