In three-dimensional Euclidean geometry, the distance r of a point from the origin, in terms of standard Cartesian coordinates, is given by r2 = x2 + y2 + z2. (See Fig. 5.18a. This is just the Pythagorean theorem – the two-dimensional case being perhaps more familiar.) In our three-dimensional Minkowskian geometry, the expression is formally very similar (Fig. 5.18b), the essential difference being that we now have two minus signs: Fig. 5.18. A comparison between the ‘distance’ measures in (a) Euclidean geometry and (b) Minkowskian geometry (where ‘distance’ means ‘time experienced’). s2 = t2
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Wow, Pythagorean theorem from Euclidean geometry can be used in minkowskis time space equations for light cones.
