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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: Geogebra?
Date: 2018 Dec 21, 18:16 -0500
Tony

When I had a problem very similar to this one,  I realized a very interesting trick you may be able to use.

My issue was to draw the outlines on the continents on the sphere and then to create illustrations using that three dimensional sphere as projected onto the two dimensional paper.

The trick is simple.  To project the X,Y,Z of the sphere onto the X,Y of the paper, simply eliminate Z!  For all Z positive, the pen is down (drawing). For all Z negative, the pen is up (not drawing).  The XY plane that bisects the sphere at its center has Z=0.  Suddenly, all those three dimensional points lose the 3D attribute and become 2D.

I was able to draw lines of latitude and longitude on a sphere tilted by 23° or so out of the Z=0 XY plane.   The appearance of the globe and continents on the paper was very professional looking.  It appeared as if you were looking at a true globe of the earth.

So any line you want to draw is feasible, as long as you know XYZ, you can determine XY.  This trick may not be suitable for purely mathematical constructs, but for simple illustrations, its very simple and accurate.

On Fri, Dec 21, 2018, 4:03 PM Tony Oz <NoReply_TonyOz@fer3.com wrote:

Dear Lars, Seasons Greetings!

May I ask you if you are familiar with the Geogebra tool?

I am creating explanations and illustrations for Haversine table - I want to include the properly drawn PZX triangle. The PX and PZ sides are easy to draw - they are just ellipses. I'm stuck with the ZX side - have no idea on how to draw a great circle not passing through poles of a sphere...

Here is where I got so far.

I want to use the same sketch for all possible (same-name, contrary-name) allocations by moving Z and X around - with minimum editing where absolutely required.

Warm regards,

Tony 60°N 30°E

File:
PZX.zip

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