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Author: Peter Hilton
Publisher: Cambridge University Press
ISBN: 1139489070
Category : Mathematics
Languages : en
Pages :
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Book Description
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.
Author: Peter Hilton
Publisher: Cambridge University Press
ISBN: 1139489070
Category : Mathematics
Languages : en
Pages :
Get Book Here
Book Description
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.
Author: Catherine Twomey Fosnot
Publisher:
ISBN: 9780873536592
Category : Mathematics
Languages : en
Pages : 195
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Book Description
Explore successful models of intervention. No Child Left Behind has set the high expectation that every child meet grade level expectations. This publication synthesises the research on intervention programmes and best practises related to mathematical instructional pedagogy and differentiation to assist teachers, schools and school districts in improving the manner in which they serve children with challenges in mathematics. Includes Professional Development Facilitator's Guide.
Author: Nicholas Mee
Publisher:
ISBN: 0198851952
Category : Art
Languages : en
Pages : 337
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Book Description
Artists, scientists, mathematicians, and mystics view the world in quite different ways. Nevertheless, they are united in an ongoing search for the hidden order beneath the surface appearance of the universe. Celestial Tapestry places mathematics within a vibrant cultural and historical context, highlighting links to the visual arts and design, as well as broader areas of artistic creativity. It is an engaging and accessible account of a fascinating subject. Book jacket.
Author: Philip Ball
Publisher: Oxford University Press, USA
ISBN: 019960486X
Category : Art
Languages : en
Pages : 323
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Book Description
"Ball takes us on an inspiring journey into the depths of nature, encompassing all the sciences, in which we discover that broad and elegant principles underpin the formation of the countless beautiful patterns around us."--Inside jacket.
Author: Ezra Brown
Publisher: American Mathematical Soc.
ISBN: 1470465094
Category : Education
Languages : en
Pages : 353
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Book Description
Combinatorics, or the art and science of counting, is a vibrant and active area of pure mathematical research with many applications. The Unity of Combinatorics succeeds in showing that the many facets of combinatorics are not merely isolated instances of clever tricks but that they have numerous connections and threads weaving them together to form a beautifully patterned tapestry of ideas. Topics include combinatorial designs, combinatorial games, matroids, difference sets, Fibonacci numbers, finite geometries, Pascal's triangle, Penrose tilings, error-correcting codes, and many others. Anyone with an interest in mathematics, professional or recreational, will be sure to find this book both enlightening and enjoyable. Few mathematicians have been as active in this area as Richard Guy, now in his eighth decade of mathematical productivity. Guy is the author of over 300 papers and twelve books in geometry, number theory, graph theory, and combinatorics. In addition to being a life-long number-theorist and combinatorialist, Guy's co-author, Ezra Brown, is a multi-award-winning expository writer. Together, Guy and Brown have produced a book that, in the spirit of the founding words of the Carus book series, is accessible “not only to mathematicians but to scientific workers and others with a modest mathematical background.”
Author: Philip Ball
Publisher:
ISBN: 9780198502432
Category : Nature
Languages : en
Pages : 316
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Book Description
For centuries, scientists have struggled to understand the origins of the patterns and forms found in nature. Now, in this lucid and accessibly written book, Philip Ball applies state-of-the-art scientific understanding from the fields of biology, chemistry, geology, physics, and mathematics to these ancient mysteries, revealing how nature's seemingly complex patterns originate in simple physical laws. Tracing the history of scientific thought about natural patterns, Ball shows how common presumptions--for example, that complex form must be guided by some intelligence or that form always follows function--are erroneous and continue to mislead scientists today. He investigates specific patterns in depth, revealing that these designs are self-organized and that simple, local interactions between component parts produce motifs like spots, stripes, branches, and honeycombs. In the process, he examines the mysterious phenomenon of symmetry and why it appears--and breaks--in similar ways in different systems. Finally, he attempts to answer this profound question: why are some patterns universal? Illustrations throughout the text, many in full color, beautifully illuminate Ball's ideas.
Author: Eric Vandendriessche
Publisher: Springer Nature
ISBN: 3030974820
Category : Education
Languages : en
Pages : 293
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Book Description
The book presents a series of ethnographic studies, which illustrate issues of wider importance, such as the role of cultural traditions, concepts and learning procedures in the development of formal (or mathematical) thinking outside of the western tradition. It focuses on research at the crossroads of anthropology and ethnomathematics to document indigenous mathematical knowledge and its inclusion in specific cultural patterns. More generally, the book demonstrates the heuristic value of crossing ethnographical, anthropological and ethnomathematical approaches to highlight and analyze—or "formalize" with a pedagogical outlook—indigenous mathematical knowledge. The book is divided into three parts. The first part extensively analyzes theoretical claims using particular ethnographic data, while revealing the structural mathematical features of different ludic, graphic, or technical/procedural practices in their links to other cultural phenomena. In the second part, new empirical studies that add data and perspectives from the body of studies on indigenous knowledge systems to the ongoing discussions in mathematics education in and for diverse cultural traditions are presented. This part considers, on the one hand, the Brazilian work in this field; on the other hand, it brings ethnographic innovation from other parts of the world. The third part comprises a broad philosophical discussion of the impact of intuitive or "ontological" premises on mathematical thinking and education in the light of recent developments within so-called indigenously inspired thinking. Finally, the editors’ conclusions aim to invite the broad and diversified field of scholars in this domain of research to seek alternative approaches for understanding mathematical reasoning and the adjacent adequate educational goals and means. This book is of interest to scholars and students in anthropology, ethnomathematics, history and philosophy of science, mathematics, and mathematics education, as well as other individuals interested in these topics.
