"Greg Egan - Foundations 1 - Special Relativity" - читать интересную книгу автора (Egan Greg)

space makes a useful rehearsal for tackling the problem in spacetime. It's easier to deal
with ordinary space, where we can rely on everyday geometrical intuition, and then the
results can be carried over to spacetime with only a few small changes.
 Egan: "Foundations 1"/p.4




First, a quick review of the geometry we'll need. Pythagoras's theorem says
that the square of the hypotenuse (OP in Figure 2) of any right-angle triangle equals the
sum of the squares of the other two sides (OQ and PQ).


OP2 OQ2 + PQ2
=

The sine of the angle marked A is equal to the ratio between the side opposite it
(PQ) and the hypotenuse (OP).


sin A = PQ / OP
PQ = OP sin A


The cosine of A is equal to the ratio between the side adjacent to it (OQ) and the
hypotenuse (OP).


cos A = OQ / OP
OQ = OP cos A


The tangent of A is equal to the ratio between the side opposite it (PQ), and the
side adjacent to it (OQ).


tan A = PQ / OQ
= (OP sin A) / (OP cos A)
= sin A / cos A
 Egan: "Foundations 1"/p.5



There's a simple relationship between the sine and cosine of an angle, which
comes straight from the definitions and Pythagoras's theorem:


(cos A)2 + (sin A)2 (OQ / OP)2 + (PQ / OP)2
=
(OQ2 + PQ2) / OP2