Oof, Gene is quite right, of course. (Is there a sign change in the signature of spacetime that would make it be tan instead of tanh?) --Michael On Sun, Apr 23, 2017 at 10:14 AM, Eugene Salamin via math-fun < math-fun@mailman.xmission.com> wrote:
That's not correct. Let v/c = tanh q. Then the relativistic formula for velocity addition is q = q1 + q2. That is, the parameter q is like a rotation angle.
-- Gene
On Saturday, April 22, 2017, 7:36:18 PM PDT, Michael Kleber < michael.kleber@gmail.com> wrote:This is the special-relativity rule for addition of fractions of the speed of light. That is, if you observe someone going 0.9c and they observe someone else going 0.9c in the same direction, then the faster traveller looks to you like they're going at arctan( tan(0.9 * pi/2) + tan(0.9 * pi/2) ) / (pi/2).
On Sat, Apr 22, 2017 at 12:27 AM, Dan Asimov <dasimov@earthlink.net> wrote:
Yes, it's very interesting, and if I get any time soon I will write up why.
—Dan
----- Is there anything mathematically interesting about the function f(a, b) = arctan(tan(a) + tan(b))? -----
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