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Geometry and its Applications in Arts, Nature and Technology

2020-12-18 Mathematics
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Release : 2020-12-18
Genre : Mathematics
Kind : eBook
Book Rating : 984/5 ( reviews)

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Book Synopsis Geometry and its Applications in Arts, Nature and Technology by : Georg Glaeser

Download or read book Geometry and its Applications in Arts, Nature and Technology written by Georg Glaeser. This book was released on 2020-12-18. Available in PDF, EPUB and Kindle. Book excerpt: This book returns geometry to its natural habitats: the arts, nature and technology. Throughout the book, geometry comes alive as a tool to unlock the understanding of our world. Assuming only familiarity with high school mathematics, the book invites the reader to discover geometry through examples from biology, astronomy, architecture, design, photography, drawing, engineering and more. Lavishly illustrated with over 1200 figures, all of the geometric results are carefully derived from scratch, with topics from differential, projective and non-Euclidean geometry, as well as kinematics, introduced as the need arises. The mathematical results contained in the book range from very basic facts to recent results, and mathematical proofs are included although not necessary for comprehension. With its wide range of geometric applications, this self-contained volume demonstrates the ubiquity of geometry in our world, and may serve as a source of inspiration for architects, artists, designers, engineers, and natural scientists. This new edition has been completely revised and updated, with new topics and many new illustrations.

Connections

2001 Science
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Release : 2001
Genre : Science
Kind : eBook
Book Rating : 394/5 ( reviews)

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Book Synopsis Connections by : Jay Kappraff

Download or read book Connections written by Jay Kappraff. This book was released on 2001. Available in PDF, EPUB and Kindle. Book excerpt: The first edition of Connections was chosen by the National Association of Publishers (USA) as the best book in OC Mathematics, Chemistry, and Astronomy OCo Professional and ReferenceOCO in 1991. It has been a comprehensive reference in design science, bringing together in a single volume material from the areas of proportion in architecture and design, tilings and patterns, polyhedra, and symmetry. The book presents both theory and practice and has more than 750 illustrations. It is suitable for research in a variety of fields and as an aid to teaching a course in the mathematics of design. It has been influential in stimulating the burgeoning interest in the relationship between mathematics and design. In the second edition there are five new sections, supplementary, as well as a new preface describing the advances in design science since the publication of the first edition. Contents: Proportion in Architecture; Similarity; The Golden Mean; Graphs; Tilings with Polygons; Two-Dimensional Networks and Lattices; Polyhedra: Platonic Solids; Transformation of the Platonic Solids I; Transformation of the Platonic Solids II; Polyhedra: Space Filling; Isometries and Mirrors; Symmetry of the Plane. Readership: Polytechnic students, architects, designers, mathematicians and general readers."

The Fractal Geometry of Nature

2021-07-16
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Release : 2021-07-16
Genre :
Kind : eBook
Book Rating : 410/5 ( reviews)

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Book Synopsis The Fractal Geometry of Nature by : Benoit Mandelbrot

Download or read book The Fractal Geometry of Nature written by Benoit Mandelbrot. This book was released on 2021-07-16. Available in PDF, EPUB and Kindle. Book excerpt: Written in a style that is accessible to a wide audience, The Fractal Geometry of Nature inspired popular interest in this emerging field. Mandelbrot's unique style, and rich illustrations will inspire readers of all backgrounds.

Connections Between Mathematics, the Arts and Architecture

2019 Architecture
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Release : 2019
Genre : Architecture
Kind : eBook
Book Rating : 954/5 ( reviews)

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Book Synopsis Connections Between Mathematics, the Arts and Architecture by : Nicoletta Sala

Download or read book Connections Between Mathematics, the Arts and Architecture written by Nicoletta Sala. This book was released on 2019. Available in PDF, EPUB and Kindle. Book excerpt: The purpose of this book is to analyze the interdisciplinary aspects of mathematics and geometry in reference to nature, art, and architecture.In Chapter 1, we introduce symmetry and its different meanings. Symmetry is a notion, which has been applied in the arts and architecture to find harmony and beauty. It joins aesthetics and practice, science and economy, mathematics and philosophy. In this chapter, we also analyze the influence of Vitruvius and the concept of old symmetry, received by the Renaissance. It is also interesting to note how in contemporary architecture there is often the presence of the "break" of symmetry (for example in the Frank O. Gehry's works).Chapter 2 explains how proportions, and in particular, the golden section, has introduced aesthetic canons that have strongly influenced many artists like Polycletus, and architects, from Ictinus to Le Corbusier.In Chapter 3, we discover how curves and spirals find their application in artistic works, for example in Mycenaean jewelry, and architectural works, from the Baroque of Francesco Borromini to the Land Art of Smithson.Chapter 4 presents the importance and influence that Platonic solids and polyhedrons have had on philosophy and art through different historical periods and different cultures. For instance, we look at how Platonic solids are connected to the theory of Empedocles' elements and Hippocrates' theory of humors.Chapter 5 describes surfaces, discovering how different cultures have used them in different manners, including Roman aqueducts, iron bridges, and finally arriving on modern structures that base their forms on hyperboloids and paraboloids.In Chapter 6, we introduce fractal geometry, as a geometry that tries to explain nature's irregular shapes, trying to overcome the limitations imposed by "old" Euclidean geometry. We also analyze how fractal geometry has influenced architecture in this century.

A Course in Morphometrics for Biologists

2018-10-04 Medical
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Release : 2018-10-04
Genre : Medical
Kind : eBook
Book Rating : 065/5 ( reviews)

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Book Synopsis A Course in Morphometrics for Biologists by : Fred L. Bookstein

Download or read book A Course in Morphometrics for Biologists written by Fred L. Bookstein. This book was released on 2018-10-04. Available in PDF, EPUB and Kindle. Book excerpt: This book builds a much-needed bridge between biostatistics and organismal biology by linking the arithmetic of statistical studies of organismal form to the biological inferences that may follow from it. It incorporates a cascade of new explanations of regression, correlation, covariance analysis, and principal components analysis, before applying these techniques to an increasingly common data resource: the description of organismal forms by sets of landmark point configurations. For each data set, multiple analyses are interpreted and compared for insight into the relation between the arithmetic of the measurements and the rhetoric of the subsequent biological explanations. The text includes examples that range broadly over growth, evolution, and disease. For graduate students and researchers alike, this book offers a unique consideration of the scientific context surrounding the analysis of form in today's biosciences.

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