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Author: Eric A. Lord
Publisher:
ISBN: 9780853127222
Category : Geometry
Languages : en
Pages : 260
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Book Description
Author: Eric A. Lord
Publisher:
ISBN: 9780853127222
Category : Geometry
Languages : en
Pages : 260
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Book Description
Author: Jordan Ellenberg
Publisher: Penguin
ISBN: 1984879065
Category : Mathematics
Languages : en
Pages : 481
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Book Description
An instant New York Times Bestseller! “Unreasonably entertaining . . . reveals how geometric thinking can allow for everything from fairer American elections to better pandemic planning.” —The New York Times From the New York Times-bestselling author of How Not to Be Wrong—himself a world-class geometer—a far-ranging exploration of the power of geometry, which turns out to help us think better about practically everything. How should a democracy choose its representatives? How can you stop a pandemic from sweeping the world? How do computers learn to play Go, and why is learning Go so much easier for them than learning to read a sentence? Can ancient Greek proportions predict the stock market? (Sorry, no.) What should your kids learn in school if they really want to learn to think? All these are questions about geometry. For real. If you're like most people, geometry is a sterile and dimly remembered exercise you gladly left behind in the dust of ninth grade, along with your braces and active romantic interest in pop singers. If you recall any of it, it's plodding through a series of miniscule steps only to prove some fact about triangles that was obvious to you in the first place. That's not geometry. Okay, it is geometry, but only a tiny part, which has as much to do with geometry in all its flush modern richness as conjugating a verb has to do with a great novel. Shape reveals the geometry underneath some of the most important scientific, political, and philosophical problems we face. Geometry asks: Where are things? Which things are near each other? How can you get from one thing to another thing? Those are important questions. The word "geometry"comes from the Greek for "measuring the world." If anything, that's an undersell. Geometry doesn't just measure the world—it explains it. Shape shows us how.
Author: Stefan Hildebrandt
Publisher: Springer Science & Business Media
ISBN: 9780387979915
Category : Science
Languages : en
Pages : 370
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Book Description
Why does nature prefer some shapes and not others? The variety of sizes, shapes, and irregularities in nature is endless. Skillfully integrating striking full-color illustrations, the authors describe the efforts by scientists and mathematicians since the Renaissance to identify and describe the principles underlying the shape of natural forms. But can one set of laws account for both the symmetry and irregularity as well as the infinite variety of nature's designs? A complete answer to this question is likely never to be discovered. Yet, it is fascinating to see how the search for some simple universal laws down through the ages has increased our understanding of nature. The Parsimonious Universe looks at examples from the world around us at a non-mathematical, non-technical level to show that nature achieves efficiency by being stingy with the energy it expends.
Author: Stefan Hildebrandt
Publisher: Copernicus
ISBN: 9781461224242
Category : Science
Languages : en
Pages : 0
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Book Description
Why does nature prefer some shapes and not others? The variety of sizes, shapes, and irregularities in nature is endless. Skillfully integrating striking full-color illustrations, the authors describe the efforts by scientists and mathematicians since the Renaissance to identify and describe the principles underlying the shape of natural forms. But can one set of laws account for both the symmetry and irregularity as well as the infinite variety of nature's designs? A complete answer to this question is likely never to be discovered. Yet, it is fascinating to see how the search for some simple universal laws down through the ages has increased our understanding of nature. The Parsimonious Universe looks at examples from the world around us at a non-mathematical, non-technical level to show that nature achieves efficiency by being stingy with the energy it expends.
Author: Silvia Biasotti
Publisher: Springer Nature
ISBN: 303179558X
Category : Mathematics
Languages : en
Pages : 124
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Book Description
This book is a guide for researchers and practitioners to the new frontiers of 3D shape analysis and the complex mathematical tools most methods rely on. The target reader includes students, researchers and professionals with an undergraduate mathematics background, who wish to understand the mathematics behind shape analysis. The authors begin with a quick review of basic concepts in geometry, topology, differential geometry, and proceed to advanced notions of algebraic topology, always keeping an eye on the application of the theory, through examples of shape analysis methods such as 3D segmentation, correspondence, and retrieval. A number of research solutions in the field come from advances in pure and applied mathematics, as well as from the re-reading of classical theories and their adaptation to the discrete setting. In a world where disciplines (fortunately) have blurred boundaries, the authors believe that this guide will help to bridge the distance between theory and practice. Table of Contents: Acknowledgments / Figure Credits / About this Book / 3D Shape Analysis in a Nutshell / Geometry, Topology, and Shape Representation / Differential Geometry and Shape Analysis / Spectral Methods for Shape Analysis / Maps and Distances between Spaces / Algebraic Topology and Topology Invariants / Differential Topology and Shape Analysis / Reeb Graphs / Morse and Morse-Smale Complexes / Topological Persistence / Beyond Geometry and Topology / Resources / Bibliography / Authors' Biographies
Author: Saunders MacLane
Publisher: Springer Science & Business Media
ISBN: 1461248728
Category : Mathematics
Languages : en
Pages : 486
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Book Description
This book records my efforts over the past four years to capture in words a description of the form and function of Mathematics, as a background for the Philosophy of Mathematics. My efforts have been encouraged by lec tures that I have given at Heidelberg under the auspices of the Alexander von Humboldt Stiftung, at the University of Chicago, and at the University of Minnesota, the latter under the auspices of the Institute for Mathematics and Its Applications. Jean Benabou has carefully read the entire manuscript and has offered incisive comments. George Glauberman, Car los Kenig, Christopher Mulvey, R. Narasimhan, and Dieter Puppe have provided similar comments on chosen chapters. Fred Linton has pointed out places requiring a more exact choice of wording. Many conversations with George Mackey have given me important insights on the nature of Mathematics. I have had similar help from Alfred Aeppli, John Gray, Jay Goldman, Peter Johnstone, Bill Lawvere, and Roger Lyndon. Over the years, I have profited from discussions of general issues with my colleagues Felix Browder and Melvin Rothenberg. Ideas from Tammo Tom Dieck, Albrecht Dold, Richard Lashof, and Ib Madsen have assisted in my study of geometry. Jerry Bona and B.L. Foster have helped with my examina tion of mechanics. My observations about logic have been subject to con structive scrutiny by Gert Miiller, Marian Boykan Pour-El, Ted Slaman, R. Voreadou, Volker Weispfennig, and Hugh Woodin.
