From Pythagoras to Einstein (Paperback)

~ K. O. Friedrichs (Author) "The theorem ascribed to Pythagoras is concerned with the sides of a right triangle..." (more)
Key Phrases: inelastic impact, event vector, classical kinematics (more...)

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Product Description

The main thread running through this somewhat unorthodox approach to the special theory of relativity is the Pythagorean theorem. It appears in its most elementary geometric form in the very beginning of this monograph. Then it reappears in algebraic garb, is further modified and finally reinterpreted to play the role of one of the main characters in the special theory of relativity.

The first four chapters are easily accessible to high school sophmores or juniors. the remaining part of the book may be a little difficult for students who never studied physics, although the author actually employs only the notion of impact and presupposes no background in physics. With the aid of the vector geometry introduced earlier, he leads the reader from the impact conversation laws to the famous formula e=mc2.

About the Author

Kurt O. Friedrichsreceived his doctor's degree in Gottingen in 1925, and in 1930 became professor of mathematics at the Technische Hochschule in Braunschweig. In 1937 he joined his former teacher, Richard Courant, at New York University.

Product Details

• Paperback: 88 pages
• Publisher: Mathematical Association of America (MAA) (June 1975)
• Language: English
• ISBN-10: 0883856166
• ISBN-13: 978-0883856161
• Product Dimensions: 8.7 x 5.8 x 0.2 inches
• Shipping Weight: 2.4 ounces (View shipping rates and policies)
• Average Customer Review: 4.0 out of 5 stars  See all reviews (1 customer review)
• Amazon.com Sales Rank: #1,178,674 in Books (See Bestsellers in Books)

Customer Reviews

Most Helpful Customer Reviews

12 of 12 people found the following review helpful:

4.0 out of 5 stars The Pythagorean theorem as a unifying theme, April 22, 2001

By	Charles Ashbacher "([e-mail])" (Marion, Iowa United States([e-mail])) - See all my reviews (TOP 50 REVIEWER)

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.