Geometry In Our Three Dimensional World

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Geometry In Our Three Dimensional World

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Author : Alfred S Posamentier
language : en
Publisher: World Scientific
Release Date : 2021-11-24

Geometry In Our Three Dimensional World written by Alfred S Posamentier and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-11-24 with Mathematics categories.

The book presents a comprehensive overview of various aspects of three-dimensional geometry that can be experienced on a daily basis. By covering the wide range of topics — from the psychology of spatial perception to the principles of 3D modelling and printing, from the invention of perspective by Renaissance artists to the art of Origami, from polyhedral shapes to the theory of knots, from patterns in space to the problem of optimal packing, and from the problems of cartography to the geometry of solar and lunar eclipses — this book provides deep insight into phenomena related to the geometry of space and exposes incredible nuances that can enrich our lives.The book is aimed at the general readership and provides more than 420 color illustrations that support the explanations and replace formal mathematical arguments with clear graphical representations.

Shapes In Our World

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Author : Moira Anderson
language : en
Publisher: Teacher Created Materials
Release Date : 2008-10-10

Shapes In Our World written by Moira Anderson and has been published by Teacher Created Materials this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-10-10 with Juvenile Nonfiction categories.

Identify three-dimensional shapes all around the world! This vibrant title gives readers practice identifying familiar shapes like cones, cylinders, pentagons, polygons, and prisms, while familiarizing them with STEM themes and more advanced geometry concepts. Children will learn more about vertices, symmetry, and bases. With each shape, this book gives readers information about an example of the shape, be it a building, a honeycomb, or a tree trunk! With an accessible glossary, clear mathematical diagrams, practical examples, and easy-to-read text, readers will have all the tools they need to improve their geometry skills and find shapes on their own!

Euclid S Heritage Is Space Three Dimensional

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Author : P. Janich
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-09

Euclid S Heritage Is Space Three Dimensional written by P. Janich and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-09 with Science categories.

We live in a space, we get about in it. We also quantify it, we think of it as having dimensions. Ever since Euclid's ancient geometry, we have thought of bodies occupying parts of this space (including our own bodies), the space of our practical orientations (our 'moving abouts'), as having three dimensions. Bodies have volume specified by measures of length, breadth and height. But how do we know that the space we live in has just these three dimensions? It is theoreti cally possible that some spaces might exist that are not correctly described by Euclidean geometry. After all, there are the non Euclidian geometries, descriptions of spaces not conforming to the axioms and theorems of Euclid's geometry. As one might expect, there is a history of philosophers' attempts to 'prove' that space is three-dimensional. The present volume surveys these attempts from Aristotle, through Leibniz and Kant, to more recent philosophy. As you will learn, the historical theories are rife with terminology, with language, already tainted by the as sumed, but by no means obvious, clarity of terms like 'dimension', 'line', 'point' and others. Prior to that language there are actions, ways of getting around in the world, building things, being interested in things, in the more specific case of dimensionality, cutting things. It is to these actions that we must eventually appeal if we are to understand how science is grounded.

Three Dimensional Geometry And Topology Volume 1

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Author : William P. Thurston
language : en
Publisher: Princeton University Press
Release Date : 2014-10-31

Three Dimensional Geometry And Topology Volume 1 written by William P. Thurston and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-10-31 with Mathematics categories.

This book develops some of the extraordinary richness, beauty, and power of geometry in two and three dimensions, and the strong connection of geometry with topology. Hyperbolic geometry is the star. A strong effort has been made to convey not just denatured formal reasoning (definitions, theorems, and proofs), but a living feeling for the subject. There are many figures, examples, and exercises of varying difficulty. This book was the origin of a grand scheme developed by Thurston that is now coming to fruition. In the 1920s and 1930s the mathematics of two-dimensional spaces was formalized. It was Thurston's goal to do the same for three-dimensional spaces. To do this, he had to establish the strong connection of geometry to topology--the study of qualitative questions about geometrical structures. The author created a new set of concepts, and the expression "Thurston-type geometry" has become a commonplace. Three-Dimensional Geometry and Topology had its origins in the form of notes for a graduate course the author taught at Princeton University between 1978 and 1980. Thurston shared his notes, duplicating and sending them to whoever requested them. Eventually, the mailing list grew to more than one thousand names. The book is the culmination of two decades of research and has become the most important and influential text in the field. Its content also provided the methods needed to solve one of mathematics' oldest unsolved problems--the Poincaré Conjecture. In 2005 Thurston won the first AMS Book Prize, for Three-dimensional Geometry and Topology. The prize recognizes an outstanding research book that makes a seminal contribution to the research literature. Thurston received the Fields Medal, the mathematical equivalent of the Nobel Prize, in 1982 for the depth and originality of his contributions to mathematics. In 1979 he was awarded the Alan T. Waterman Award, which recognizes an outstanding young researcher in any field of science or engineering supported by the National Science Foundation.

Why Three Dimensional Space

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Author : Henri Poincare
language : en
Publisher: BEYOND BOOKS HUB
Release Date : 2024-07-28

Why Three Dimensional Space written by Henri Poincare and has been published by BEYOND BOOKS HUB this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-07-28 with categories.

Discover the fascinating reasons behind our three-dimensional reality in Henri Poincare's thought-provoking book, "Why Three-Dimensional Space." This book delves into the mathematical and physical principles that define the dimensions of our universe. Poincare's engaging narrative and profound insights will challenge your perceptions and deepen your appreciation for the structure of space. Uncover the mysteries of three-dimensional space and gain a new perspective on the world around you.

The Fourth Dimension

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Author : Charles Howard Hinton
language : en
Publisher: Good Press
Release Date : 2022-08-21

The Fourth Dimension written by Charles Howard Hinton and has been published by Good Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-08-21 with Fiction categories.

