Description of CYCLOIDS
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Executable on Psion machines (ER5) leike Psion 5,  5mx, 5mxPro,
Ericsson MC218, Netbook. Tested on MC218 only.

Program to draw animated graphs of cycloids, epicycloids and
hypocycloids.
Programm zum animierten Zeichnen von Zykloiden, Epizykloiden und
Hypozykloiden.

General info on cycloids can easily be found in Wikipedia:

* "A cycloid is the curve defined by the path of a point on the
  edge of circular wheel as the wheel rolls along a straight line.
* If we further allow the line on which the circle rolls to be
  an arbitrary circle then we get the epicycloid (circle rolling on
  outside of another circle, point on the rim)"
*  If we further allow the line on which the circle rolls to be
  an arbitrary circle with the moving circle on the inside, point
  on the rim, then we get the hypocycloid.

This program was originally quickly written for my nephew Joel
Krause. We studied the mechanism of high and low tides of the
oceans. One of the factors is the centrifugal force of the earth
while rotating around an axis which is not going through the
earth's center. This program can be used to show the movement of
the center of the earth (or moon) when looking at the earth-moon
system.

The common center of gravity of this system is 4671 km away from
the center of the earth. If we simplify the ellipse of the path
of the earth-moon system around the sun to a circle,
then the center of the earth walks on a epicycloid line around
the sun, showing about 12 bumps on its path, 1 per month. While
travelling on this epicycloid path, it rotates around itself,
producing day and night. Altogether a not very simple movement.
The moon, of course, travels on another epicycloid with larger
'bumps' in opposition to the earth.

"Cycloids.opo" can calculate and display these routes, and many
more, but not to scale, and only one at a time.

INSTALLING AND RUNNING
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The program is published including the source code. Just put the
Cycloids.opo file in any folder of your choice and run it (mark
it and press enter).
If you want to play with the code also, put the Cycloids.opl file
into the same folder, run it as above (the program editor will
open), translate and execute.
Operate the program using Enter, Escape, q, p, s and r keypresses
as applicable.

Smallprint
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Be sure to obey my disclaimer on http://psion.uh-lab.de. There
you can find the newest version and an email contact address,
should you wish to contact me.

Greetings from Freiburg, Germany,
Ulrich Hornstein

19.4.2008