Needham, Chapter 6, Visual Complex Analysis—PDF files with notes, figures, and some answers for exercises

The figures in this list pertain to Visual Complex Analysis (1997) by Tristan Needham. The illustrations pertain to suggested exercises in the text, to exercises at ends of chapters, and to ideas suggested by the text. In a some cases, they are attempts to reproduce figures found in the text. See also the animated demos. Both the figures and demos are plotted with Mathematica 10.

Some answers to exercises are provided without figures. The answers are my own and they are not endorsed by the author of Visual Complex Analysis. The answers in the archives of Vasco are in general more consistent and reliable. I have consulted them frequently in my own studies. Current discussions of the book and the exercises appear on Vasco's forum.

Notes
  • Notes on Chapter 6, pp. 273-292. (PDF)
  • Notes on presentation of spherical geometry and quaterions (PDF)
  • Multiplier as amplitwist (PDF)
  • Projection of inversions in C to Sigma (PDF)
  • Notes and questions on Section III Hyperbolic Geometry, pp. 293-306 (PDF)
  • Notes on transformations in the hyperbolic plane, Comparisons to Chapter 3 (PDF)
  • Notes on reflections in hyperbolic map, figure [32], p. 313 (PDF)
  • Rotations of h-lines in hyperbolic map, figure [32a], p. 318 (PDF, Source code)
  • [Exercise], p. 325, Inversion in hemisphere is reflection of hyperbolic space (PDF)
Exercises
  1. Additivity of Angular Excess E(T) (PDF)
  2. Preliminaries. (PDF) Ex. 2. Inversions in a sphere (PDF)
  3. Projections touching Riemann sphere (PDF)
  4. Rotation on sphere to Möbius transformation (PDF)
  5. Möbius transformations satisfy differential equation (PDF)
  6. Conjugate of Quaternion (i, ii) (PDF)
  7. Quaternion Rotations (PDF)
  8. ---
  9. Klein hemisphere model, pp. 330-331 (PDF)
  10. Map of sphere, p. 331 (PDF)
  11. Hyperbolic radii and circumference, p. 331 (PDF)
  12. Representations of h-lines in Poincare disc and Klein hemisphere, pp. 331,332 (PDF)
  13. (i). Klein model orthogonality of circles and rays, p. 332 (PDF)
  14. (i). Projections, In progress, p. 333 (PDF) (ii-vi). Projections and metrics, p. 333-334 (PDF)
  15. ---
  16. Geodesics on tractrix, p. 334 (PDF)
  17. Curvature and Laplacian, p. 335 (PDF)
  18. Angle of Parallelism of Asymptotes, p. 335 (PDF)
  19. Derive PD Metric from UHP metric, p. 335 (PDF)
  20. Preservation of Metric of PD under Möbius Transformation, p. 335 (PDF)
  21. Möbius transformation of PD with rotation (PDF)
  22. Cross-ratio and Poincaré upper half-plane (PDF)
  23. Alternative metrics on sphere and PD (PDF)
  24. Möbius transformations and fixed points in hyperbolic plane (PDF)
  25. Chain of orthogonal h-lines and asymptotic lines (PDF)
  26. Hyperbolic triangle (PDF)
  27. Hyperbolic space in unit sphere (PDF)
Last modified on May 9, 2020.

My email address has no duplicates, spaces, or special characters except "@". Add "icloud".

# g ! pp && aa l + m * er % nc