This encyclopedia contains trigonometric identity proofs for some three hundred identities. The book is presented in the form of mathematical games for the reader's enjoyment and includes a concordance of trigonometric identities, enabling easy reference.Trig or Treat is a must-have for: ? every student of trigonometry, to find the proofs for trigonometric identities that may be set in class or in exams;? every teacher of trigonometry, to have easy access to trigonometric identities of different levels of difficulty, to set assignments for different levels of students;? every library, to provide a ready resource for students? every aficionado of Sudoku, crossword puzzles, jigsaw puzzles, Tetris, and other games, who love an intellectual challenge.

This encyclopedia contains trigonometric identity proofs for some three hundred identities. The book is presented in the form of mathematical games for the reader's enjoyment and includes a concordance of trigonometric identities, enabling easy reference.Trig or Treat is a must-have for:• every student of trigonometry, to find the proofs for trigonometric identities that may be set in class or in exams;• every teacher of trigonometry, to have easy access to trigonometric identities of different levels of difficulty, to set assignments for different levels of students;• every library, to provide a ready resource for students• every aficionado of Sudoku, crossword puzzles, jigsaw puzzles, Tetris, and other games, who love an intellectual challenge.

Martin Gardner's Mathematical Games columns in Scientific American inspired and entertained several generations of mathematicians and scientists. Gardner in his crystal-clear prose illuminated corners of mathematics, especially recreational mathematics, that most people had no idea existed. His playful spirit and inquisitive nature invite the reader into an exploration of beautiful mathematical ideas along with him. These columns were both a revelation and a gift when he wrote them; no one--before Gardner--had written about mathematics like this. They continue to be a marvel. This is the original 1988 edition and contains columns published from 1974-1976.

The wide availability of digital educational resources for mathematics teaching and learning is indisputable, with some notable genres of technologies having evolved, such as graphing calculators, dynamic graphing, dynamic geometry and data visualization tools. But what does this mean for teachers of mathematics, and how do their roles evolve within this digital landscape? This essential book offers an international perspective to help bridge theory and practice, including coverage of networking theories, curriculum design, task implementation, online resources and assessment. Mathematics Education in the Digital Age details the impacts this digital age has, and will continue to have, on the parallel aspects of learning and teaching mathematics within formal education systems and settings. Written by a group of international authors, the chapters address the following themes: Mathematics teacher education and professional development Mathematics curriculum development and task design The assessment of mathematics Theoretical perspectives and methodologies/approaches for researching mathematics education in the digital age This book highlights not only the complex nature of the field, but also the advancements in theoretical and practical knowledge that is enabling the mathematics education community to continue to learn in this increasingly digital age. It is an essential read for all mathematics teacher educators and master teachers.

*THIS BOOK IS AVAILABLE AS OPEN ACCESS BOOK ON SPRINGERLINK* One of the most significant tasks facing mathematics educators is to understand the role of mathematical reasoning and proving in mathematics teaching, so that its presence in instruction can be enhanced. This challenge has been given even greater importance by the assignment to proof of a more prominent place in the mathematics curriculum at all levels. Along with this renewed emphasis, there has been an upsurge in research on the teaching and learning of proof at all grade levels, leading to a re-examination of the role of proof in the curriculum and of its relation to other forms of explanation, illustration and justification. This book, resulting from the 19th ICMI Study, brings together a variety of viewpoints on issues such as: The potential role of reasoning and proof in deepening mathematical understanding in the classroom as it does in mathematical practice. The developmental nature of mathematical reasoning and proof in teaching and learning from the earliest grades. The development of suitable curriculum materials and teacher education programs to support the teaching of proof and proving. The book considers proof and proving as complex but foundational in mathematics. Through the systematic examination of recent research this volume offers new ideas aimed at enhancing the place of proof and proving in our classrooms.

​The book records the essential discoveries of mathematical and computational scientists in chronological order, following the birth of ideas on the basis of prior ideas ad infinitum. The authors document the winding path of mathematical scholarship throughout history, and most importantly, the thought process of each individual that resulted in the mastery of their subject. The book implicitly addresses the nature and character of every scientist as one tries to understand their visible actions in both adverse and congenial environments. The authors hope that this will enable the reader to understand their mode of thinking, and perhaps even to emulate their virtues in life.

Since precious few architectural drawings and no theoretical treatises on architecture remain from the premodern Islamic world, the Timurid pattern scroll in the collection of the Topkapi Palace Museum Library is an exceedingly rich and valuable source of information. In the course of her in-depth analysis of this scroll dating from the late fifteenth or early sixteenth century, Gülru Necipoğlu throws new light on the conceptualization, recording, and transmission of architectural design in the Islamic world between the tenth and sixteenth centuries. Her text has particularly far-reaching implications for recent discussions on vision, subjectivity, and the semiotics of abstract representation. She also compares the Islamic understanding of geometry with that found in medieval Western art, making this book particularly valuable for all historians and critics of architecture. The scroll, with its 114 individual geometric patterns for wall surfaces and vaulting, is reproduced entirely in color in this elegant, large-format volume. An extensive catalogue includes illustrations showing the underlying geometries (in the form of incised “dead” drawings) from which the individual patterns are generated. An essay by Mohammad al-Asad discusses the geometry of the muqarnas and demonstrates by means of CAD drawings how one of the scroll’s patterns could be used co design a three-dimensional vault.

Foundations of Mathematics offers the university student or interested reader a unique reference book by covering the basics of algebra, trigonometry, geometry, and calculus. There are many instances in the book to demonstrate the interplay and interconnectedness of these topics. The book presents definitions and examples throughout for clear, easy learning. Numerous exercises are included at the ends of the chapters, and readers are encouraged to complete all of them as an essential part of working through the book. It offers a unique experience for readers to understand different areas of mathematics in one clear, concise text. Instructors’ resources are available upon adoption. Features: •Covers the basics of algebra, trigonometry, geometry, and calculus •Includes all of the mathematics needed to learn calculus •Demonstrates the interplay and interconnectedness of these topics •Uses numerous examples and exercises to reinforce concepts

A multifaceted biography of a brilliant mathematician and iconoclast A mathematician unlike any other, John Horton Conway (1937–2020) possessed a rock star’s charisma, a polymath’s promiscuous curiosity, and a sly sense of humor. Conway found fame as a barefoot professor at Cambridge, where he discovered the Conway groups in mathematical symmetry and the aptly named surreal numbers. He also invented the cult classic Game of Life, a cellular automaton that demonstrates how simplicity generates complexity—and provides an analogy for mathematics and the entire universe. Moving to Princeton in 1987, Conway used ropes, dice, pennies, coat hangers, and the occasional Slinky to illustrate his winning imagination and share his nerdish delights. Genius at Play tells the story of this ambassador-at-large for the beauties and joys of mathematics, lays bare Conway’s personal and professional idiosyncrasies, and offers an intimate look into the mind of one of the twentieth century’s most endearing and original intellectuals.