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AW: Need help writing geology software using cirlces

  • To: mathgroup at smc.vnet.net
  • Subject: [mg29137] AW: [mg29117] Need help writing geology software using cirlces
  • From: Matthias.Bode at oppenheim.de
  • Date: Wed, 30 May 2001 23:28:24 -0400 (EDT)
  • Sender: owner-wri-mathgroup at wolfram.com

Hello Peter,

this idea may yield the results you have in mind:

In[1]:=
(ArcSin[Sin[0/180*Pi]]+ArcSin[Sin[45/180*Pi]])/2*180/Pi //N

Out[1]=
22.5

In[2]:=
(ArcSin[Sin[350/180*Pi]]+ArcSin[Sin[45/180*Pi]])/2*180/Pi //N

Out[2]=
17.5

In[3]:=
(ArcSin[Sin[0/180*Pi]]+ArcSin[Sin[180/180*Pi]])/2*180/Pi //N

Out[3]=
0.

In[4]:=
((ArcSin[Sin[0/180*Pi]]+ArcSin[Sin[90/180*Pi]]+ArcSin[Sin[180/180*Pi]]+
            ArcSin[Sin[270/180*Pi]])/4)*180/Pi //N

Out[4]=
0.

Please note that your examples

3): average of "one vector north plus one vector south"
and
4): average of "one vector north plus one vector south plus one vector east
plus one vector west"

will both evaluate to zero for vectors of even length.
(Vector and matrix operations are dealt with in section 1.8.3 of THE
MATHEMATICA BOOK; 
<< Miscellaneous`Geodesy` might inspire you as well in determining the whims
of rivers.)

Best regards,

Matthias Bode
Sal. Oppenheim jr. & Cie. KGaA
Koenigsberger Strasse 29
D-60487 Frankfurt am Main
GERMANY
Tel.: +49(0)69 71 34 53 80
Mobile: +49(0)172 6 74 95 77
Fax: +49(0)69 71 34 6380
E-mail: matthias.bode at oppenheim.de
Internet: http://www.oppenheim.de



-----Ursprungliche Nachricht-----
Von: Peter Wilson [mailto:peter at midar.com]In[50]:=
Gesendet: Mittwoch, 30. Mai 2001 11:51
An: mathgroup at smc.vnet.net
Betreff: [mg29117] Need help writing geology software using cirlces


I am currently writing a computer program that needs to calculate the
average angle, given numerous angles in a previous sequence.

Examples:
1) Given the angles, 0? and 45?  the average is definitely 22.5?

2) Given 2 angles of 350 and 45, the average should be 17.5 degrees
(hmmm...Is that right?)

3) Given 0 and 180 the average can be considered either 90 or 270

4) Given 0, 90, 180 and 270, the average may? be considered 0. In such cases
my program will cope fine.


=============
Here's my question
=============
Q. What formula can I use to find the average angle in a circle, from a
series of angles?
i.e.. 0,45,56,135,270,360,2,18... etc.

Please note that I understand basic trigonometry, but that's about it.  I'm
a computer programmer, not a mathematician.

I would appreciate any help.  My computer program is currently used in
Geology to track the course of a river, and to provide a predictive model of
the same river in previous and future years.  It currently works, however
it's a bit rough and I'm currently looking for refinement algorithms.

Cheers,

Pete




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