Is the interval the height of the triangle?

[Saw]

I probably don't have anything else to contribute that would not get us into a monitor's lock down.

Well, yes, I see that we are lately running into circles in our respective comments. I understand you drop from the thread for that reason. I may post some developments in case someone else wants to comment, but in any case I thank you again for your very helpful intervention. You have told me about Loedel diagrams, which is a very interesting tool. It is curious that by adapting an Epstein diagram I had hit on the idea of this sort of diagrams, just with a different inclination, but I was not placing photon lines where they should and might have never realized this without your indication. We have agreed that at least in timelike events the interval is the height of a right triangle, so math and geometry are consistent. We have some discrepancies as to other types of events, but the discussion was fun. Thanks bobc2.

 

[bobc2]

Well, yes, I see that we are lately running into circles in our respective comments. I understand you drop from the thread for that reason. I may post some developments in case someone else wants to comment, but in any case I thank you again for your very helpful intervention. You have told me about Loedel diagrams, which is a very interesting tool. It is curious that by adapting an Epstein diagram I had hit on the idea of this sort of diagrams, just with a different inclination, but I was not placing photon lines where they should and might have never realized this without your indication. We have agreed that at least in timelike events the interval is the height of a right triangle, so math and geometry are consistent. We have some discrepancies as to other types of events, but the discussion was fun. Thanks bobc2.

And thanks to you, Saw. You brought some goot stuff in here. My feelings about the Minkowski metric not really being a metric (true metrics are positive definite) and therefore not applicable to yielding lengths of sides of triangles in general gets out of bounds for this forum.