"The Fourth Dimension" by Charles Howard Hinton. Published by Good Press. Good Press publishes a wide range of titles that encompasses every genre. From well-known classics & literary fiction and non-fiction to forgotten−or yet undiscovered gems−of world literature, we issue the books that need to be read. Each Good Press edition has been meticulously edited and formatted to boost readability for all e-readers and devices. Our goal is to produce eBooks that are user-friendly and accessible to everyone in a high-quality digital format.

Essential 3d Geometry

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Author : Bernardo Camou
language : en
Publisher: University Readers
Release Date : 2011-07-26

Essential 3d Geometry written by Bernardo Camou and has been published by University Readers this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-07-26 with categories.

We live out our lives in a three dimensional world. However, our understanding of what this means is meager, and the study of 3D Geometry is markedly absent from our educational system. Essential 3D Geometry: Unraveling the Mathematical Wonders bridges the gap between current mathematical knowledge and our fascinating--and unexplored--3D world. Originally developed by and for high school students, the material in Essential 3D Geometry has been successfully developed into a college-level text for pre-service teachers. The book offers an original and unique approach for learning mathematics--iMAT engineering--which is based on the principle that learning mathematics is an integrated activity calling for multi-type presentations of mathematical objects through the use of different technologies. The text begins with a thorough study of the building blocks of spatial structures, the five Platonic Solids. The material integrates 2D and 3D geometry, as well as algebra and trigonometry. Subsequent chapters cover a variety of topics including Thales' Theorem, the volume of the Platonic solids and non-regular tetrahedrons, circumcircles and circum-spheres, Archimedean Bodies, and spatial transformations. Students will learn to produce and make use of three types of representation of 3D objects: solids or lattice models, Cabri 3D or GSP files, and constructions using a straight-edge and compass or free hand drawings. Representations will be developed using paper and pencil, craft technology, and computer technology. Essential 3D Geometry is an excellent tool for introducing math educators to the concepts of 3D geometry, helping them go on to develop similar courses for their own students. Bernardo Camou has 20 years of experience teaching mathematics in secondary education. In 2009, he began work on his Ph.D. in mathematics education at the University of Georgia, graduating in May 2012. His dissertation topic, and his passion, is to help others discover the wonders of 3D Geometry. Graciela García studied economics at the Universidad de la Republica for two years before going on to earn the title of Math Teacher at the Instituto de Profesores Artigas. She currently teaches at the Woodlands School, after having spent 37 years teaching math in public high schools. Maria Margarita Colucci earned the title of Math Teacher at the Instituto de Profesores Artigas. For the past fifteen years she has been a high school math teacher at the Liceo N 15, as well as teaching at the Woodlands School where she is also coordinator of M.I.P. Dr. John Olive is Professor Emeritus of Mathematics Education at the University of Georgia. For over 30 years his research has focused on students' mathematical thinking, and the development and use of technological tools to support that thinking.

Elements Of The Geometry And Topology Of Minimal Surfaces In Three Dimensional Space

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Author : A. T. Fomenko
language : en
Publisher: American Mathematical Soc.
Release Date : 2005

Elements Of The Geometry And Topology Of Minimal Surfaces In Three Dimensional Space written by A. T. Fomenko and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005 with Mathematics categories.

This book grew out of lectures presented to students of mathematics, physics, and mechanics by A. T. Fomenko at Moscow University, under the auspices of the Moscow Mathematical Society. The book describes modern and visual aspects of the theory of minimal, two-dimensional surfaces in three-dimensional space. The main topics covered are: topological properties of minimal surfaces, stable and unstable minimal films, classical examples, the Morse-Smale index of minimal two-surfaces in Euclidean space, and minimal films in Lobachevskian space. Requiring only a standard first-year calculus and elementary notions of geometry, this book brings the reader rapidly into this fascinating branch of modern geometry.

Developments In 3d Geo Information Sciences

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Author : Tijs Neutens
language : en
Publisher: Springer Science & Business Media
Release Date : 2009-10-16

Developments In 3d Geo Information Sciences written by Tijs Neutens and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-10-16 with Science categories.

Realistically representing our three-dimensional world has been the subject of many (philosophical) discussions since ancient times. While the recognition of the globular shape of the Earth goes back to Pythagoras’ statements of the sixth century B. C. , the two-dimensional, circular depiction of the Earth’s surface has remained prevailing and also dominated the art of painting until the late Middle Ages. Given the immature technological means, objects on the Earth’s surface were often represented in academic and technical disciplines by two-dimensional cross-sections oriented along combinations of three mutually perpendicular directions. As soon as computer science evolved, scientists have steadily been improving the three-dimensional representation of the Earth and developed techniques to analyze the many natural processes and phenomena taking part on its surface. Both computer aided design (CAD) and geographical information systems (GIS) have been developed in parallel during the last three decades. While the former concentrates more on the detailed design of geometric models of object shapes, the latter emphasizes the topological relationships between geographical objects and analysis of spatial patterns. Nonetheless, this distinction has become increasingly blurred and both approaches have been integrated into commercial software packages. In recent years, an active line of inquiry has emerged along the junctures of CAD and GIS, viz. 3D geoinformation science. Studies along this line have recently made significant inroads in terms of 3D modeling and data acquisition.

The Father Of Geometry

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Author : Paul W. Hightower
language : en
Publisher: Enslow Publishing, LLC
Release Date : 2010-07-01

The Father Of Geometry written by Paul W. Hightower and has been published by Enslow Publishing, LLC this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-07-01 with Juvenile Nonfiction categories.

"A biography of ancient Greek mathematician Euclid, known as the father of geometry and author of the mathematics textbook Elements"--Provided by publisher.