Beautiful geometry (Q2872664)

This is indeed a beautiful book. In each of the fifty chapters Eli Maor chooses a topic and explains a theorem or a mathematical concept within the chosen topic. For each of the chapters there is a beautiful colorful painting by Eugen Jost that illustrates the topic chosen. There are chapters on basic theorems on triangles, there are the traditional theorems that are always present is this type of work but there are also some that are not so usual. As an example let us look at the Pythagorean theorem. It is a usual subject in this type of works but the author actually presents Euclid's proof explaining it and explaining the reader why it is still so important ``Yet of the 400 or so demonstrations of the theorem, Euclid's proof stands out in its sheer austerity, relying on just a bare minimum of previously established theorem''. One can find theorems stated and some of them proved in this book that are not found in elementary books since the beginning of the 20th century.NEWLINENEWLINENEWLINEThere are several other propositions from Euclid, chapter 2 deals with proposition 38, and chapter 11 explains propositions 35 and 36. In chapter 12 it is given a more detailed interpretation on these two theorems (``Different, yet the same''). There are chapters on Quadrilaterals (connect the midpoints of any quadrilateral and you obtain a parallelogram), on Pentagons (the relation of the regular pentagon and the golden ratio) on Hexagons (related with tessellations of the plane and Euclidean constructions). There is a chapter on the 17-sided regular polygon. There are chapters that deal with properties of numbers (perfect numbers, triangular numbers, primes, and so on). The chapters dealing with \(\pi\) include references to the Rhind Papyrus and citations from the bible with references to the measures of a pond that adorned the entrance to the Holy Temple in Jerusalem.NEWLINENEWLINENEWLINEThe authors include some chapters dedicated to special lines, conics, the logarithmic spiral, the cycloid, epicycloids, hypocycloids, the Euler Line among others. In order to illustrate the diversity of themes I will mention the chapter on Lissajous figures, following the chapter ``The Audible Made Visible''.NEWLINENEWLINENEWLINEThe book has 187 pages including bibliography and index and the authors give each chapter usually four pages, one of which is a full page with the plate designed by Jost.NEWLINENEWLINENEWLINEThese pages include historical data; sometimes complete proofs and sometimes drawings to illustrate the text. In order to maintain the size of the chapters the authors chose to let some subjects occupy more than one chapter.NEWLINENEWLINENEWLINEThe authors include an Appendix of 6 pages where they show the proofs of some theorems that are mentioned and not proved within the text because they are more technical. This appendix includes the proof of the theorem for the midpoint of the sides of quadrilaterals mentioned above, the proof that \(\sqrt{2}\) is irrational, Euclid's proof of the infinitude of the primes, the sum of a geometric progression and the sum of the first \(n\) Fibonacci numbers, the construction of a regular Pentagon, the proof of Ceva's theorem, some properties of the inversion and the proof a property of Pythagorean triplets.NEWLINENEWLINENEWLINEFor all subjects the visual interpretation in very important and the plates created or chosen for each topic are very well adjusted and give an invaluable contribution for the graphic aspect of the book and also for the understanding of what is being explained. For example plate 3, plate 48, plate 41, plate 39, plate 9 among others are explaining what the theorem is saying showing examples.NEWLINENEWLINENEWLINEA beautiful book that is as delightful to see as to read. Once you start you are compelled to read the next subject, and the next, and the next.