Diese fünfte deutsche Auflage enthält ein ganz neues Kapitel über van der Waerdens Permanenten-Vermutung, sowie weitere neue, originelle und elegante Beweise in anderen Kapiteln. Aus den Rezensionen: “... es ist fast unmöglich, ein Mathematikbuch zu schreiben, das von jedermann gelesen und genossen werden kann, aber Aigner und Ziegler gelingt diese Meisterleistung in virtuosem Stil. [...] Dieses Buch erweist der Mathematik einen unschätzbaren Dienst, indem es Nicht-Mathematikern vorführt, was Mathematiker meinen, wenn sie über Schönheit sprechen.” Aus der Laudatio für den “Steele Prize for Mathematical Exposition” 2018 "Was hier vorliegt ist eine Sammlung von Beweisen, die in das von Paul Erdös immer wieder zitierte BUCH gehören, das vom lieben (?) Gott verwahrt wird und das die perfekten Beweise aller mathematischen Sätze enthält. Manchmal lässt der Herrgott auch einige von uns Sterblichen in das BUCH blicken, und die so resultierenden Geistesblitze erhellen den Mathematikeralltag mit eleganten Argumenten, überraschenden Zusammenhängen und unerwarteten Volten." www.mathematik.de, Mai 2002 "Eine einzigartige Sammlung eleganter mathematischer Beweise nach der Idee von Paul Erdös, verständlich geschrieben von exzellenten Mathematikern. Dieses Buch gibt anregende Lösungen mit Aha-Effekt, auch für Nicht-Mathematiker." www.vismath.de "Ein prächtiges, äußerst sorgfältig und liebevoll gestaltetes Buch! Erdös hatte die Idee DES BUCHES, in dem Gott die perfekten Beweise mathematischer Sätze eingeschrieben hat. Das hier gedruckte Buch will eine "very modest approximation" an dieses BUCH sein.... Das Buch von Aigner und Ziegler ist gelungen ..." Mathematische Semesterberichte, November 1999 "Wer (wie ich) bislang vergeblich versucht hat, einen Blick ins BUCH zu werfen, wird begierig in Aigners und Zieglers BUCH der Beweise schmökern." www.mathematik.de, Mai 2002
The Key to Fully Understanding the Basics of a 3D World Prominently used in games, movies, and on television, 3D graphics are tools of creation used to enhance how material and light come together to manipulate objects in 3D space. A game-changer written for the non-technical mind, Essential Skills for 3D Modeling, Rendering, and Animation examines the complexities of 3D computer-generated art, and outlines the basics of how things work and are used in 3D. This text describes the three cornerstones of 3D—modeling, rendering, and animation; focuses on common elements; and provides a full understanding of the foundational concepts involved. Detailing the skills and knowledge needed to become an accomplished 3D artist, it includes step-by-step instruction with ample examples, and allows absolute beginners to move at their own pace. Master Anything You Are Tasked to Model The author incorporates historical information—presenting a contextual understanding of the various techniques and methodologies in their historical place. Each chapter builds on the fundamentals of 3D computer graphics and augments skills based on the concepts, enabling the student to learn both theory and application simultaneously. The book highlights two basic geometry types, polygons and NURBS surfaces, showing the student basic modeling techniques with both. While more techniques are available, an artist can cover any model by grasping these basic techniques. Supplies examples that are specifically taken from Autodesk Maya Contains exercises that are meant to be used in conjunction with the training videos on the website Includes a documented history of computer graphics Essential Skills for 3D Modeling, Rendering, and Animation offers a fundamental understanding of the mechanics of 3D graphics to modelers, animators, texture artists, render artists, game developers, and production artists, as well as educators teaching an undergrad or tech course in 3D animation.
A flexagon is a motion structure that has the appearance of a ring of hinged polygons. It can be flexed to display different pairs of faces, usually in cyclic order. Flexagons can be appreciated as toys or puzzles, as a recreational mathematics topic, and as the subject of serious mathematical study. Workable paper models of flexagons are easy to make and entertaining to manipulate. The mathematics of flexagons is complex, and how a flexagon works is not immediately obvious on examination of a paper model. Recent geometric analysis, included in the book, has improved theoretical understanding of flexagons, especially relationships between different types. This profusely illustrated book is arranged in a logical order appropriate for a textbook on the geometry of flexagons. It is written so that it can be enjoyed at both the recreational mathematics level, and at the serious mathematics level. The only prerequisite is some knowledge of elementary geometry, including properties of polygons. A feature of the book is a compendium of over 100 nets for making paper models of some of the more interesting flexagons, chosen to complement the text. These are accurately drawn and reproduced at half full size. Many of the nets have not previously been published. Instructions for assembling and manipulating the flexagons are included.
Das Buch bietet eine Einführung in die Theorie der automorphen Formen. Beginnend bei klassischen Modulformen führt der Autor seine Leser hin zur modernen, darstellungstheoretischen Beschreibung von automorphen Formen und ihren L-Funktionen. Das Hauptgewicht legt er auf den Übergang von der klassischen, elementaren Sichtweise zu der modernen, durch die Darstellungstheorie begründete Herangehensweise. Diese Art der Verbindung von klassischer und moderner Sichtweise war in der Lehrbuchliteratur bisher nicht zu finden.
What sorts of mathematics competencies must teachers have in order to teach the discipline well? This book offers a novel take on the question. Most research is focused on explicit knowledge–that is, on the sorts of insights that might be specified, catalogued, taught, and tested. In contrast, this book focuses on the tacit dimensions of teachers’ mathematics knowledge that precede and enable their competencies with formal mathematics. It highlights the complexity of this knowledge and offers strategies to uncover it, analyze it, and re-synthesize it in ways that will make it more available for teaching. Emerging from 10 years of collaborative inquiry with practicing teachers, it is simultaneously informed by the most recent research and anchored to the realities of teachers’ lives in classrooms.