Author: Christopher Alexander
Publisher: Harvard University Press
ISBN: 9780674627512
Category : Architecture
Languages : en
Pages : 228
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Book Description
"These notes are about the process of design: the process of inventing things which display new physical order, organization, form, in response to function." This book, opening with these words, presents an entirely new theory of the process of design. In the first part of the book, Christopher Alexander discusses the process by which a form is adapted to the context of human needs and demands that has called it into being. He shows that such an adaptive process will be successful only if it proceeds piecemeal instead of all at once. It is for this reason that forms from traditional un-self-conscious cultures, molded not by designers but by the slow pattern of changes within tradition, are so beautifully organized and adapted. When the designer, in our own self-conscious culture, is called on to create a form that is adapted to its context he is unsuccessful, because the preconceived categories out of which he builds his picture of the problem do not correspond to the inherent components of the problem, and therefore lead only to the arbitrariness, willfulness, and lack of understanding which plague the design of modern buildings and modern cities. In the second part, Mr. Alexander presents a method by which the designer may bring his full creative imagination into play, and yet avoid the traps of irrelevant preconception. He shows that, whenever a problem is stated, it is possible to ignore existing concepts and to create new concepts, out of the structure of the problem itself, which do correspond correctly to what he calls the subsystems of the adaptive process. By treating each of these subsystems as a separate subproblem, the designer can translate the new concepts into form. The form, because of the process, will be well-adapted to its context, non-arbitrary, and correct. The mathematics underlying this method, based mainly on set theory, is fully developed in a long appendix. Another appendix demonstrates the application of the method to the design of an Indian village.
Author: Shawn W. Walker
Publisher: SIAM
ISBN: 1611973961
Category : Mathematics
Languages : en
Pages : 152
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Book Description
Many things around us have properties that depend on their shape--for example, the drag characteristics of a rigid body in a flow. This self-contained overview of differential geometry explains how to differentiate a function (in the calculus sense) with respect to a "shape variable." This approach, which is useful for understanding mathematical models containing geometric partial differential equations (PDEs), allows readers to obtain formulas for geometric quantities (such as curvature) that are clearer than those usually offered in differential geometry texts. Readers will learn how to compute sensitivities with respect to geometry by developing basic calculus tools on surfaces and combining them with the calculus of variations. Several applications that utilize shape derivatives and many illustrations that help build intuition are included.
Author:
Publisher:
ISBN:
Category : Global analysis (Mathematics)
Languages : en
Pages : 814
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Book Description
Author: Philip Ball
Publisher: OUP Oxford
ISBN: 0191528730
Category : Nature
Languages : en
Pages : 328
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Book Description
Patterns are everywhere in nature - in the ranks of clouds in the sky, the stripes of an angelfish, the arrangement of petals in flowers. Where does this order and regularity come from? It creates itself. The patterns we see come from self-organization. Whether living or non-living, scientists have found that there is a pattern-forming tendency inherent in the basic structure and processes of nature, so that from a few simple themes, and the repetition of simple rules, endless beautiful variations can arise. Part of a trilogy of books exploring the science of patterns in nature, acclaimed science writer Philip Ball here looks at how shapes form. From soap bubbles to honeycombs, delicate shell patterns, and even the developing body parts of a complex animal like ourselves, he uncovers patterns in growth and form in all corners of the natural world, explains how these patterns are self-made, and why similar shapes and structures may be found in very different settings, orchestrated by nothing more than simple physical forces. This book will make you look at the world with fresh eyes, seeing order and form even in the places you'd least expect.
