{"title":"Joseph O'rourke","description":null,"products":[{"product_id":"pop-up-geometry-book-joseph-o-rourke-9781009096263","title":"Pop-Up Geometry","description":"The incredible 3-D dynamics of pop-up cards can be analyzed using high-school mathematics - a bit of trigonometry, but no calculus necessary. This book explores the beautifully intricate constructions, revealing a tangible, focused employment of mathematics in contrast to the often unmotivated presentation in traditional curricula.","brand":"WoB","offers":[{"title":"GB \/ NEW \/ GARDNERS","offer_id":49744362144017,"sku":"NGR9781009096263","price":0.0,"currency_code":"GBP","in_stock":true},{"title":"US \/ NEW \/ INGRAM","offer_id":51012365451537,"sku":"NIN9781009096263","price":0.0,"currency_code":"GBP","in_stock":true},{"title":"GB \/ NEW \/ INGRAM","offer_id":52516697080081,"sku":"NLS9781009096263","price":0.0,"currency_code":"GBP","in_stock":true},{"title":"US \/ WELL_READ \/ SBYB","offer_id":52782457258257,"sku":"CIN1009096265A","price":0.0,"currency_code":"GBP","in_stock":false},{"title":"US \/ VERY_GOOD \/ SBYB","offer_id":52973142049041,"sku":"CIN1009096265VG","price":0.0,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/1009096265.jpg?v=1763226024"},{"product_id":"computational-geometry-in-c-book-joseph-o-rourke-9780521649766","title":"Computational Geometry in C","description":"This is the revised and expanded 1998 edition of a popular tutorial on the design and implementation of geometry algorithms. The self-contained treatment presumes only an elementary knowledge of mathematics but includes the latest research topics, making it an excellent resource for programmers in computer graphics, robotics, and engineering design.","brand":"WoB","offers":[{"title":"US \/ GOOD \/ SBYB","offer_id":49996456984849,"sku":"CIN0521649765G","price":0.0,"currency_code":"GBP","in_stock":true},{"title":"GB \/ GOOD \/ INTERNAL","offer_id":50669608075537,"sku":"GOR004816368","price":0.0,"currency_code":"GBP","in_stock":false},{"title":"GB \/ NEW \/ GARDNERS","offer_id":50697140633873,"sku":"NGR9780521649766","price":0.0,"currency_code":"GBP","in_stock":false},{"title":"US \/ VERY_GOOD \/ SBYB","offer_id":51694104215825,"sku":"CIN0521649765VG","price":0.0,"currency_code":"GBP","in_stock":false},{"title":"GB \/ VERY_GOOD \/ INTERNAL","offer_id":52108530417937,"sku":"GOR004022434","price":0.0,"currency_code":"GBP","in_stock":false},{"title":"GB \/ NEW \/ INGRAM","offer_id":52122134151441,"sku":"NLS9780521649766","price":0.0,"currency_code":"GBP","in_stock":true},{"title":"US \/ NEW \/ INGRAM","offer_id":52735579062545,"sku":"NIN9780521649766","price":0.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/0521649765.jpg?v=1751452605"},{"product_id":"computational-geometry-in-c-book-joseph-o-rourke-9780521445924","title":"Computational Geometry in C","description":"A textbook which introduces undergraduates to the design of geometry algorithms, which arise in a range of practical areas such as computer graphics, robotics and pattern recognition. The basic techniques used in computational geometry are covered - polygon triangulations and so on.","brand":"WoB","offers":[{"title":"US \/ GOOD \/ SBYB","offer_id":50311590084881,"sku":"CIN0521445922G","price":0.0,"currency_code":"GBP","in_stock":false},{"title":"US \/ VERY_GOOD \/ SBYB","offer_id":50430944248081,"sku":"CIN0521445922VG","price":0.0,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/0521445922.jpg?v=1750846453"},{"product_id":"how-to-fold-it-book-joseph-orourke-9780521145473","title":"How to Fold It","description":"Discover and understand  mathematical theorems through paper folding, starting with high school algebra and geometry through to more advanced concepts.","brand":"WoB","offers":[{"title":"GB \/ VERY_GOOD \/ INTERNAL","offer_id":50695945683217,"sku":"GOR006272463","price":0.0,"currency_code":"GBP","in_stock":false},{"title":"US \/ NEW \/ INGRAM","offer_id":51003034435857,"sku":"NIN9780521145473","price":0.0,"currency_code":"GBP","in_stock":true},{"title":"US \/ GOOD \/ SBYB","offer_id":51746191999249,"sku":"CIN0521145473G","price":0.0,"currency_code":"GBP","in_stock":false},{"title":"GB \/ NEW \/ INGRAM","offer_id":52335815852305,"sku":"NLS9780521145473","price":0.