Dreiecke, Rechtecke, Quader; alles schon einmal geh?rt. Aber wie rechnet man noch einmal ihre Fl?cheninhalte aus? Wie kommt man noch einmal auf die Winkelhalbierenden und wo schneiden sie sich? Es ist ganz einfach. Versprochen. Man muss nur wissen, wann welche Rechnung wo die richtige ist. ?Geometrie f?r Dummies? erkl?rt den Lesern, wie sie zu den richtigen Ergebnissen kommen, wie sie die Geometrie beherrschen und nicht die Geometrie sie. Das Buch nimmt dieser Disziplin der Mathematik auf nette Art den Schrecken.
A world-renowned mathematician takes a lighthearted look at the philosophy, form, and re-creations of mathematics, discussing the science's charm as well as its utility and historical role. 1958 edition.
You, too, can understand geometry -- just ask Dr. Math! Are things starting to get tougher in geometry class? Don't panic. Dr. Math--the popular online math resource--is here to help you figure out even the trickiest of your geometry problems. Students just like you have been turning to Dr. Math for years asking questions about math problems, and the math doctors at The Math Forum have helped them find the answers with lots of clear explanations and helpful hints. Now, with Dr. Math Presents More Geometry, you'll learn just what it takes to succeed in this subject. You'll find the answers to dozens of real questions from students in a typical geometry class. You'll also find plenty of hints and shortcuts for using coordinate geometry, finding angle relationships, and working with circles. Pretty soon, everything from the Pythagorean theorem to logic and proofs will make more sense. Plus, you'll get plenty of tips for working with all kinds of real-life problems. You won't find a better explanation of high school geometry anywhere!
This easy-to-read 2010 book demonstrates how a simple geometric idea reveals fascinating connections and results in number theory, the mathematics of polyhedra, combinatorial geometry, and group theory. Using a systematic paper-folding procedure it is possible to construct a regular polygon with any number of sides. This remarkable algorithm has led to interesting proofs of certain results in number theory, has been used to answer combinatorial questions involving partitions of space, and has enabled the authors to obtain the formula for the volume of a regular tetrahedron in around three steps, using nothing more complicated than basic arithmetic and the most elementary plane geometry. All of these ideas, and more, reveal the beauty of mathematics and the interconnectedness of its various branches. Detailed instructions, including clear illustrations, enable the reader to gain hands-on experience constructing these models and to discover for themselves the patterns and relationships they unearth.
In a new edition, fully revised and updated to reflect key new curriculum topics and methods, Maths for Mums and Dads guides you through the basics of primary school maths and covers the dilemmas and problems you are likely to be confronted with, including: * number bonds, place value and decimals * long multiplication and division * fractions, percentages and decimals * basic geometry, shapes, symmetry and angles * data-handling, combinations and chance Complete with sample questions, mock exam papers and examples of children's errors, Maths for Mums and Dads will challenge and reassure in equal measure.
How do you convey to your students, colleagues and friends some of the beauty of the kind of mathematics you are obsessed with? If you are a mathematician interested in finite or topological geometry and combinatorial designs, you could start by showing them some of the (400+) pictures in the "picture book". Pictures are what this book is all about; original pictures of everybody's favorite geometries such as configurations, projective planes and spaces, circle planes, generalized polygons, mathematical biplanes and other designs which capture much of the beauty, construction principles, particularities, substructures and interconnections of these geometries. The level of the text is suitable for advanced undergraduates and graduate students. Even if you are a mathematician who just wants some interesting reading you will enjoy the author's very original and comprehensive guided tour of small finite geometries and geometries on surfaces This guided tour includes lots of sterograms of the spatial models, games and puzzles and instructions on how to construct your own pictures and build some of the spatial models yourself.
a wise and witty introduction to the joy of numbers
Author: David G. Wells
Publisher: John Wiley & Sons Inc
A guide to the potential and pleasures of math explores the patterns and properties associated with numbers, reveals the origins of mathematical theories and principles, and includes more than one hundred mathematical puzzles
Although it can seem a daunting task to individualize learning for all students, this book provides specific "how-to" techniques to make it happen, equipping you with the tools you need to differentiate instruction for all students: general education, gifted and talented, challenged, or English Language Learners (ELL). Addressing the reader with an engaging personalized tone, expert Dr. Shellie Hipsky demystifies the process of differentiated instruction as you tour elementary school classrooms with diverse populations and observe research-based strategies that transform theory into practical differentiated instructional techniques for literacy and language arts skills. You will gain valuable insights from seasoned elementary teachers through real life concrete examples, find advice for implementing strategies in literacy-based classrooms, learn how to create an effective learning environment, and utilize appropriate instructional techniques based on students' abilities, learning profiles, and interests. Additionally, you will explore strategies to differentiate in the reading areas of emerging literacy skills, vocabulary, comprehension, and fluency as well as writing, speaking, listening, and content area reading. Every chapter in the book includes specific illuminating classroom examples, questions for reflecting on the reading, active engagement ideas for further exploration of the topic, and conclusions. Strategies to simplify documentation, including the use of the Literacy and Language Arts Learning Skills Check Sheet, Differentiated Choice Chart, and a Portfolio Record Sheet, provide ways to organize important student information. A unique journal kept by an elementary teacher, whose classroom is visited in the text, rounds out the book as it demonstrates a year's worth of successful implementation of differentiation assessment and instruction. Differentiated Literacy and Language Arts Strategies for the Elementary Classroom focuses on the needs of pre-service teachers and yet it has ample strategies to positively impact the classrooms of current teachers.