Science,People&Politics issn:1751598x online/print/pdf. Issue three, 2017.

HUMANITIES SCIENCE POLITICS

HOME | ISSUE THREE (July - Sept.) 2017 HTML

Science, People & Politics ISSN 1751-598X ISSUE THREE (July - Sept) 2017 PAGE 9

An interesting point the author makes is that most of us, when questioned about the Pythagorean theorem, state it in algebraic form: a ² + b² = c². We then link the theorem to calculation of a right triangle's side, when the length of the other two are known.

Yet Euclid, and all Greeks before him, did not have algebra. Their train of thought must have been different from ours...

There are two classical demonstrations of the famous theorem: one, very popular, from Euclid I.47 (the familiar algebraic expression), and one, much less known, from Euclid VI.31. The latter follows a line of reasoning which is completely different from the former: and is based on ratios, proportions, and similarities.

From the less popular Euclidean proposition, a fundamental fact emerges. Every rectilinear figure, that is every polygonal figure traced on a plane, can be dissected into triangles. And, most importantly, each triangle can be reduced to two right triangles. As this can be applied down to infinitely small scales, the metaphysical role of the right triangle as the founding block of the whole cosmos stems out of the ancient pages from which Euclid drew inspiration, namely Egyptian and Babylonian math.

Or so maintains the author.

Robert Hahn declares he has written this book with three audiences in mind:

scholars and students interested in ancient Greek philosophy and its origins;

advanced seminars at the graduate level in philosophy and history of mathematics, and;

high school students and math clubs. Probably because of these deliberate targets, the book is an interesting reading, but it is certainly not for the casual reader, because it is full of geometrical arguments, of drawings and of demon-strations. But it is not only geometry hindering the reader.

The line of thought is not always easy to follow for a non-expert. At times, it is easy to get lost in philosophical arguments. In all fairness, one must say that there are also very amusing parts, which become obvious after the author has explained them to you.

One for all: the hypotenuse theorem, which is a most appropriate name, applies not only to squares built on the sides of a right triangle, but also to any triplet of similar figures (semicircles, triangles, or any polygon).

Indeed, if you are interested in understanding how Pythagoras' Theorem came to be, and the philosophy and history of mathematics are your passion, you will like this book a lot. In this respect, the author has certainly reached his declared goal.

*Ferdinando Patat is head of the Observing Programmes Office of the European Southern Observatory (ESO), which is the European Organization for Astronomical Research.

9 SCIENCE, PEOPLE & POLITICS [ISSN 1751-598X]

|
|
|
|

PAGE 7
BOOK REVIEWS:Ethics, Pythagoras, Megatech

PAGE 8
BOOK REVIEWS:Ethics, Pythagoras, Megatech

PAGE 9
BOOK REVIEWS:Ethics, Pythagoras, Megatech

PAGE 13
BOOK REVIEWS:Ethics, Pythagoras, Megatech

PAGE 14
From British Courts

PAGE 15
From British Courts

PAGE 16
From British Courts

PAGE 17
Poems of Science

PAGE 18
Poems of Science

HTML/CSS by Helen Gavaghan©