Posted: Mar 05, 2011 9:33 am
by twistor59
Animavore wrote:How is he making a hyperbola with only one point? How does he know the shape of the hyperbola with just one point? And I still don't get why a hyperbola and why it goes away from the centre?

ETA Not referring to the video here, just to the hyperbola that appears in special relativity:

Using t for time and x for space, take t2 - x2 = 1 for example

rewrite as t2 = 1 + x2

rewrite again as t = sqrt(1 + x2)

Let's just take positive square roots for now:

if x = 0, shoving it in that last equation gives t = 1
Letting x start to go positive, say x = 0.0001, gives t just a titchy bit greater than 1, and as x increases t goes even greater than one. It never gets closer. Letting x go negative, say x = -0.0001, ALSO gives t just a titchy bit greater than 1, since x gets squared, in the formula, so again as x goes negative t increases and stays greater than 1.

So 1 is the smallest t ever gets, and you get the hyperbola-in-the-top-half shape.

But of course when you take the square root of a number, you can take the negative square root as well as the positive one, so the hyperbola in the top half gets mirrored in the bottom half.