| LDR | | 05023cmm u2200565Ki 4500 |
| 001 | | 000000321648 |
| 003 | | OCoLC |
| 005 | | 20230613111325 |
| 006 | | m d |
| 007 | | cr cnu---unuuu |
| 008 | | 210619s2021 nju o 000 0 eng d |
| 020 | |
▼a 0691219893
▼q electronic book |
| 020 | |
▼a 9780691219899
▼q (electronic bk.) |
| 035 | |
▼a 2714027
▼b (N$T) |
| 035 | |
▼a (OCoLC)1257077763 |
| 037 | |
▼a 22573/ctv1cksvx4
▼b JSTOR |
| 040 | |
▼a EBLCP
▼b eng
▼e rda
▼c EBLCP
▼d YDX
▼d OCLCO
▼d N$T
▼d EBLCP
▼d JSTOR
▼d 248032 |
| 049 | |
▼a MAIN |
| 050 | 4 |
▼a QA641
▼b .N44 2021 |
| 072 | 7 |
▼a MAT
▼x 012030
▼2 bisacsh |
| 072 | 7 |
▼a MAT
▼x 038000
▼2 bisacsh |
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▼a MAT
▼x 005000
▼2 bisacsh |
| 072 | 7 |
▼a SCI
▼x 061000
▼2 bisacsh |
| 082 | 04 |
▼a 516.3/6
▼2 23 |
| 100 | 1 |
▼a Needham, Tristan,
▼e author. |
| 245 | 10 |
▼a Visual Differential Geometry and Forms :
▼b A Mathematical Drama in Five Acts /
▼c Tristan Needham.
▼h [electronic resource] |
| 260 | |
▼a Princeton :
▼b Princeton University Press,
▼c [2021] |
| 300 | |
▼a 1 online resource (531 p.) |
| 336 | |
▼a text
▼b txt
▼2 rdacontent |
| 337 | |
▼a computer
▼b c
▼2 rdamedia |
| 338 | |
▼a online resource
▼b cr
▼2 rdacarrier |
| 500 | |
▼a 15.1 Directional Derivatives. |
| 505 | 0 |
▼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 | 8 |
▼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-Poincare? Half-Plane -- 5.5 Using Optics to Find the Geodesics -- 5.6 The Angle of Parallelism -- 5.7 The Beltrami-Poincare? Disc |
| 505 | 8 |
▼a 6. Isometries and Complex Numbers -- 6.1 Introduction -- 6.2 Mo?bius 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 | 8 |
▼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 | 8 |
▼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 |
| 650 | 0 |
▼a Geometry, Differential. |
| 650 | 0 |
▼a Differential forms. |
| 650 | 7 |
▼a MATHEMATICS / Geometry / Differential
▼2 bisacsh |
| 655 | 0 |
▼a Electronic books. |
| 655 | 4 |
▼a Electronic books. |
| 776 | 08 |
▼i Print version:
▼a Needham, Tristan
▼t Visual Differential Geometry and Forms
▼d Princeton : Princeton University Press,c2021
▼z 9780691203690 |
| 856 | 40 |
▼3 EBSCOhost
▼u https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&db=nlabk&AN=2714027 |
| 938 | |
▼a YBP Library Services
▼b YANK
▼n 301868764 |
| 938 | |
▼a ProQuest Ebook Central
▼b EBLB
▼n EBL6554358 |
| 938 | |
▼a EBSCOhost
▼b EBSC
▼n 2714027 |
| 990 | |
▼a 관리자 |
| 994 | |
▼a 92
▼b N$T |