Foreword

To many generations trigonometry was one of the mathematical subjects taught in school, along with arithmetic, algebra, geometry, and analysis. For some time now, due to the need to diminish the syllabus, trigonometry stops being considered a distinct subject with its own handbook, and is included in the syllabus for algebra, geometry and analysis. Under these circumstances, the unitary nature of trigonometry is sacrificed. But there are still enough pupils interested in mathematics, enough graduates and students, not to mention the math teachers, the numerous engineers and economists that are still fond of elementary, school mathematics, but who would like to reconsider it from a superior point of view, that is from the perspective of mathematic knowledge accumulated in time. This book, written rigorously, but passionately, has a perspective that is equally based on the ensemblist structure of modern mathematics, on the elements of real analysis and the axiomatic fundaments of geometry, and it reaches climax with the applications that imply analytic algebraic and geometric abilities. From the historical presentation of mathematics given in the book the reader can, for example, learn the surprising fact that, from a chronologically point of view, plane trigonometry was preceded by spherical trigonometry, necessary in astronomy, although the latter is more complex than the former. The author of this book, Professor Vasile Postolică, teaching at “Vasile Alecsandri” University of Bacău, is a mathematician that has convincingly asserted himself in research, with results published in exacting publications, results that have become a part of the international circuit. His vast experience in school and university teaching made possible the development of this successful experiment, experienced by few professors: the re-writing of a chapter of school mathematics from a superior point of view. This adventurous path has been taken by mathematicians like Felix Klein and Jacques Hadamard, hence this is a very serious project. We congratulate Professor Vasile Postolică for this success. At the same time, supposing that he will continue this adventure, we suggest that he broaden the perspective by introducing elements of trigonometric series and Fourier series, that are, probably, the most important use of the trigonometric functions, having a particular relevance in physics. Some elements of spherical trigonometry would be also timely. The present book deserves to be successful in book stores and justifies every one of our praises to its author.