From Osher Doctorow
Readers have probably mostly seen my "transformation":
1) y/x --> 1 + y - x
assuming that x and y don't have common integer factors for example.
Let's apply this to sqrt(1 - v^2/c^2) with y = v^2, x = c^2:
2) sqrt(1 - v^2/c^2) --> sqrt(1- (1 + v^2 - c^2)) = sqrt(c^2 - v^2)
Hence sqrt(1 - v^2/c^2) > 1/2 transforms to:
3) sqrt(c^2 - v^2) > 1/2
and squaring both sides:
4) c^2 - v^2 > 1/4
This seems rather "mysterious" until we adopt the commonly expressed c
= 1, in which case we get:
5) 1 - v^2 > 1/4
and therefore:
6) v^2 < 3/4
from which:
7) v < sqrt(3)/2
This is remarkable in view of the results previously obtained for v or
v^2 with sqrt(3)/2 without the "transformation".
Osher Doctorow
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