Experiencing Geometry

Author : Georg Glaeser,Franz Gruber
Publisher : Walter de Gruyter GmbH & Co KG
Page : 248 pages
File Size : 54,6 Mb
Release : 2023-11-20
Category : Electronic
ISBN : 9783111365787

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Experiencing Geometry, Physics, and Biology by Georg Glaeser,Franz Gruber Pdf

Geometrie, Physik und Biologie verstehen Das vorliegende Buch ist ein lehrreiches und reich bebildertes Sachbuch, das naturwissenschaftliche Inhalte auf anschauliche und verständliche Weise vermittelt. Anhand zahlreicher Beispiele erläutert es Themen aus Geometrie, Physik und Biologie und zeigt Gemeinsamkeiten zwischen den Disziplinen auf. Das Buch enthält rund 300 Links zu Videoanimationen; weiters steht eine frei zugängliche interaktive Software zur Verfügung, zur weiteren Vertiefung der Inhalte. Die Inhalte des Buches, die Videos und die Software wurden am Institut für Geometrie an der Universität für angewandte Kunst Wien entwickelt: Georg Glaeser forscht insbesondere zu interdisziplinären mathematischen und biologischen Fragestellungen und arbeitete viele Jahre gemeinsam mit Franz Gruber, einem Meister im Visualisieren komplexer Sachverhalte. Enthält Links zu rund 300 Videoanimationen, abrufbar über QR-Codes Kompakte, informative und leicht verständliche Erklärungen zu naturwissenschaftlichen Fragestellungen aus den Bereichen Geometrie, Physik und Biologie Mit zahlreichen Abbildungen und Illustrationen

Author : David Wilson Henderson,Daina Taimin̦a
Publisher : Prentice Hall
Page : 438 pages
File Size : 48,5 Mb
Release : 2005
Category : Mathematics
ISBN : STANFORD:36105114443091

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Experiencing Geometry by David Wilson Henderson,Daina Taimin̦a Pdf

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.

Author : David Wilson Henderson
Publisher : Unknown
Page : 158 pages
File Size : 45,6 Mb
Release : 1994
Category : Geometry
ISBN : CORNELL:31924073537510

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Experiencing Geometry on Plane and Sphere by David Wilson Henderson Pdf

Author : James V. Bruni
Publisher : Unknown
Page : 324 pages
File Size : 54,6 Mb
Release : 1977
Category : Mathematics
ISBN : UOM:49015000689290

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Experiencing Geometry by James V. Bruni Pdf

Author : Nathalie Sinclair,William Higginson
Publisher : Springer Science & Business Media
Page : 288 pages
File Size : 43,9 Mb
Release : 2007-12-28
Category : Mathematics
ISBN : 9780387381459

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Mathematics and the Aesthetic by Nathalie Sinclair,William Higginson Pdf

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.

Author : David Wilson Henderson
Publisher : Unknown
Page : 392 pages
File Size : 41,7 Mb
Release : 2001
Category : Geometry
ISBN : UCSC:32106015132829

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Experiencing Geometry by David Wilson Henderson Pdf

For undergraduate-level courses in Geometry. Henderson invites students to explore the basic ideas of geometry beyond the formulation of proofs. The text conveys a distinctive approach, stimulating students to develop a broader, deeper understanding of mathematics through active participation including discovery, discussion, and writing about fundamental ideas. It provides a series of interesting, challenging problems, then encourages students to gather their reasonings and understandings of each problem and discuss their findings in an open forum.

Author : L. Christine Kinsey,Teresa E. Moore,Efstratios Prassidis
Publisher : John Wiley & Sons
Page : 960 pages
File Size : 53,9 Mb
Release : 2010-04-19
Category : Mathematics
ISBN : 9780470499498

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Geometry and Symmetry by L. Christine Kinsey,Teresa E. Moore,Efstratios Prassidis Pdf

This new book 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 Euclidean geometry. The second covers non-Euclidean geometry. The last part explores symmetry. Exercises and activities are interwoven with the text to enable them to explore geometry. The activities take advantage of geometric software so they'll gain a better understanding of its capabilities. Mathematics teachers will be able to use this material to create exciting and engaging projects in the classroom.

Author : Edward C. Wallace,Stephen F. West
Publisher : Waveland Press
Page : 510 pages
File Size : 49,8 Mb
Release : 2015-10-23
Category : Mathematics
ISBN : 9781478632047

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Roads to Geometry by Edward C. Wallace,Stephen F. West Pdf

Now available from Waveland Press, the Third Edition of Roads to Geometry is appropriate for several kinds of students. Pre-service teachers of geometry are provided with a thorough yet accessible treatment of plane geometry in a historical context. Mathematics majors will find its axiomatic development sufficiently rigorous to provide a foundation for further study in the areas of Euclidean and non-Euclidean geometry. By using the SMSG postulate set as a basis for the development of plane geometry, the authors avoid the pitfalls of many “foundations of geometry” texts that encumber the reader with such a detailed development of preliminary results that many other substantive and elegant results are inaccessible in a one-semester course. At the end of each section is an ample collection of exercises of varying difficulty that provides problems that both extend and clarify results of that section, as well as problems that apply those results. At the end of chapters 3–7, a summary list of the new definitions and theorems of each chapter is included.

