Customer Reviews

From Pythagoras to Einstein

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The mathematical theorem with the greatest name recognition is the Pythagorean theorem. Originating as an empirical fact used in land surveying, it is easy to prove and the number of distinct proofs is rather large. People from many walks of life have devised a proof, one of which was even the president of the United States (Garfield). The Pythagorean theorem is the unifying theme of the topics in this book. Considered as a special case of more general operations, it is the base for the explanation of some advanced physics and mathematics.
Vector analysis is a direct extension of the measuring of distance, in that direction is included. The basic operations on vectors involves the use of triangles, and the notion of perpendicular is based on the Pythagorean theorem. Since a vector can also denote velocity, it is an easy generalization to include the kinetic energy of motion. Finally, by adding in the potential energy of position and rest mass, the end result is a description of the special theory of relativity. Each step follows as a logical consequence of the previous, giving a unique and understandable derivation of the most famous equation of all e = m(c^2).
With the exception of the last chapters, where some of the transformations are mathematically more difficult, basic high school algebra is all that is needed to understand the material. Even then, a concerted effort will lead to understanding. This is an approach that can be used for several purposes, the foremost of which is to demonstrate how basic, empirical mathematics was the starting point for the development of explanations of the most complex phenomena.
I found this thematic approach to be a very successful one. This is a book that could be used as a supplement in high school and college physics courses. It would also work well as a demonstration of how applied mathematics led to a theorem which eventually led back to more applied mathematics.