How Many Points are there in a Line Segment? – A New Answer from a Discrete Cellular Space Viewpoint

Abstract

While it is known that Euclid’s five axioms include a proposition that a line consists at least of two points, modern geometry consistently avoids any discussion on the precise definition of points, lines, etc. It is our aim to clarify one of notorious question in Euclidean geometry from discrete cellular space (DCS) viewpoint: How many points are there in a line segment? In retrospect, it may offer an alternative for quantum gravity, i.e., by exploring discrete gravitational theories. To elucidate our propositions, in the last section we will discuss some implications of the discrete cellular space model in several areas of interest: (a) cell biology, (b) cellular computing, (c) Maxwell equations, (d) low energy fusion, and (e) cosmology modeling.