Exploring Classical Greek Construction Problems With Interactive Geometry Software

In this book the classical Greek construction problems are explored in a didactical, enquiry based fashion using Interactive Geometry Software (IGS). The book traces the history of these problems, stating them in modern terminology. By focusing on constructions and the use of IGS the reader is confronted with the same problems that ancient mathematicians once faced. The reader can step into the footsteps of Euclid, Viète and Cusanus amongst others and then by experimenting and discovering geometric relationships far exceed their accomplishments. Exploring these problems with the neusis-method lets him discover a class of interesting curves. By experimenting he will gain a deeper understanding of how mathematics is created. More than 100 exercises guide him through methods which were developed to try and solve the problems. The exercises are at the level of undergraduate students and only require knowledge of elementary Euclidean geometry and pre-calculus algebra. It is especially well-suited for those students who are thinking of becoming a mathematics teacher and for mathematics teachers.

This book offers an analysis of the ground breaking mathematical work of Gregorio a San Vicente and his student and shows that the Flemish Jesuit Mathematics School had profound influence on mathematics in the seventeenth century.

The innovative volume seeks to broaden the scope of research on mathematical problem solving in different educational environments. It brings together contributions not only from leading researchers, but also highlights collaborations with younger researchers to broadly explore mathematical problem-solving across many fields: mathematics education, psychology of education, technology education, mathematics popularization, and more. The volume’s three major themes—technology, creativity, and affect—represent key issues that are crucially embedded in the activity of problem solving in mathematics teaching and learning, both within the school setting and beyond the school. Through the book’s new pedagogical perspectives on these themes, it advances the field of research towards a more comprehensive approach on mathematical problem solving. Broadening the Scope of Research on Mathematical Problem Solving will prove to be a valuable resource for researchers and teachers interested in mathematical problem solving, as well as researchers and teachers interested in technology, creativity, and affect.

An intriguing look at the "impossible" geometric constructions (those that defy completion with just a ruler and a compass), this book covers angle trisection and circle division. 1970 edition.

What is the role of mathematics in the secondary classroom? What is expected of a would-be maths teacher? How is mathematics best taught and learnt? Learning to Teach Mathematics in the Secondary School combines theory and practice to present a broad introduction to the opportunities and challenges of teaching mathematics in the modern secondary school classroom. Written specifically with the new and student teacher in mind, the book covers a wide range of issues related to the teaching of mathematics, including: The role of ICT Assessment for Learning NEW Using mathematics in context NEW Communicating mathematically Planning mathematics lessons Including special-needs pupils Teaching mathematics post-16 Professional Development Already a major text for many university teaching courses, this fully revised third edition takes into account new developments in the National Curriculum as well as recent changes to the standards for Qualified Teacher Status. Featuring two brand new chapters, a glossary of useful terms, addresses for resources and organisations, and tasks designed to prompt critical reflection and support thinking and writing at Masters level, this book will help you make the most of school experience, during your training and beyond. Designed for use as a core textbook, this new edition of Learning to Teach Mathematics in the Secondary School provides essential guidance and advice for all trainee and practising teachers of secondary mathematics.

Geometry: The Line and the Circle is an undergraduate text with a strong narrative that is written at the appropriate level of rigor for an upper-level survey or axiomatic course in geometry. Starting with Euclid's Elements, the book connects topics in Euclidean and non-Euclidean geometry in an intentional and meaningful way, with historical context. The line and the circle are the principal characters driving the narrative. In every geometry considered—which include spherical, hyperbolic, and taxicab, as well as finite affine and projective geometries—these two objects are analyzed and highlighted. Along the way, the reader contemplates fundamental questions such as: What is a straight line? What does parallel mean? What is distance? What is area? There is a strong focus on axiomatic structures throughout the text. While Euclid is a constant inspiration and the Elements is repeatedly revisited with substantial coverage of Books I, II, III, IV, and VI, non-Euclidean geometries are introduced very early to give the reader perspective on questions of axiomatics. Rounding out the thorough coverage of axiomatics are concluding chapters on transformations and constructibility. The book is compulsively readable with great attention paid to the historical narrative and hundreds of attractive problems.

Sacred geometry is at the heart of a thousand years of art and architecture as represented in mosques, temples and churches around the world. Stunning in their search of perfection amid countless symmetries the art achieves a beauty inspired by its divine motivations. On a more practical side, sacred art represents an excellent application of the principles of geometry as illustrated by Euclid in the Elements. Countless constructions and theorems first discovered by the ancient Greek mathematicians are carefully merged with craftsmanship to produce murals, paintings and mosaics of infinite variety. This book grew out of a set of workshops done primarily through the Monterey Bay Area Math Project over the last several years. The book begins with a discussion of compass-straightedge constructions of polygons and the variety of regular and semi-regular tilings. The Polygon-in-Contact method as initially documented in the Topkapi Scrolls and further developed by contemporary scholars and artists is introduced as a method of generating traditional Islamic Geometric patterns. Many examples are illustrated with varying degrees of complexity suitable for all age groups. In addition to developing traditional patterns, the methods shown illustrate areas of generalization constrained only by students imagination.