This book focuses on the classic Steiner Problem and illustrates how results of the problem's development have generated the Theory of Minimal Networks, that is systems of "rubber" branching threads of minimal length. This theory demonstrates a brilliant interconnection among differential and computational geometry, topology, variational calculus, and graph theory. All necessary preliminary information is included, and the book's simplified format and nearly 150 illustrations and tables will help readers develop a concrete understanding of the material. All nontrivial statements are proved, and plenty of exercises are included.
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Inside This Book
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First Sentence:
This chapter introduces the main definitions and results from graph theory and differential geometry necessary for what follows. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
closed minimal network, mobile vertices, net geodesics, twisting number, parametric networks, arbitrary skeleton, minimal snake, mobile vertex, nonboundary vertex, periodic net geodesic, deformational equivalent, embedded polygonal line, tiling realization, tree tilings, branching macroelements, extreme simplex, pointwise networks, classifying skeletons, admissible angle, admissible triplet, nondegenerate edges, canonical numeration, homotopic type, minimal networks, snake emitted Key Phrases - Capitalized Phrases (CAPs): (learn more)
Local Structure Characteristic System, Prove Assertion, Mechanical-Mathematical Department of Moscow State University New!
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Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
This chapter introduces the main definitions and results from graph theory and differential geometry necessary for what follows. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
closed minimal network, mobile vertices, net geodesics, twisting number, parametric networks, arbitrary skeleton, minimal snake, mobile vertex, nonboundary vertex, periodic net geodesic, deformational equivalent, embedded polygonal line, tiling realization, tree tilings, branching macroelements, extreme simplex, pointwise networks, classifying skeletons, admissible angle, admissible triplet, nondegenerate edges, canonical numeration, homotopic type, minimal networks, snake emitted Key Phrases - Capitalized Phrases (CAPs): (learn more)
Local Structure Characteristic System, Prove Assertion, Mechanical-Mathematical Department of Moscow State University New!
Books on Related Topics | Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
Citations (learn more)
This book cites 5
books:
- The Steiner Tree Problem (Annals of Discrete Mathematics) by Frank K. Hwang in Front Matter, and Back Matter
- Computer Science by C.S. French in Front Matter
- Studies in Optimization (Studies in mathematics) by George Bernard Dantzig in Back Matter
- Computer Science by Carl French in Front Matter
- Mathematics and Optimal Form: Coll.Pa (Scientific American Library) by Stefan Hildebrandt in Back Matter
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