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/0521145473.jpg?v=1751443056"},{"product_id":"discrete-and-computational-geometry-book-joseph-o-rourke-9780691145532","title":"Discrete and Computational Geometry","description":"Offers a comprehensive introduction to discrete geometry. This book covers traditional topics such as convex hulls, triangulations, and Voronoi diagrams, as well as subjects like pseudotriangulations, curve reconstruction, and locked chains. It is suitable for sophomores in mathematics, computer science, engineering, or physics.","brand":"WoB","offers":[{"title":"US \/ NEW \/ INGRAM","offer_id":51005694443793,"sku":"NIN9780691145532","price":0.0,"currency_code":"GBP","in_stock":false},{"title":"US \/ GOOD \/ SBYB","offer_id":52693818114321,"sku":"CIN0691145539G","price":0.0,"currency_code":"GBP","in_stock":false},{"title":"US \/ VERY_GOOD \/ SBYB","offer_id":53247125946641,"sku":"CIN0691145539VG","price":0.0,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/0691145539.jpg?v=1751168288"},{"product_id":"pop-up-geometry-book-joseph-o-rourke-9781009098403","title":"Pop-Up Geometry","description":"Anyone browsing at the stationery store will see an incredible array of pop-up cards available for any occasion. The workings of pop-up cards and pop-up books can be remarkably intricate. Behind such designs lies beautiful geometry involving the intersection of circles, cones, and spheres, the movements of linkages, and other constructions. The geometry can be modelled by algebraic equations, whose solutions explain the dynamics. For example, several pop-up motions rely on the intersection of three spheres, a computation made every second for GPS location. Connecting the motions of the card structures with the algebra and geometry reveals abstract mathematics performing tangible calculations. Beginning with the nephroid in the 19th-century, the mathematics of pop-up design is now at the frontiers of rigid origami and algorithmic computational complexity. All topics are accessible to those familiar with high-school mathematics; no calculus required. Explanations are supplemented by 140+ figures and 20 animations.","brand":"WoB","offers":[{"title":"- \/ - \/ -","offer_id":51012323803409,"sku":"","price":0.0,"currency_code":"GBP","in_stock":true},{"title":"US \/ NEW \/ INGRAM","offer_id":51012326326545,"sku":"NIN9781009098403","price":0.0,"currency_code":"GBP","in_stock":true},{"title":"GB \/ NEW \/ INGRAM","offer_id":52530436636945,"sku":"NLS9781009098403","price":0.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/1009098403.jpg?v=1750982129"},{"product_id":"mathematics-of-origami-book-joseph-o-rourke-9781009687355","title":"The Mathematics of Origami","description":"When you see a paper crane, what do you think of? A symbol of hope, a delicate craft, The Karate Kid? What you might not see, but is ever present, is the fascinating mathematics underlying it. Origami is increasingly applied to engineering problems, including origami-based stents, deployment of solar arrays in space, architecture, and even furniture design. The topic is actively developing, with recent discoveries at the frontier (e.g., in rigid origami and in curved-crease origami) and an infusion of techniques and algorithms from theoretical computer science. The mathematics is often advanced, but this book instead relies on geometric intuition, making it accessible to readers with only a high school geometry and trigonometry background. Through careful exposition, more than 160 color figures, and 49 exercises all completely solved in an Appendix, the