Author: Avi Wigderson
Publisher: Princeton University Press
ISBN: 0691189137
Category : Computers
Languages : en
Pages : 434
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Book Description
From the winner of the Turing Award and the Abel Prize, an introduction to computational complexity theory, its connections and interactions with mathematics, and its central role in the natural and social sciences, technology, and philosophy Mathematics and Computation provides a broad, conceptual overview of computational complexity theory—the mathematical study of efficient computation. With important practical applications to computer science and industry, computational complexity theory has evolved into a highly interdisciplinary field, with strong links to most mathematical areas and to a growing number of scientific endeavors. Avi Wigderson takes a sweeping survey of complexity theory, emphasizing the field’s insights and challenges. He explains the ideas and motivations leading to key models, notions, and results. In particular, he looks at algorithms and complexity, computations and proofs, randomness and interaction, quantum and arithmetic computation, and cryptography and learning, all as parts of a cohesive whole with numerous cross-influences. Wigderson illustrates the immense breadth of the field, its beauty and richness, and its diverse and growing interactions with other areas of mathematics. He ends with a comprehensive look at the theory of computation, its methodology and aspirations, and the unique and fundamental ways in which it has shaped and will further shape science, technology, and society. For further reading, an extensive bibliography is provided for all topics covered. Mathematics and Computation is useful for undergraduate and graduate students in mathematics, computer science, and related fields, as well as researchers and teachers in these fields. Many parts require little background, and serve as an invitation to newcomers seeking an introduction to the theory of computation. Comprehensive coverage of computational complexity theory, and beyond High-level, intuitive exposition, which brings conceptual clarity to this central and dynamic scientific discipline Historical accounts of the evolution and motivations of central concepts and models A broad view of the theory of computation's influence on science, technology, and society Extensive bibliography
Author: Bulent Atalay
Publisher: Smithsonian Institution
ISBN: 1588343537
Category : Art
Languages : en
Pages : 297
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Book Description
Leonardo da Vinci was one of history's true geniuses, equally brilliant as an artist, scientist, and mathematician. Readers of The Da Vinci Code were given a glimpse of the mysterious connections between math, science, and Leonardo's art. Math and the Mona Lisa picks up where The Da Vinci Code left off, illuminating Leonardo's life and work to uncover connections that, until now, have been known only to scholars. Bülent Atalay, a distinguished scientist and artist, examines the science and mathematics that underlie Leonardo's work, paying special attention to the proportions, patterns, shapes, and symmetries that scientists and mathematicians have also identified in nature. Following Leonardo's own unique model, Atalay searches for the internal dynamics of art and science, revealing to us the deep unity of the two cultures. He provides a broad overview of the development of science from the dawn of civilization to today's quantum mechanics. From this base of information, Atalay offers a fascinating view into Leonardo's restless intellect and modus operandi, allowing us to see the source of his ideas and to appreciate his art from a new perspective.
Author: Leslie P. Steffe
Publisher: Springer Science & Business Media
ISBN: 1461231787
Category : Psychology
Languages : en
Pages : 257
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Book Description
On the 26th, 27th, and 28th of February of 1988, a conference was held on the epistemological foundations of mathematical experience as part of the activities of NSF Grant No. MDR-8550463, Child Generated Multiplying and Dividing Algorithms: A Teaching Experiment. I had just completed work on the book Construction of Arithmetical Meanings and Strategies with Paul Cobb and Ernst von Glasersfeld and felt that substantial progress had been made in understanding the early numerical experiences of the six children who were the subjects of study in that book. While the book was in preparation, I was also engaged in the teaching experiment on mUltiplying and dividing algorithms. My focus in this teaching experiment was on investigating the mathematical experiences of the involved children and on developing a language through which those experiences might be expressed. However, prior to immersing myself in the conceptual analysis of the mathematical experiences of the children, I felt that it was crucial to critically evaluate the progress that we felt we had made in our earlier work. It was toward achieving this goal that I organized the conference. When trying to understand the mathematical experiences of a child, one can do no better than to interact with the child in a mathematical context guided by the intention to specify the child's current knowledge and the progress the child might make.
