Author: AlbertitoAlbertito
Date: Apr 24, 2008 03:32
In mathematics and the arts, two quantities are in
the golden ratio if the ratio between the sum of those
quantities and the larger one is the same as the ratio
between the larger one and the smaller. The golden
ratio is approximately phi =1.6180339887.... So, two
quantities, a and b, with a>b, are in the golden ratio, if
(a+b)/a = a/b.
Let three bodies, A, B and C, be in inertial motion
and aligned along a straight line, where v_ba is the
speed of body B wrt A, and v_cb is the speed of body
C wrt B. Then, by Einstein's addition of velocities, we
get the speed v_ca of body C wrt A, as
v_ca = (v_ba + v_cb) / ( 1 + v_ba v_cb/c^2).
v_ca is the relativistic sum of v_ba and v_cb, then
we can define
v_ca/v_ba = v_ba/v_cb
as the RELATIVISTIC GOLDEN RATIO of v_ba and
v_cb. So, we get
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