You can make something like this properly by defining a different metric. For example with metric dl2 = dx2 - dy2 the vector (1, 1) has length 0, so you can make a “triangle” with sides of lengths 1, -1 and 0.
You can make something like this properly by defining a different metric. For example with metric dl2 = dx2 - dy2 the vector (1, 1) has length 0, so you can make a “triangle” with sides of lengths 1, -1 and 0.
It depends which metric definition are you using. The one I wrote is a pseudo-Riemannian metric that is not positive defined.
Normally physicists use that generalized metric definition because spacetime in most cases has a metric signature of (-1, 1, 1, 1). Points with zero distance are not necessarily the same point, they just are in the same null geodesic.