J. Versluys' 1914 Book
Ching-Kuang Shene (冼鏡光), Professor Emeritus
Department of Computer Science
Michigan Technological University
Houghton, MI 49931
USA
Created September 17, 2025
Ching-Kuang Shene (冼鏡光), Professor Emeritus
Department of Computer Science
Michigan Technological University
Houghton, MI 49931
USA
Created September 17, 2025
J. Versluys published a book in 1914 in which he collected 96 proofs of the Pythagorean Theorem. Loomis critized Versluys' book because Versluys used the Pythagorean Identity to prove the Pythagorean Theorem as shown below.
|
Versluys' book is difficult to find nowadays; however, we are able to find a digital copy of this book as shown in the left image below and page 98 of this book here (right image).
|
|
With Google Translation, the original Dutch language text is translated to the following:
|
From this translation, it is obvious that Loomis missed the first sentence In trigonometry, it is usually shown without the aid of the Pythagorean theorm that ... We have shown that the angle sum identity of the sine function can be proved without using the Pythagorean Theorem on a previous page and in a textbook by Schur. Therefore, Loomis' criticism is incorrect and may be the origin of the false claim of the impossible proof.
Now let us move on to the Coordinate Axes Rotation topic to understand more about that Zimba's proof is nothing but a repeated one of the coordinate axes rotation, a typical topic in a coordinate/analytic geometry textbook, discussed more than hundred years ago.
Go back to Home Page.