This is the second of the little booklets, published by Wooden Books, which investigates really fascinating aspects of the natural world (as well as of the mind) in small digestable snippets for the interested reader.
This time its the concept and prevalence of symmetry as it is found in all manner of phenomena such as crystal structures, the Platonic solids, animal body plans, in physics and art.
Firstly, the book shows the reader how symmetry arises in the first place, in other words it answers the question: how is symmetry possible? An answer to such a question involves a set of identical objects or patterns, which are arranged in some form of (usually infinite) pattern whereby one such object may be transformed into the other with a simple operation such as a reflection about a line, a rotation about a point or a translation along a line. These kinds of transformations are the simplest forms of symmetry operations which maintain patternm invariance. The next set of far more intersting kinds of transformatioon are constant dilation symmetries whereby an object is magnified in size along a set of curves followed by fractal symmetries whereby the pattern present in one length scale persists into multiple, higher scales. Naturally, this automatically leads into the idea of asymmetry and also dynamic symmetry wheresymmetry is created as part of a process.