Euclid’s Geometry seemed pretty immutable…that is until Riemann came along in the mid 19th century and created new axioms of geometry. They were as follows:
A. Two points may determine more than one line
B. All lines are finite in length but endless– i.e. circles
C. There are no parallel lines
A. All perpendiculars to a straight line meet at one point (lines of longitude are perpendicular to the equator but meet at north pole)
B. Two straight lines enclose an area (Any two lines of longitude meet at both north and south pole, thus enclose an area)
C. The sum of the angles of any triangle is greater than 180 degrees.
Einstein further muddled (or clarified) the picture with his new Laws Of Physics embodied in Relativity. Here, he too saw space as curved and not flat. Thus, the geometry that applied to Einsteins’ physical laws are more Riemann than Euclid.
Andrei Linde and his “Expansionary Theory” researchers made similar revolutionary claims that were rejected until they recently received amazing scientific evidence supporting their theories regarding the origins of the universe…more on that in a later post!!!!