beautiful mathematics leading to stunning origami designs can be appreciated by students, teachers, engineers, and artists alike.","brand":"WoB","offers":[{"title":"- \/ - \/ -","offer_id":51883504009489,"sku":null,"price":0.0,"currency_code":"GBP","in_stock":true},{"title":"GB \/ NEW \/ GARDNERS","offer_id":51883504107793,"sku":"NGR9781009687355","price":0.0,"currency_code":"GBP","in_stock":false},{"title":"GB \/ NEW \/ INGRAM","offer_id":52855203922193,"sku":"NLS9781009687355","price":0.0,"currency_code":"GBP","in_stock":true},{"title":"US \/ NEW \/ INGRAM","offer_id":53009069670673,"sku":"NIN9781009687355","price":0.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/9781009687355.jpg?v=1782827755"},{"product_id":"mathematics-of-origami-book-joseph-o-rourke-9781009687386","title":"The Mathematics of Origami","description":"When you see a paper crane, what do you think of? A symbol of hope, a delicate craft, The Karate Kid? What you might not see, but is ever present, is the fascinating mathematics underlying it. Origami is increasingly applied to engineering problems, including origami-based stents, deployment of solar arrays in space, architecture, and even furniture design. The topic is actively developing, with recent discoveries at the frontier (e.g., in rigid origami and in curved-crease origami) and an infusion of techniques and algorithms from theoretical computer science. The mathematics is often advanced, but this book instead relies on geometric intuition, making it accessible to readers with only a high school geometry and trigonometry background. Through careful exposition, more than 160 color figures, and 49 exercises all completely solved in an Appendix, the beautiful mathematics leading to stunning origami designs can be appreciated by students, teachers, engineers, and artists alike.","brand":"WoB","offers":[{"title":"- \/ - \/ -","offer_id":51883506630929,"sku":null,"price":0.0,"currency_code":"GBP","in_stock":true},{"title":"GB \/ NEW \/ GARDNERS","offer_id":51883506696465,"sku":"NGR9781009687386","price":0.0,"currency_code":"GBP","in_stock":true},{"title":"GB \/ NEW \/ INGRAM","offer_id":52855204905233,"sku":"NLS9781009687386","price":0.0,"currency_code":"GBP","in_stock":true},{"title":"US \/ NEW \/ INGRAM","offer_id":52960965394705,"sku":"NIN9781009687386","price":0.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/9781009687386_b89e7312-34f2-413d-8378-a7f7204d0b28.jpg?v=1782827756"},{"product_id":"reshaping-convex-polyhedra-book-joseph-o-rourke-9783031475139","title":"Reshaping Convex Polyhedra","description":"\u003cp\u003e^ the=\"\" study=\"\" of=\"\" convex=\"\" polyhedra=\"\" in=\"\" ordinary=\"\" space=\"\" is=\"\" a=\"\" central=\"\" piece=\"\" classical=\"\" and=\"\" modern=\"\" geometry=\"\" that=\"\" has=\"\" had=\"\" significant=\"\" impact=\"\" on=\"\" many=\"\" areas=\"\" mathematics=\"\" also=\"\" computer=\"\" science.=\"\" present=\"\" book=\"\" project=\"\" by=\"\" joseph=\"\" o’rourke=\"\" costin=\"\" vîlcu=\"\" brings=\"\" together=\"\" two=\"\" important=\"\" strands=\"\" subject=\"\" —=\"\" combinatorics=\"\" polyhedra,=\"\" intrinsic=\"\" underlying=\"\" surface.=\"\" this=\"\" leads=\"\" to=\"\" remarkable=\"\" interplay=\"\" concepts=\"\" come=\"\" life=\"\" wide=\"\" range=\"\" very=\"\" attractive=\"\" topics=\"\" concerning=\"\" polyhedra.=\"\" gets=\"\" message=\"\" across=\"\" thetheory=\"\" although=\"\" with=\"\" roots,=\"\" still=\"\" much=\"\" alive=\"\" today=\"\" continues=\"\" be=\"\" inspiration=\"\" basis=\"\" lot=\"\" current=\"\" research=\"\" activity.=\"\" work=\"\" presented=\"\" manuscript=\"\" interesting=\"\" applications=\"\" discrete=\"\" computational=\"\" geometry,=\"\" as=\"\" well=\"\" other=\"\" mathematics.=\"\" treated=\"\" detail=\"\" include=\"\" unfolding=\"\" onto=\"\" surfaces,=\"\" continuous=\"\" flattening=\"\" convexity=\"\" theory=\"\" minimal=\"\" length=\"\" enclosing=\"\" polygons.