Author : Tristan Needham
Publisher : Princeton University Press
Page : 584 pages
File Size : 42,9 Mb
Release : 2021-07-13
Category : Mathematics
ISBN : 9780691219899

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Visual Differential Geometry and Forms by Tristan Needham Pdf

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.

Author : Wolff-Michael Roth
Publisher : Routledge
Page : 341 pages
File Size : 49,8 Mb
Release : 2011-05-09
Category : Education
ISBN : 9781136732201

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Geometry as Objective Science in Elementary School Classrooms by Wolff-Michael Roth Pdf

This study examines the origins of geometry in and out of the intuitively given everyday lifeworlds of children in a second-grade mathematics class. These lifeworlds, though pre-geometric, are not without model objects that denote and come to anchor geometric idealities that they will understand at later points in their lives. Roth's analyses explain how geometry, an objective science, arises anew from the pre-scientific but nevertheless methodic actions of children in a structured world always already shot through with significations. He presents a way of understanding knowing and learning in mathematics that differs from other current approaches, using case studies to demonstrate contradictions and incongruences of other theories – Immanuel Kant, Jean Piaget, and more recent forms of (radical, social) constructivism, embodiment theories, and enactivism – and to show how material phenomenology fused with phenomenological sociology provides answers to the problems that these other paradigms do not answer.

Author : Marshall A. Whittlesey
Publisher : CRC Press
Page : 262 pages
File Size : 47,9 Mb
Release : 2019-11-14
Category : Mathematics
ISBN : 9781000627527

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Spherical Geometry and Its Applications by Marshall A. Whittlesey Pdf

Spherical Geometry and Its Applications introduces spherical geometry and its practical applications in a mathematically rigorous form. The text can serve as a course in spherical geometry for mathematics majors. Readers from various academic backgrounds can comprehend various approaches to the subject. The book introduces an axiomatic system for spherical geometry and uses it to prove the main theorems of the subject. It also provides an alternate approach using quaternions. The author illustrates how a traditional axiomatic system for plane geometry can be modified to produce a different geometric world – but a geometric world that is no less real than the geometric world of the plane. Features: A well-rounded introduction to spherical geometry Provides several proofs of some theorems to appeal to larger audiences Presents principal applications: the study of the surface of the earth, the study of stars and planets in the sky, the study of three- and four-dimensional polyhedra, mappings of the sphere, and crystallography Many problems are based on propositions from the ancient text Sphaerica of Menelaus

Author : Catherine A. Gorini
Publisher : Infobase Publishing
Page : 289 pages
File Size : 40,9 Mb
Release : 2014-05-14
Category : Mathematics
ISBN : 9781438109572

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The Facts on File Geometry Handbook by Catherine A. Gorini Pdf

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.

Author : Maureen T. Carroll,Elyn Rykken
Publisher : American Mathematical Soc.
Page : 480 pages
File Size : 46,7 Mb
Release : 2018-12-20
Category : Geometry
ISBN : 9781470448431

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Geometry: The Line and the Circle by Maureen T. Carroll,Elyn Rykken Pdf

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.

Author : C. Mammana,V. Villani
Publisher : Springer Science & Business Media
Page : 353 pages
File Size : 44,6 Mb
Release : 2012-12-06
Category : Education
ISBN : 9789401152266

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Perspectives on the Teaching of Geometry for the 21st Century by C. Mammana,V. Villani Pdf

In recent years geometry seems to have lost large parts of its former central position in mathematics teaching in most countries. However, new trends have begun to counteract this tendency. There is an increasing awareness that geometry plays a key role in mathematics and learning mathematics. Although geometry has been eclipsed in the mathematics curriculum, research in geometry has blossomed as new ideas have arisen from inside mathematics and other disciplines, including computer science. Due to reassessment of the role of geometry, mathematics educators and mathematicians face new challenges. In the present ICMI study, the whole spectrum of teaching and learning of geometry is analysed. Experts from all over the world took part in this study, which was conducted on the basis of recent international research, case studies, and reports on actual school practice. This book will be of particular interest to mathematics educators and mathematicians who are involved in the teaching of geometry at all educational levels, as well as to researchers in mathematics education.

Author : Giandomenico Sica
Publisher : Polimetrica s.a.s.
Page : 270 pages
File Size : 50,7 Mb
Release : 2006
Category : Mathematics
ISBN : 9788876990304

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What is Geometry? by Giandomenico Sica Pdf