Experiencing Geometry, Physics, and Biology

Experiencing Geometry, Physics, and Biology PDF

Author: Georg Glaeser

Publisher: Walter de Gruyter GmbH & Co KG

Published: 2023-11-20

Total Pages: 248

ISBN-13: 3111365786

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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

Experiencing Geometry

Experiencing Geometry PDF

Author: David Wilson Henderson

Publisher:

Published: 2001

Total Pages: 392

ISBN-13:

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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.

Mathematics and the Aesthetic

Mathematics and the Aesthetic PDF

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.

Experiencing Geometry

Experiencing Geometry PDF

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.

Geometry as Objective Science in Elementary School Classrooms

Geometry as Objective Science in Elementary School Classrooms PDF

Author: Wolff-Michael Roth

Publisher: Routledge

Published: 2011-05-09

Total Pages: 341

ISBN-13: 1136732209

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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.

Perspectives on the Teaching of Geometry for the 21st Century

Perspectives on the Teaching of Geometry for the 21st Century PDF

Author: C. Mammana

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 353

ISBN-13: 9401152268

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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.

Geometry and Symmetry

Geometry and Symmetry PDF

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 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.

Walking the city. Barcelona as an urban experience

Walking the city. Barcelona as an urban experience PDF

Author: Estanislau Roca

Publisher: Edicions Universitat Barcelona

Published: 2015-03-26

Total Pages: 374

ISBN-13: 8447538788

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This book presents an exciting and colorful route for Barcelona and his neighborhoods. Written by recognised specialists in architecture, urbanism or art history, and based in an awarded and expor­ted teaching and research project which uses the city as a classroom and labora­tory, its aim is to deepen one’s knowledge about the city, through tours as a way of approaching architecture, urbanism, socio­logy and history.

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