The mathematical mechanic

• Verfasst von: Levi, Mark [VerfasserIn]
• Titel: The mathematical mechanic
• Titelzusatz: using physical reasoning to solve problems
• Verf.angabe: Mark Levi ; with a new preface by the author
• Ausgabe: First Princeton science library edition
• Verlagsort: Princeton ; Oxford
• Verlag: Princeton University Press
• Jahr: 2023
• Umfang: 1 Online-Ressource (XII, 186 Seiten)
• Illustrationen: Illustrationen
• Gesamttitel/Reihe: Princeton science library
• Fussnoten: Description based on publisher supplied metadata and other sources
• ISBN: 978-1-4008-3047-3
• Schlagwörter: (s)Aufgabensammlung / (s)Mechanik
• Datenträger: Online-Ressource
• Sprache: eng
• Bibliogr. Hinweis: Erscheint auch als : Druck-Ausgabe: Levi, Mark, 1951 - : The mathematical mechanic. - First Princeton science library edition. - Princeton : Princeton University Press, 2023. - xii, 186 Seiten
• RVK-Notation: SK 950
• K10plus-PPN: 1886550271
• K10plus-PPN:
  Universitätsbibliothek
• Lokale URL UB: Zum Volltext

Abstract

No detailed description available for "The Mathematical Mechanic".

Abstract

Cover -- Contents -- Preface -- 1. Introduction -- 1.1 Math versus Physics -- 1.2 What This Book Is About -- 1.3 A Physical versus a Mathematical Solution: An Example -- 1.4 Acknowledgments -- 2. The Pythagorean Theorem -- 2.1 Introduction -- 2.2 The "Fish Tank" Proof of the Pythagorean Theorem -- 2.3 Converting a Physical Argument into a Rigorous Proof -- 2.4 The Fundamental Theorem of Calculus -- 2.5 The Determinant by Sweeping -- 2.6 The Pythagorean Theorem by Rotation -- 2.7 Still Water Runs Deep -- 2.8 A Three-Dimensional Pythagorean Theorem -- 2.9 A Surprising Equilibrium -- 2.10 Pythagorean Theorem by Springs -- 2.11 More Geometry with Springs -- 2.12 A Kinetic Energy Proof: Pythagoras on Ice -- 2.13 Pythagoras and Einstein? -- 3. Minima and Maxima -- 3.1 The Optical Property of Ellipses -- 3.2 More about the Optical Property -- 3.3 Linear Regression (The Best Fit) via Springs -- 3.4 The Polygon of Least Area -- 3.5 The Pyramid of Least Volume -- 3.6 A Theorem on Centroids -- 3.7 An Isoperimetric Problem -- 3.8 The Cheapest Can -- 3.9 The Cheapest Pot -- 3.10 The Best Spot in a Drive-In Theater -- 3.11 The Inscribed Angle -- 3.12 Fermat's Principle and Snell's Law -- 3.13 Saving a Drowning Victim by Fermat's Principle -- 3.14 The Least Sum of Squares to a Point -- 3.15 Why Does a Triangle Balance on the Point of Intersection of the Medians? -- 3.16 The Least Sum of Distances to Four Points in Space -- 3.17 Shortest Distance to the Sides of an Angle -- 3.18 The Shortest Segment through a Point -- 3.19 Maneuvering a Ladder -- 3.20 The Most Capacious Paper Cup -- 3.21 Minimal-Perimeter Triangles -- 3.22 An Ellipse in the Corner -- 3.23 Problems -- 4. Inequalities by Electric Shorting -- 4.1 Introduction -- 4.2 The Arithmetic Mean Is Greater than the Geometric Mean by Throwing a Switch -- 4.3 Arithmetic Mean ≥ Harmonic Mean for n Numbers.