A Study of Vectors and the Geometry of Space

Space is a term that can refer to various phenomena in science, mathematics, and communications. This Research Group explored modern geometry and the concept of space. Although a divide between ancient and modern geometry can be framed in different ways, the most useful one may well be the emergence of the consideration of space itself as an object of geometrical investigation. Greek mathematics understood geometry as a study of straight lines, angles, circles and planes, or in more general terms as a science of figures conceived against an amorphous background space whose definition lies outside the limits of the theory. This understanding was superseded by a conception of space (and spaces, now plural for the first time) itself endowed with geometrical properties. The main concern of this new geometrical science is to characterize the structures and features of geometrical space in axioms and demonstration. Although it is quite clear that this revolution in geometry helped shape the scientific world such that contemporary mathematics remains incomprehensible without it, the questions of when, why and how this revolution took place, prior to this research, were still to some extent obscure.Space is usually thought to begin at the lowest altitude at which satellites can maintain orbits for a reasonable time without falling into the atmosphere. This is approximately 160 kilometers (100 miles) above the surface. Astronomers may speak of interplanetary space (the space between planets in our solar system), interstellar space (the space between stars in our galaxy), or intergalactic space (the space between galaxies in the universe). Some scientists believe that space extends infinitely far in all directions, while others believe that space is finite but unbounded, just as the 2-space surface of the earth has finite area yet no beginning nor end.