=\"\" along=\"\" way,=\"\" open=\"\" problems=\"\" suitable=\"\" for=\"\" graduate=\"\" students=\"\" are=\"\" raised,=\"\" both=\"\" a\u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e\u003cp\u003eThe focus of this monograph is converting—reshaping—one 3D convex polyhedron to another via an operation the authors call “tailoring.” A convex polyhedron is a gem-like shape composed of flat facets, the focus of study since Plato and Euclid. The tailoring operation snips off a corner (a “vertex”) of a polyhedron and sutures closed the hole. This is akin to Johannes Kepler’s “vertex truncation,” but differs in that the hole left by a truncated vertex is filled with new surface, whereas tailoring zips the hole closed. A powerful “gluing” theorem of A.D. Alexandrov from 1950 guarantees that, after closing the hole, the result is a new convex polyhedron. Given two convex polyhedra P, and Q inside P, repeated tailoringallows P to be reshaped to Q. Rescaling any Q to fit inside P, the result is universal: any P can be reshaped to any Q. This is one of the main theorems in Part I, with unexpected theoretical consequences.\u003c\/p\u003e\u003cp\u003ePart II carries out a systematic study of “vertex-merging,” a technique that can be viewed as a type of inverse operation to tailoring. Here the start is P which is gradually enlarged as much as possible, by inserting new surface along slits. In a sense, repeated vertex-merging reshapes P to be closer to planarity. One endpoint of such a process leads to P being cut up and “pasted” inside a cylinder. Then rolling the cylinder on a plane achieves an unfolding of P. The underlying subtext is a question posed by Geoffrey Shephard in 1975 and already implied by drawings by Albrecht Dürer in the 15th century: whether every convex polyhedron can be unfolded to a planar “net.” Toward this end, the authors initiate an exploration of convexity on convex polyhedra, a topic rarely studiedin the literature but with considerable promise for future development.\u003cbr\u003e\u003c\/p\u003e\u003cp\u003eThis monograph uncovers new research directions and reveals connections among several, apparently distant, topics in geometry: Alexandrov’s Gluing Theorem, shortest paths and cut loci, Cauchy’s Arm Lemma, domes, quasigeodesics, convexity, and algorithms throughout. The interplay between these topics and the way the main ideas develop throughout the book could make the “journey” worthwhile for students and researchers in geometry, even if not directly interested in specific topics. Parts of the material will be of interest and accessible even to undergraduates. Although the proof difficulty varies from simple to quite intricate, with some proofs spanning several chapters, many examples and 125 figures help ease the exposition and illustrate the concepts.\u003cbr\u003e\u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e^\u0026gt;","brand":"WoB","offers":[{"title":"GB \/ NEW \/ GARDNERS","offer_id":52152654790929,"sku":"NGR9783031475139","price":0.0,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/9783031475139.jpg?v=1757617398"},{"product_id":"reshaping-convex-polyhedra-book-joseph-o-rourke-9783031475108","title":"Reshaping Convex Polyhedra","description":"\u003cp\u003e^ the=\"\" study=\"\" of=\"\" convex=\"\" polyhedra=\"\" in=\"\" ordinary=\"\" space=\"\" is=\"\" a=\"\" central=\"\" piece=\"\" classical=\"\" and=\"\" modern=\"\" geometry=\"\" that=\"\" has=\"\" had=\"\" significant=\"\" impact=\"\" on=\"\" many=\"\" areas=\"\" mathematics=\"\" also=\"\" computer=\"\" science.=\"\" present=\"\" book=\"\" project=\"\" by=\"\" joseph=\"\" o’rourke=\"\" costin=\"\" vîlcu=\"\" brings=\"\" together=\"\" two=\"\" important=\"\" strands=\"\" subject=\"\" —=\"\" combinatorics=\"\" polyhedra,=\"\" intrinsic=\"\" underlying=\"\" surface.=\"\" this=\"\" leads=\"\" to=\"\" remarkable=\"\" interplay=\"\" concepts=\"\" come=\"\" life=\"\" wide=\"\" range=\"\" very=\"\" attractive=\"\" topics=\"\" concerning=\"\" polyhedra.