Certainly as far back as the era of ancient Egypt. The form of the pyramids, and their alignment is remarkably true. And even then, this was almost after a lengthy period of cerebration and measuremnt.
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One main characteristic of non-Euclidean geometry is hyperbolic geometry. The other is elliptic geometry. Non-Euclidean geometry is still closely related to Euclidean geometry.
molecular geometry is bent, electron geometry is tetrahedral
Molecular geometry will be bent, electron geometry will be trigonal planar
It has seesaw geometry.
Geometry is based on logic.