A rectangle whose sides are related by Phi (1.618033...) is said to be a golden rectangle. If a new rectangle
is drawn by swinging the long side around one of a golden rectangle's ends as its new long side, the new rectangle is also of golden
ratio (ref. sketches).
Phi is frequently observed in many natural growths as well as in architecture and ergonomics. Default home flash
display of this site is proportioned according to the golden mean geometry
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EASTERN SKIES BEFORE DARK
Astronomy was fairly advanced until several centuries ago. The founder of an observatory
in the 13th century, Nasir al-Din al-Tusi notably contributed to the solution of the centuries-old Ptolemaic problem of how circular motion can be translated
into linear motion. The solution, known as the Tusi couple, can generate linear motion from uniform circular motion.
In the Java animation of the Tusi Couple (ref.
),
the blue circle carries the red circle in a clockwise direction, while the red circle rotates counterclockwise on its central
axis. The two circular motions result in a linear motion (circular in 3D) of the red ball
(drag circles with mouse pointer to view from different angles).
In a corollary to the Tusi couple, the interactive couple (ref.
),
the large circle represents a planet's orbit and the small circle represents the epicycle
that carries the planet; parametric changes produce changes in tracks.
The instrumentation in another observatory founded by Taqi al-Din in Istanbul in 1575 was
comparable only to that of the contemporary observatory founded by Tycho Brahe in 1576.
During the brief existence of this observatory, a comet was observed in the skies of Istanbul in 1577 (ref.
the miniatures by Ottoman observers of the comet known as Tycho Brahe).
Unfortunately, a year after the comet passed by, a plague epidemic broke out in Istanbul claiming many lives. This calamity
was linked by the religious dignitaries to the existence of the observatory, and it was duly destroyed in 1580.
And, thus began a five-century lapse of indifference to natural phenomena.
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