Up to the work of Riemann and Gauss, this definition would have made clear to me examples of geometrical objects: a line, square, cube, hypercube; each of these possessing geometrical properties such as the number of sides, angles between faces, the dimension of space that contains them etc. Hence a geometrical object was a set of measurements associated with an object using a ruler.

After the work of Einstein and Minkowski who showed that time and space were a part of one another, would it be correct to say:

1. a geometrical object is a set of measurements associated with an object of distance and time using a ruler and a clock?

2. Geometrical objects includes an interval of time, the invariant space-time interval?

After the work of Einstein and Minkowski who showed that time and space were a part of one another, would it be correct to say:

1. a geometrical object is a set of measurements associated with an object of distance and time using a ruler and a clock?

2. Geometrical objects includes an interval of time, the invariant space-time interval?