Mathematics and the Imagination
Title | Mathematics and the Imagination PDF eBook |
Author | Edward Kasner |
Publisher | Courier Corporation |
Total Pages | 400 |
Release | 2013-04-22 |
Genre | Mathematics |
ISBN | 0486320278 |
With wit and clarity, the authors progress from simple arithmetic to calculus and non-Euclidean geometry. Their subjects: geometry, plane and fancy; puzzles that made mathematical history; tantalizing paradoxes; more. Includes 169 figures.
Mathematics and the Imagination
Title | Mathematics and the Imagination PDF eBook |
Author | Edward Kasner |
Publisher | |
Total Pages | 380 |
Release | 1949 |
Genre | |
ISBN |
Mathematics for the Imagination
Title | Mathematics for the Imagination PDF eBook |
Author | Peter Higgins |
Publisher | OUP Oxford |
Total Pages | 238 |
Release | 2002-09-26 |
Genre | Mathematics |
ISBN | 0191500534 |
Mathematics for the Imagination provides an accessible and entertaining investigation into mathematical problems in the world around us. From world navigation, family trees, and calendars to patterns, tessellations, and number tricks, this informative and fun new book helps you to understand the maths behind real-life questions and rediscover your arithmetical mind. This is a follow-up to the popular Mathematics for the Curious, Peter Higgins's first investigation into real-life mathematical problems. A highly involving book which encourages the reader to enter into the spirit of mathematical exploration.
Geometry and the Imagination
Title | Geometry and the Imagination PDF eBook |
Author | D. Hilbert |
Publisher | American Mathematical Soc. |
Total Pages | 357 |
Release | 2021-03-17 |
Genre | Education |
ISBN | 1470463024 |
This remarkable book has endured as a true masterpiece of mathematical exposition. There are few mathematics books that are still so widely read and continue to have so much to offer—even after more than half a century has passed! The book is overflowing with mathematical ideas, which are always explained clearly and elegantly, and above all, with penetrating insight. It is a joy to read, both for beginners and experienced mathematicians. “Hilbert and Cohn-Vossen” is full of interesting facts, many of which you wish you had known before. It's also likely that you have heard those facts before, but surely wondered where they could be found. The book begins with examples of the simplest curves and surfaces, including thread constructions of certain quadrics and other surfaces. The chapter on regular systems of points leads to the crystallographic groups and the regular polyhedra in R 3 R3. In this chapter, they also discuss plane lattices. By considering unit lattices, and throwing in a small amount of number theory when necessary, they effortlessly derive Leibniz's series: π/4=1−1/3+1/5−1/7+−… π/4=1−1/3+1/5−1/7+−…. In the section on lattices in three and more dimensions, the authors consider sphere-packing problems, including the famous Kepler problem. One of the most remarkable chapters is “Projective Configurations”. In a short introductory section, Hilbert and Cohn-Vossen give perhaps the most concise and lucid description of why a general geometer would care about projective geometry and why such an ostensibly plain setup is truly rich in structure and ideas. Here, we see regular polyhedra again, from a different perspective. One of the high points of the chapter is the discussion of Schlafli's Double-Six, which leads to the description of the 27 lines on the general smooth cubic surface. As is true throughout the book, the magnificent drawings in this chapter immeasurably help the reader. A particularly intriguing section in the chapter on differential geometry is Eleven Properties of the Sphere. Which eleven properties of such a ubiquitous mathematical object caught their discerning eye and why? Many mathematicians are familiar with the plaster models of surfaces found in many mathematics departments. The book includes pictures of some of the models that are found in the Göttingen collection. Furthermore, the mysterious lines that mark these surfaces are finally explained! The chapter on kinematics includes a nice discussion of linkages and the geometry of configurations of points and rods that are connected and, perhaps, constrained in some way. This topic in geometry has become increasingly important in recent times, especially in applications to robotics. This is another example of a simple situation that leads to a rich geometry. It would be hard to overestimate the continuing influence Hilbert-Cohn-Vossen's book has had on mathematicians of this century. It surely belongs in the “pantheon” of great mathematics books.
Math Imagination
Title | Math Imagination PDF eBook |
Author | Edward Kasner |
Publisher | |
Total Pages | |
Release | 1974-09-15 |
Genre | |
ISBN | 9780671208547 |
MATHEMATICS AND THE IMAGINATION. EDWARD KASNER AND JAMES NEWMAN. WITH DRAWINGS AND DIAGRAMS BY RUFUS ISAACS.
Title | MATHEMATICS AND THE IMAGINATION. EDWARD KASNER AND JAMES NEWMAN. WITH DRAWINGS AND DIAGRAMS BY RUFUS ISAACS. PDF eBook |
Author | Edward Kasner |
Publisher | |
Total Pages | 380 |
Release | 1963 |
Genre | |
ISBN |
Innovation beyond Fiction
Title | Innovation beyond Fiction PDF eBook |
Author | Mathias Béjean |
Publisher | Cambridge Scholars Publishing |
Total Pages | 165 |
Release | 2022-02-15 |
Genre | Business & Economics |
ISBN | 1527579999 |
This book is about mathematics in the management of innovation, showing how recent advances in mathematics help us grasp and support innovation as a social activity of thinking and imagining together. It will make the reader rethink both innovation and mathematics by having them interplay in practical organizational settings. Told as fiction to make its argument more accessible, the book is nonetheless grounded in theoretical reflections and recent mathematical advances. In recounting the adventures of a committed and enthusiastic inventor-designer hampered by the increasing industrial bureaucratization of his world, it accounts for the fate of many innovation processes in large companies and administrations. Successful innovation hinges on having everyone involved in the process share a space of conceptual exploration. This philosophical aspect of the innovation process is about collective imagination, a notion that customary styles of thought have great difficulty dealing with. This is where mathematics, of a new kind, might prove to be a new platform for better management of innovation.