Question

What is the geometric explanation for why the interior angles of a triangle sum to 180 degrees in both Euclidean space and Minkowski spacetime?

Answer 1

Four-dimensional Euclidean space has the same topology and affine structure as Minkowski spacetime, though the two have different metric structures. Given that the interior angles of a triangle always sum to 180 degrees in both four-dimensional Euclidean space, and in Minkowski spacetime, is this fact due to both spaces having the same topology and/or affine structure, or is there some other explanation

Answer 2

$\huge{\bf{\color{magenta}{\huge{\bf{\color{magenta}{Minkowski \: spacetime \: IS \: Euclidean \: space \: (with \: the \: addition \: of \: time), therefore \: the \: properties \: of \: Minkowski \: space, \: should be the \: same/apply \: in \: Euclidean \: space. }}}}}}$