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  ▼a  0691219893
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  ▼a  9780691219899
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  ▼a  2714027
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  ▼a  (OCoLC)1257077763

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  ▼a  MAIN

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  ▼a  QA641
  ▼b  .N44 2021

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  ▼a  MAT
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  ▼a  516.3/6
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  ▼a  Needham, Tristan,
  ▼e  author.

• 245

  ▼a  Visual Differential Geometry and Forms:
  ▼b  A Mathematical Drama in Five Acts /
  ▼c  Tristan Needham.

• 260

  ▼a  Princeton:
  ▼b  Princeton University Press,
  ▼c  [2021].

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  ▼a  1 online resource (531 p.).

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  ▼a  text
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  ▼a  computer
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  ▼a  online resource
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  ▼a  15.1 Directional Derivatives.

• 505

  ▼a  Intro -- Contents -- ACT I. The Nature of Space -- 1. Euclidean and Non-Euclidean Geometry -- 1.1 Euclidean and Hyperbolic Geometry -- 1.2 Spherical Geometry -- 1.3 The Angular Excess of a Spherical Triangle -- 1.4 Intrinsic and Extrinsic Geometry of Curved Surfaces -- 1.5 Constructing Geodesics via Their Straightness -- 1.6 The Nature of Space -- 2. Gaussian Curvature -- 2.1 Introduction -- 2.2 The Circumference and Area of a Circle -- 2.3 The Local Gauss-Bonnet Theorem -- 3. Exercises for Prologue and Act I -- ACT II. The Metric -- 4. Mapping Surfaces: The Metric -- 4.1 Introduction

• 505

  ▼a  4.2 The Projective Map of the Sphere -- 4.3 The Metric of a General Surface -- 4.4 The Metric Curvature Formula -- 4.5 Conformal Maps -- 4.6 Some Visual Complex Analysis -- 4.7 The Conformal Stereographic Map of the Sphere -- 4.8 Stereographic Formulas -- 4.9 Stereographic Preservation of Circles -- 5. The Pseudosphere and the Hyperbolic Plane -- 5.1 Beltrami's Insight -- 5.2 The Tractrix and the Pseudosphere -- 5.3 A Conformal Map of the Pseudosphere -- 5.4 The Beltrami-Poincaré Half-Plane -- 5.5 Using Optics to Find the Geodesics -- 5.6 The Angle of Parallelism -- 5.7 The Beltrami-Poincaré Disc

• 505

  ▼a  6. Isometries and Complex Numbers -- 6.1 Introduction -- 6.2 Möbius Transformations -- 6.3 The Main Result -- 6.4 Einstein's Spacetime Geometry -- 6.5 Three-Dimensional Hyperbolic Geometry -- 7. Exercises for Act II -- ACT III. Curvature -- 8. Curvature of Plane Curves -- 8.1 Introduction -- 8.2 The Circle of Curvature -- 8.3 Newton's Curvature Formula -- 8.4 Curvature as Rate of Turning -- 8.5 Example: Newton's Tractrix -- 9. Curves in 3-Space -- 10. The Principal Curvatures of a Surface -- 10.1 Euler's Curvature Formula -- 10.2 Proof of Euler's Curvature Formula -- 10.3 Surfaces of Revolution

• 505

  ▼a  11. Geodesics and Geodesic Curvature -- 11.1 Geodesic Curvature and Normal Curvature -- 11.2 Meusnier's Theorem -- 11.3 Geodesics are "Straight" -- 11.4 Intrinsic Measurement of Geodesic Curvature -- 11.5 A Simple Extrinsic Way to Measure Geodesic Curvature -- 11.6 A New Explanation of the Sticky-Tape Construction of Geodesics -- 11.7 Geodesics on Surfaces of Revolution -- 11.7.1 Clairaut's Theorem on the Sphere -- 11.7.2 Kepler's Second Law -- 11.7.3 Newton's Geometrical Demonstration of Kepler's Second Law -- 11.7.4 Dynamical Proof of Clairaut's Theorem

• 505

  ▼a  11.7.5 Application: Geodesics in the Hyperbolic Plane (Revisited) -- 12. The Extrinsic Curvature of a Surface -- 12.1 Introduction -- 12.2 The Spherical Map -- 12.3 Extrinsic Curvature of Surfaces -- 12.4 What Shapes Are Possible? -- 13. Gauss's Theorema Egregium -- 13.1 Introduction -- 13.2 Gauss's Beautiful Theorem (1816) -- 13.3 Gauss's Theorema Egregium (1827) -- 14. The Curvature of a Spike -- 14.1 Introduction -- 14.2 Curvature of a Conical Spike -- 14.3 The Intrinsic and Extrinsic Curvature of a Polyhedral Spike -- 14.4 The Polyhedral Theorema Egregium -- 15. The Shape Operator

• 588

  ▼a  Description based on online resource; title from digital title page (viewed on July 08, 2021).

• 590

  ▼a  Master record variable field(s) change: 072

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  ▼a  Geometry, Differential.

• 650

  ▼a  Differential forms.

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  ▼a  MATHEMATICS / Geometry / Differential
  ▼2  bisacsh

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  ▼a  Electronic books.

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  ▼a  Electronic books.

• 776

  ▼i  Print version:
  ▼a  Needham, Tristan
  ▼t  Visual Differential Geometry and Forms.
  ▼d  Princeton : Princeton University Press,c2021,
  ▼z  9780691203690

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  ▼3  EBSCOhost
  ▼u  https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&db=nlabk&AN=2714027

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  ▼a  YBP Library Services
  ▼b  YANK
  ▼n  301868764

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  ▼a  ProQuest Ebook Central
  ▼b  EBLB
  ▼n  EBL6554358

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  ▼a  EBSCOhost
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  ▼a  eBook

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