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At the beginning of the twentieth century, the American mathematics teacher Elisha Scott Loomis compiled a set of different proofs of the Pythagorean theorem, which he discovered in magazines and books or developed himself. The second edition of the book, published in 1940, contained about 370 pieces of evidence. The collection was reprinted unchanged in 1968 on behalf of the National Council of Teachers of Mathematics (NCTM), but is rarely found in antique books.
Mario Gerwig, a teacher of mathematics and chemistry at the Grammar School in Basel, has now set himself the task of translating the body of evidence in English into German, as well as sifting, organizing, adding to and – amazingly. Number of places – remove errors.
Wide and understandable set of evidence
The result is a comprehensive work with structured, easy-to-understand comments on the steps of the individual guides as well as carefully crafted drawings (using Cinderella software), which are more than just replacing the hand drawings by Loomis. Above all, Gerwig sought to fill in the gaps in the evidence and to show links with other engineering theories.
At the end of the 24-page introduction, in which Gerwig explains his approach, he makes a recommendation as to which evidence readers should particularly look at – in almost all cases this is evidence of famous mathematicians such as Fibonacci or Bhascara.
In the first chapter the author provides an overview of what was known about the Pythagoras and the mathematical facts with which they were familiar. In the next section there are a total of 109 proofs that Loomis and Gerwig call algebraically. The chapter breaks down into ideas of proof that can be derived from considerations of similarity that relate to the geometric mean of path lengths or the result of circular shapes and their dendrites or tangents. The relationship equations after transformation lead to the desired equation A2 + b2 = c2. The broad aggregate considerations, of which individual road conditions can be seen in individual figures, are impressive.
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