دانلود کتاب سورپرایزهای ریاضی

Mathematics, when appropriately approached, can provide us with plentiful pleasant surprises. This is confirmed by a Google search of “mathematical surprises,” which, surprisingly, yields almost half a billion items. What is a surprise? The origins of the word trace back to Old French with roots in Latin: “sur” (over) and “prendre” (to take, to grasp, to seize). Literally, to surprise is to overtake. As a noun, surprise is both an unanticipated or bewildering event or circumstance, as well as the emotion caused by it. Consider, for example, an extract from a lecture by Maxim Bruckheimer1 on the Feuerbach circle: “Two points lie on one and only one straight line, this is no surprise. However, three points are not necessarily on one straight line and if, during a geometrical exploration, three points ‘fall into’ a straight line, this is a surprise and frequently we need to refer to this fact as a theorem to be proven. Any three points not on a straight line lie on one circle. However, if four points lie on the same circle, this is a surprise that should be formulated as a theorem. . . . Insofar as the number of points on a straight line is larger than 3, so is the theorem the more surprising. Likewise, insofar as the number of points lying on one circle is larger than 4, so is the theorem the more surprising. Thus, the statement that for any triangle there are nine related points on the same circle . . . is very surprising. Moreover, in spite of the magnitude of the surprise, its proof is elegant and easy.” In this book Mordechai Ben-Ari offers a rich collection of mathematical surprises, most of them less well known than the Feuerbach Circle and with sound reasons for including them. First, in spite of being absent from textbooks, the mathematical gems of this book are accessible with just a high school background (and patience, and paper and pencil, since fun does not come for free). Second, when a mathematical result challenges what we take for granted, we are indeed surprised (Chaps. 1, 13). Similarly, we are surprised by: the cleverness of an argument (Chaps. 2, 3), the justification of the possibility of a geometric construction by algebraic means (Chap. 16), a proof relying on an apparently unrelated topic (Chaps. 4, 5), a strange proof by induction (Chap. 6), new ways of looking at a well-known result (Chap. 7), a seemingly minor theorem becoming the foundation of a whole field of mathematics (Chap. 8), unexpected sources of inspiration (Chap. 9), rich formalizations emerging from purely recreational activities such as origami (Chaps. 10–12). These are all different reasons for the inclusion of the pleasant, beautiful and memorable mathematical surprises in this lovely book. So far I have addressed how the book relates to the first part of the definition of surprise, the cognitive rational reasons for the unexpected. As to the second aspect, the emotional aspect, this book is a vivid instantiation of what many mathematicians claim regarding the primary reason for doing mathematics: it is fascinating! Moreover, they claim that mathematics stimulates both our intellectual curiosity and our esthetic sensibilities, and that solving a problem or understanding a concept provides a spiritual reward, which entices us to keep working on more problems and concepts. It has been said that the function of a foreword tell readers why they should read the book. I have tried to accomplish this, but I believe that the fuller answer will come from you, the reader, after reading it and experiencing what the etymology of the word surprise suggests: to be overtaken by it!