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## A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding

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Re: Graphically solving haversine calculation
From: Jaap vd Heide
Date: 2015 Nov 14, 11:29 -0800

Hi Andrés,

I use Geogebra ( http://www.geogebra.org ) for this.

It is free for non-commercial use and comes in several versions. It can be used either online, like through the link to tube.geogebra.org I posted before.

Geogebra is basically for and by the worldwide mathematics teaching society. Besides the 2D environment I have been using in this thread, it also includes a 3D module, an algebra module and even a reasonable CAS (Computer Algebra System).

The plots are then very easily made (you can do it yourself with the sheet I put on Geogebra tube): CTRL-SHIFT-C for copying the 2D graphics window and then just paste into Word (which is what did) or whatever text processing software you are using.

I am working on an interactive version of the sheet, with sliders for input of B, Dec and LHA, which I will put online. Then everyone can have a go at it.

In the meantime you may take a look at the worksheet I made showing Cassini's method for resolving position P by Snellius' theory. (for coastal piloting by 3 known points on the shore with the aid of a sextant flipped on its side - drag points A, B, C and/or P around in http://tube.geogebra.org/m/1907805 and see what happens :) A 3-arm protractor works too, the underlying ideas remain the same) In this worksheet I did not turn off the algebra window, so you can see what happens and change it if you want. you can also download the file and play with or work on it offline.

Regards,

Jaap

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