By Alessio Corti
By Alessio Corti
By David S. Richeson
Leonhard Euler's polyhedron formulation describes the constitution of many objects--from football balls and gems to Buckminster Fuller's constructions and colossal all-carbon molecules. but Euler's formulation is so easy it may be defined to a toddler. Euler's Gem tells the illuminating tale of this essential mathematical idea.
From historical Greek geometry to latest state-of-the-art examine, Euler's Gem celebrates the invention of Euler's loved polyhedron formulation and its far-reaching influence on topology, the examine of shapes. In 1750, Euler saw that any polyhedron composed of V vertices, E edges, and F faces satisfies the equation V-E+F=2. David Richeson tells how the Greeks overlooked the formulation completely; how Descartes virtually came upon it yet fell brief; how nineteenth-century mathematicians widened the formula's scope in ways in which Euler by no means anticipated through adapting it to be used with doughnut shapes, gentle surfaces, and better dimensional shapes; and the way twentieth-century mathematicians stumbled on that each form has its personal Euler's formulation. utilizing remarkable examples and various illustrations, Richeson offers the formula's many stylish and unforeseen purposes, akin to exhibiting why there's regularly a few windless spot in the world, the way to degree the acreage of a tree farm by way of counting timber, and the way many crayons are had to colour any map.
full of a who is who of remarkable mathematicians who puzzled, subtle, and contributed to a outstanding theorem's improvement, Euler's Gem will fascinate each arithmetic enthusiast.
By I. M. James
By David Hestenes,Anthony Lasenby
This small publication began a profound revolution within the improvement of mathematical physics, one that has reached many operating physicists already, and which stands poised to result in far-reaching switch within the future.
At its center is using Clifford algebra to unify another way disparate mathematical languages, relatively these of spinors, quaternions, tensors and differential kinds. It offers a unified procedure protecting a majority of these parts and hence ends up in a really effective ‘toolkit’ to be used in actual difficulties together with quantum mechanics, classical mechanics, electromagnetism and relativity (both particular and basic) – just one mathematical approach should be realized and understood, and you possibly can use it at degrees which expand during to present learn issues in every one of those components.
These comparable options, within the kind of the ‘Geometric Algebra’, might be utilized in lots of components of engineering, robotics and computing device technological know-how, without adjustments precious – it's the related underlying arithmetic, and permits physicists to appreciate themes in engineering, and engineers to appreciate subject matters in physics (including facets in frontier areas), in a fashion which no different unmarried mathematical process may perhaps wish to make possible.
There is one other point to Geometric Algebra, that's much less tangible, and is going past questions of mathematical strength and diversity. this is often the outstanding perception it offers to actual difficulties, and how it regularly indicates new good points of the physics itself, not only the math. Examples of this are peppered all through ‘Space-Time Algebra’, regardless of its brief size, and a few of them are successfully nonetheless learn subject matters for the future.
From the Foreward through Anthony Lasenby
By Gregory L. Naber
By Abraham Adrian Albert
By Gerard Walschap
This e-book deals an advent to the idea of differentiable manifolds and fiber bundles. It examines bundles from the perspective of metric differential geometry: Euclidean bundles, Riemannian connections, curvature, and Chern-Weil conception are mentioned, together with the Pontrjagin, Euler, and Chern attribute sessions of a vector package. those options are illustrated intimately for bundles over spheres.
By Matthias Ludwig,Andreas Filler,Anselm Lambert
Mathematische Grundvorstellungen sind im Bereich der Arithmetik und Algebra umfassend bearbeitet worden, für die Geometrie gilt dies bislang nicht. Dieser Band beleuchtet erste wesentliche Schritte in diese Richtung und versucht die fehlenden Konzepte der Grundvorstellungen in der Geometriedidaktik aufzuarbeiten. In engem Zusammenhang mit Grundvorstellungen stehen Begriffsbildungen, denen ein hoher Stellenwert im Geometrieunterricht zukommt. Das Buch enthält die ausformulierten Vorträge der 30. Herbsttagung 2013 des Arbeitskreis Geometrie in der Gesellschaft für Didaktik der Mathematik (GDM).
By Helga Baum,Andreas Juhl
Conformal invariants (conformally invariant tensors, conformally covariant differential operators, conformal holonomy teams etc.) are of important importance in differential geometry and physics. famous examples of such operators are the Yamabe-, the Paneitz-, the Dirac- and the twistor operator. the purpose of the seminar was once to provide the elemental principles and a few of the hot advancements round Q-curvature and conformal holonomy. The half on Q-curvature discusses its beginning, its relevance in geometry, spectral thought and physics. right here the impression of principles that have their beginning within the AdS/CFT-correspondence turns into seen.
The half on conformal holonomy describes fresh type effects, its relation to Einstein metrics and to conformal Killing spinors, and comparable specific geometries.
By Valery Alexeev,Gilberto Bini,Martí Lahoz,Emanuele Macrí,Paolo Stellari