- #1
Vorde
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In one of the early chapters of Gravity by Hartle, he is developing the line element on a sphere in preparation for developing the concept of a spacetime interval. Whilst finishing up the proof Hartle sort of implicitly says that if two lines are orthogonal the line element connecting two points on the two lines can be given by a pythagorean-like equation (the distance)2=(position on one line)2+(position on the other)2.
Is the more general question of a line element being the sum of the squares of the two orthogonal lines true?
Sorry if this question is a bit messy.
Is the more general question of a line element being the sum of the squares of the two orthogonal lines true?
Sorry if this question is a bit messy.