SYMMETRY AS GEOMETRY KUWAIT INTERNATIONAL AIRPORT

摘要

Since the launch of German mathematician Felix Klein's Erlangen programme of 1872, the notions of symmetry and geometry have been tied together in an understanding of space that has changed the way in which we appreciate the universe. For example, together with Bernhard Riemann's ideas a few years earlier, Klein's concepts were arguably a big part of the conceptual foundation of the physics that was necessary for Albert Einstein to describe his theory of general relativity. Klein defines a geometry to be exactly the objects of a space that are invariant under -that is, not changed by - a symmetry acting on the space. A basic example is a circle that is invariant under arbitrary rotations, and an example with a subset of the symmetries of the circle is the equilateral triangle that is invariant under rotations of 120 degrees and mirroring along its three axes (the dihedral group of order 6, D3).