{"product_id":"shape-and-energies-of-geometric-kauffman-louis-h-9789819819454","title":"Shape and Energies of Geometric Objects","description":"\u003cp\u003eIn 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.\u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e\u003cp\u003eWe 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.\u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e\u003cp\u003eA 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.\u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eAuthor:\u003c\/b\u003e Kauffman Louis H\u003cbr\u003e\u003cb\u003eISBN-10:\u003c\/b\u003e 9819819458\u003cbr\u003e\u003cb\u003eISBN-13:\u003c\/b\u003e 9789819819454\u003cbr\u003e\u003cb\u003ePublisher:\u003c\/b\u003e World Scientific Publishing Company\u003cbr\u003e\u003cb\u003eLanguage:\u003c\/b\u003e English\u003cbr\u003e\u003cb\u003ePublished:\u003c\/b\u003e 03\/05\/2026\u003cbr\u003e\u003cb\u003ePages:\u003c\/b\u003e 260\u003cbr\u003e\u003cb\u003eFormat:\u003c\/b\u003e Hardcover\u003cbr\u003e\u003cb\u003eWeight:\u003c\/b\u003e 1.24lbs\u003cbr\u003e\u003cb\u003eSize:\u003c\/b\u003e 9.00h x 6.00w x 0.69d","brand":"Kauffman Louis H","offers":[{"title":"Hardcover","offer_id":48487409189119,"sku":"9789819819454","price":98.0,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0662\/2982\/9887\/files\/img_3fc3b8a8-75c1-4c54-82aa-e738c4abc329.jpg?v=1778060327","url":"https:\/\/www.whiterainbookhouse.com\/products\/shape-and-energies-of-geometric-kauffman-louis-h-9789819819454","provider":"WR Book House","version":"1.0","type":"link"}