=\"\" gets=\"\" message=\"\" across=\"\" thetheory=\"\" although=\"\" with=\"\" roots,=\"\" still=\"\" much=\"\" alive=\"\" today=\"\" continues=\"\" be=\"\" inspiration=\"\" basis=\"\" lot=\"\" current=\"\" research=\"\" activity.=\"\" work=\"\" presented=\"\" manuscript=\"\" interesting=\"\" applications=\"\" discrete=\"\" computational=\"\" geometry,=\"\" as=\"\" well=\"\" other=\"\" mathematics.=\"\" treated=\"\" detail=\"\" include=\"\" unfolding=\"\" onto=\"\" surfaces,=\"\" continuous=\"\" flattening=\"\" convexity=\"\" theory=\"\" minimal=\"\" length=\"\" enclosing=\"\" polygons.=\"\" along=\"\" way,=\"\" open=\"\" problems=\"\" suitable=\"\" for=\"\" graduate=\"\" students=\"\" are=\"\" raised,=\"\" both=\"\" a\u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e\u003cp\u003eThe focus of this monograph is converting—reshaping—one 3D convex polyhedron to another via an operation the authors call “tailoring.” A convex polyhedron is a gem-like shape composed of flat facets, the focus of study since Plato and Euclid. The tailoring operation snips off a corner (a “vertex”) of a polyhedron and sutures closed the hole. This is akin to Johannes Kepler’s “vertex truncation,” but differs in that the hole left by a truncated vertex is filled with new surface, whereas tailoring zips the hole closed. A powerful “gluing” theorem of A.D. Alexandrov from 1950 guarantees that, after closing the hole, the result is a new convex polyhedron. Given two convex polyhedra P, and Q inside P, repeated tailoringallows P to be reshaped to Q. Rescaling any Q to fit inside P, the result is universal: any P can be reshaped to any Q. This is one of the main theorems in Part I, with unexpected theoretical consequences.\u003c\/p\u003e\u003cp\u003ePart II carries out a systematic study of “vertex-merging,” a technique that can be viewed as a type of inverse operation to tailoring. Here the start is P which is gradually enlarged as much as possible, by inserting new surface along slits. In a sense, repeated vertex-merging reshapes P to be closer to planarity. One endpoint of such a process leads to P being cut up and “pasted” inside a cylinder. Then rolling the cylinder on a plane achieves an unfolding of P. The underlying subtext is a question posed by Geoffrey Shephard in 1975 and already implied by drawings by Albrecht Dürer in the 15th century: whether every convex polyhedron can be unfolded to a planar “net.” Toward this end, the authors initiate an exploration of convexity on convex polyhedra, a topic rarely studiedin the literature but with considerable promise for future development.\u003cbr\u003e\u003c\/p\u003e\u003cp\u003eThis monograph uncovers new research directions and reveals connections among several, apparently distant, topics in geometry: Alexandrov’s Gluing Theorem, shortest paths and cut loci, Cauchy’s Arm Lemma, domes, quasigeodesics, convexity, and algorithms throughout. The interplay between these topics and the way the main ideas develop throughout the book could make the “journey” worthwhile for students and researchers in geometry, even if not directly interested in specific topics. Parts of the material will be of interest and accessible even to undergraduates. Although the proof difficulty varies from simple to quite intricate, with some proofs spanning several chapters, many examples and 125 figures help ease the exposition and illustrate the concepts.\u003cbr\u003e\u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e^\u0026gt;","brand":"WoB","offers":[{"title":"GB \/ NEW \/ INGRAM","offer_id":52657215668497,"sku":"NLS9783031475108","price":0.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/9783031475108.jpg?v=1762227685"}],"url":"https:\/\/www.worldofbooks.com\/collections\/author-books-by-joseph-o-rourke.oembed","provider":"World of Books ","version":"1.0","type":"link"}