Shape And Energies Of Geometric Objects

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Louis H Kauffman (Univ Of Illinois At Chicago, Usa) Ljubica S Velimirovic (University Of Nis, Serbia)

Shape And Energies Of Geometric Objects

Name: Shape And Energies Of Geometric Objects
Price: 216.48 AUD
Availability: OutOfStock
ISBN: 9789819819454

Louis H Kauffman (Univ Of Illinois At Chicago, Usa), Ljubica S Velimirovic (University Of Nis, Serbia), Marija S Najdanovic (University Of Pristina In Kosovska Mitrovica, Serbia) , Svetozar R Rancic (University Of Nis, Serbia)

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English

World Scientific Publishing Co Pte Ltd
23 March 2026

Geometry; Topology

Series: Series on Knots & Everything

Summary
Details

In this book, we study the shape of different geometric objects (curves, surfaces, and knots) through small deformation: infinitesimal bending. The shape of geometric objects is determined by their geometric curvature as well as curvature-based functionals, which are referred to as energies. Different kinds of curvatures, their properties, and their influence on shape and energy are discussed. For the investigation of shape and energy, we use our own software visualization tools.

We aim to offer a mathematical way of considering shape. That is, all the geometrical information that is invariant to translations, rotations, and size changes. A more flexible definition of shape takes into consideration the fact that we often deal with deformable shapes in reality. By allowing also isometric (or near-isometric) deformations, such as infinitesimal bending, the intrinsic geometry of the object will stay the same, while sub-parts might be located at very different positions in space.

A special part of the book presents the construction of examples of unknots, as well as knots that can resist simplification by energy gradient and force evolution methods in programming models.

By: Louis H Kauffman (Univ Of Illinois At Chicago Usa), Ljubica S Velimirovic (University Of Nis, Serbia), Marija S Najdanovic (University Of Pristina In Kosovska Mitrovica, Serbia), Svetozar R Rancic (University Of Nis, Serbia)
Imprint: World Scientific Publishing Co Pte Ltd
Country of Publication: Singapore
Volume: 80
ISBN: 9789819819454
ISBN 10: 9819819458
Series: Series on Knots & Everything
Pages: 260
Publication Date: 23 March 2026
Audience: College/higher education , Professional and scholarly , Primary , Undergraduate
Format: Hardback
Publisher's Status: Active