Wie lautet die Formel zur Flächenberechnung eines Kreises? Diese und andere Schlüsselfragen zum Thema Geometrie können Ihre Schüler der 5. und 6. Klasse mithilfe dieser motivierenden Quizkarten beantworten. Auf spielerische Weise eignen sie sich damit grundlegende Rechenfertigkeiten und mathematisches Grundwissen an, das sie langfristig für die sichere Anwendung in den höheren Klassenstufen benötigen. Das Mathe-Quiz kann in drei Differenzierungsstufen und in Form von Einzel- oder Partnerarbeit eingesetzt werden. Es lässt sich aber auch im Plenum als spannender Mathematik-Wettkampf und zur raschen Überprüfung anwenden. Die Lösungen zu den Aufgaben stehen direkt auf den Karten in umgekehrter Schrift bereit.
This new volume of the Mathematical Olympiad Series focuses on the topic of geometry. Basic and advanced theorems commonly seen in Mathematical Olympiad are introduced and illustrated with plenty of examples. Special techniques in solving various types of geometrical problems are also introduced, while the authors elaborate extensively on how to acquire an insight and develop strategies in tackling difficult geometrical problems. This book is suitable for any reader with elementary geometrical knowledge at the lower secondary level. Each chapter includes sufficient scaffolding and is comprehensive enough for the purpose of self-study. Readers who complete the chapters on the basic theorems and techniques would acquire a good foundation in geometry and may attempt to solve many geometrical problems in various mathematical competitions. Meanwhile, experienced contestants in Mathematical Olympiad competitions will find a large collection of problems pitched at competitions at the international level, with opportunities to practise and sharpen their problem-solving skills in geometry.
Lockhart s ´´Mathematician s Lament´´ outlined how we introduce math to students in the wrong way. ´´Measurement´´ explains how math should be done. With plain English and pictures, he makes complex ideas about shape and motion intuitive and graspable, and offers a solution to math phobia by introducing us to math as an artful way of thinking and living.
This engaging review guide and workbook is the ideal tool for sharpening your Trigonometry skills! This review guide and workbook will help you strengthen your Trigonometry knowledge, and it will enable you to develop new math skills to excel in your high school classwork and on standardized tests. Clear and concise explanations will walk you step by step through each essential math concept. 500 practical review questions, in turn, provide extensive opportunities for you to practice your new skills. If you are looking for material based on national or state standards, this book is your ideal study tool! Features: .Aligned to national standards, including the Common Core State Standards, as well as the standards of non-Common Core states and Canada .Designed to help you excel in the classroom and on standardized tests .Concise, clear explanations offer step-by-step instruction so you can easily grasp key concepts .You will learn how to apply Trigonometry to practical situations .500 review questions provide extensive opportunities for you to practice what you´ve learned
This book offers complete documentation for Cinderella.2. New components feature algorithms via a specially developed scripting language, which interacts smoothly with the geometry and physics components. Cinderella.2 is Math in Motion all the way, and this book is an indispensable companion. Cinderella.2, the new version of the well-known interactive geometry software, has become an even more versatile tool than its predecessor. The geometry component extends the functionality to such spectacular objects as dynamic fractals, and the software includes two major new components: physical simulation such as of mechanical objects, virtual electronic devices, and electromagnetic properties. Cinderella.2 Documentation offers complete instruction and techniques for using Cinderella.2.
Thomas Cecil is a math professor with an unrivalled grasp of Lie Sphere Geometry. Here, he provides a clear and comprehensive modern treatment of the subject, as well as its applications to the study of Euclidean submanifolds. It begins with the construction of the space of spheres, including the fundamental notions of oriented contact, parabolic pencils of spheres, and Lie sphere transformations. This new edition contains revised sections on taut submanifolds, compact proper Dupin submanifolds, reducible Dupin submanifolds, and the cyclides of Dupin. Completely new material on isoparametric hypersurfaces in spheres and Dupin hypersurfaces with three and four principal curvatures is also included. The author surveys the known results in these fields and indicates directions for further research and wider application of the methods of Lie sphere geometry.
This book explains and helps readers to develop geometric intuition as it relates to differential forms. It includes over 250 figures to aid understanding and enable readers to visualize the concepts being discussed. The author gradually builds up to the basic ideas and concepts so that definitions, when made, do not appear out of nowhere, and both the importance and role that theorems play is evident as or before they are presented. With a clear writing style and easy-to- understand motivations for each topic, this book is primarily aimed at second- or third-year undergraduate math and physics students with a basic knowledge of vector calculus and linear algebra.
This is a textbook on differential geometry well-suited to a variety of courses on this topic. For readers seeking an elementary text, the prerequisites are minimal and include plenty of examples and intermediate steps within proofs, while providing an invitation to more excursive applications and advanced topics. For readers bound for graduate school in math or physics, this is a clear, concise, rigorous development of the topic including the deep global theorems. For the benefit of all readers, the author employs various techniques to render the difficult abstract ideas herein more understandable and engaging. Over 300 color illustrations bring the mathematics to life, instantly clarifying concepts in ways that grayscale could not. Green-boxed definitions and purple-boxed theorems help to visually organize the mathematical content. Color is even used within the text to highlight logical relationships. Applications abound! The study of conformal and equiareal functions is grounded in its application to cartography. Evolutes, involutes and cycloids are introduced through Christiaan Huygens´ fascinating story: in attempting to solve the famous longitude problem with a mathematically-improved pendulum clock, he invented mathematics that would later be applied to optics and gears. Clairaut´s Theorem is presented as a conservation law for angular momentum. Green´s Theorem makes possible a drafting tool called a planimeter. Foucault´s Pendulum helps one visualize a parallel vector field along a latitude of the earth. Even better, a south-pointing chariot helps one visualize a parallel vector field along any curve in any surface. In truth, the most profound application of differential geometry is to modern physics, which is beyond the scope of this book. The GPS in any car wouldn´t work without general relativity, formalized through the language of differential geometry. Throughout this book, applications, metaphors and visualizations are tools that motivate and clarify the rigorous mathematical content, but never replace it.
Based on a series of lectures for adult students, this lively and entertaining book proves that, far from being a dusty, dull subject, geometry is in fact full of beauty and fascination. The author´s infectious enthusiasm is put to use in explaining many of the key concepts in the field, starting with the Golden Number and taking the reader on a geometrical journey via Shapes and Solids, through the Fourth Dimension, finishing up with Einstein´s Theories of Relativity. Equally suitable as a gift for a youngster or as a nostalgic journey back into the world of mathematics for older readers, John Barnes´ book is the perfect antidote for anyone whose maths lessons at school are a source of painful memories. Where once geometry was a source of confusion and frustration, Barnes brings enlightenment and entertainment. In this second edition, stimulated by recent lectures at Oxford, further material and extra illustrations have been added on many topics including Coloured Cubes, Chaos and Crystals.