Experiencing Geometry, Physics, and Biology
Experiencing Geometry, Physics, and Biology

Author: Georg Glaeser

Publisher: Walter de Gruyter GmbH & Co KG

Published: 2023-11-20

Total Pages: 248

ISBN-13: 3111365786

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Understanding geometry, physics, and biology This is a highly informative and richly illustrated nonfiction book that conveys scientific content in a clear and understandable way. Drawing on numerous examples, it explains topics from geometry, physics, and biology and points out commonalities between the disciplines. The book contains approx. 300 links to video animations and is accompanied by a freely accessible interactive software that allows readers to delve even deeper into the content covered in the book. The content, videos, and software were developed by the Department of Geometry at the University of Applied Arts Vienna. Georg Glaeser’s research focuses particularly on interdisciplinary mathematical and biological issues, and he worked for many years with Franz Gruber, who was highly adept at visualizing complex issues. Includes links to around 300 video animations, accessible via QR codes Compact, informative, and easy-to-understand explanations of scientific issues in the disciplines of geometry, physics, and biology With numerous images and illustrations

Experiencing Geometry
Experiencing Geometry

Author: David Wilson Henderson

Publisher: Prentice Hall

Published: 2005

Total Pages: 438

ISBN-13:

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The distinctive approach of Henderson and Taimina's volume stimulates readers to develop a broader, deeper, understanding of mathematics through active experience--including discovery, discussion, writing fundamental ideas and learning about the history of those ideas. A series of interesting, challenging problems encourage readers to gather and discuss their reasonings and understanding. The volume provides an understanding of the possible shapes of the physical universe. The authors provide extensive information on historical strands of geometry, straightness on cylinders and cones and hyperbolic planes, triangles and congruencies, area and holonomy, parallel transport, SSS, ASS, SAA, and AAA, parallel postulates, isometries and patterns, dissection theory, square roots, pythagoras and similar triangles, projections of a sphere onto a plane, inversions in circles, projections (models) of hyperbolic planes, trigonometry and duality, 3-spheres and hyperbolic 3-spaces and polyhedra. For mathematics educators and other who need to understand the meaning of geometry.

Mathematics and the Aesthetic
Mathematics and the Aesthetic

Author: Nathalie Sinclair

Publisher: Springer Science & Business Media

Published: 2007-12-28

Total Pages: 299

ISBN-13: 0387381457

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This collection of essays explores the ancient affinity between the mathematical and the aesthetic, focusing on fundamental connections between these two modes of reasoning and communicating. From historical, philosophical and psychological perspectives, with particular attention to certain mathematical areas such as geometry and analysis, the authors examine ways in which the aesthetic is ever-present in mathematical thinking and contributes to the growth and value of mathematical knowledge.

Geometry and Symmetry
Geometry and Symmetry

Author: L. Christine Kinsey

Publisher: John Wiley & Sons

Published: 2010-04-19

Total Pages: 960

ISBN-13: 0470499494

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This new book for mathematics and mathematics education majors helps students gain an appreciation of geometry and its importance in the history and development of mathematics. The material is presented in three parts. The first is devoted to a rigorous introduction of Euclidean geometry, the second covers various noneuclidean geometries, and the last part delves into symmetry and polyhedra. Historical contexts accompany each topic. Exercises and activities are interwoven with the text to enable the students to explore geometry. Some of the activities take advantage of geometric software so students - in particular, future teachers - gain a better understanding of its capabilities. Others explore the construction of simple models or use manipulatives allowing students to experience the hands-on, creative side of mathematics. While this text contains a rigorous mathematical presentation, key design features and activities allow it to be used successfully in mathematics for teachers courses as well.

The Facts on File Geometry Handbook
The Facts on File Geometry Handbook

Author: Catherine A. Gorini

Publisher: Infobase Publishing

Published: 2014-05-14

Total Pages: 289

ISBN-13: 1438109571

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Contains a history of the subject of geometry, including more than 3,000 entries providing definitions and explanations of related topics, plus brief biographies of over 300 scientists.

Geometry Through Stories
Geometry Through Stories

Author: Jenny Kellett

Publisher: Bellanova Books

Published: 2023-07-22

Total Pages: 110

ISBN-13: 6192641897

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The Fun Way to Master Geometry Your journey into the world of math continues with "Geometry Through Stories," the next exciting installment in Jenny Kellett's groundbreaking educational adventure series. This is no ordinary textbook; it's a thrilling ride through the captivating world of geometry, disguised as a page-turning mystery story. Our intrepid adventurers find themselves in a world where angles hide secret messages and shapes solve time-sensitive problems in mystical lands. From the basics of points, lines, and planes to complex geometrical transformations, each chapter brings a new challenge. The race is on. Through the adventures and challenges our characters face, students will master the key concepts of geometry, including: * Basic geometric terms and definitions * Properties of 2D and 3D shapes * Angle relationships * Triangle properties and the Pythagorean theorem * Perimeter, area, and volume calculations * Transformations and symmetry Each chapter ends with practice problems, giving students the chance to apply what they've learned in a practical, engaging way. These problems are designed to help reinforce the concepts, ensuring students have a strong grasp of geometry basics. Suitable for students in the 9th grade and up (age 14), this book is the perfect supplementary guide to classroom learning. Whether you're a parent looking to support your child's education, a teacher seeking creative resources, or a student eager for a unique, engaging approach to geometry, "Geometry Through Stories" is an indispensable tool on your mathematical journey. From author Jenny Kellett, the creator of "Algebra 1: The Mystery of the Algebraic Artifact," comes another masterful blend of education and adventure. With "Geometry: Journey into the World of Shapes and Angles," learning math has never been more thrilling! Order your copy today.

Visual Differential Geometry and Forms
Visual Differential Geometry and Forms

Author: Tristan Needham

Publisher: Princeton University Press

Published: 2021-07-13

Total Pages: 530

ISBN-13: 0691203695

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An inviting, intuitive, and visual exploration of differential geometry and forms Visual Differential Geometry and Forms fulfills two principal goals. In the first four acts, Tristan Needham puts the geometry back into differential geometry. Using 235 hand-drawn diagrams, Needham deploys Newton’s geometrical methods to provide geometrical explanations of the classical results. In the fifth act, he offers the first undergraduate introduction to differential forms that treats advanced topics in an intuitive and geometrical manner. Unique features of the first four acts include: four distinct geometrical proofs of the fundamentally important Global Gauss-Bonnet theorem, providing a stunning link between local geometry and global topology; a simple, geometrical proof of Gauss’s famous Theorema Egregium; a complete geometrical treatment of the Riemann curvature tensor of an n-manifold; and a detailed geometrical treatment of Einstein’s field equation, describing gravity as curved spacetime (General Relativity), together with its implications for gravitational waves, black holes, and cosmology. The final act elucidates such topics as the unification of all the integral theorems of vector calculus; the elegant reformulation of Maxwell’s equations of electromagnetism in terms of 2-forms; de Rham cohomology; differential geometry via Cartan’s method of moving frames; and the calculation of the Riemann tensor using curvature 2-forms. Six of the seven chapters of Act V can be read completely independently from the rest of the book. Requiring only basic calculus and geometry, Visual Differential Geometry and Forms provocatively rethinks the way this important area of mathematics should be considered and taught.

Geometry: The Line and the Circle
Geometry: The Line and the Circle

Author: Maureen T. Carroll

Publisher: American Mathematical Soc.

Published: 2018-12-20

Total Pages: 502

ISBN-13: 1470448432

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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.