Needham, Chapter 3, 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. The figures are plotted with Mathematica 12.

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.

Exercises
  1. Prove inversion in circle w. three constructions (PDF)
  2. Peaucellier's linkage (PDF), animation (open file in browser) (GIF (918 KB)
  3. Second intersection point of three orthogonal spheres (PDF)
  4. Antipodes and inversions on Riemann sphere (PDF)
  5. Projections from C plane to Sigma and back (PDF)
  6. Inversion in unit circle induces reflection of Riemann sphere in C-plane (PDF)
  7. Images of concentric circles under z --> (1/z) (PDF)
  8. Penrose alternative to stereographic projection (PDF)
  9. Ptolemy's addition formulae (PDF)
  10. Inverse points of any non-intersecting, non-concentric circles (PDF)
  11. Building Mobius transformation to two concentric circles from two inversions (PDF)
  12. Chain of touching circles under Mobius transformation (PDF)
  13. Chain of touching spheres under Mobius transformation
    1. Necklace of touching spheres on table top (PDF)
    2. Necklace of touching spheres of different sizes (PDF)
  14. Preservation of the cross-ratio with moving perspective (PDF)
  15. Preservation of the cross-ratio on a circle (PDF)
  16. Cross-ratios as Mobius transformations (PDF)
  17. Mobius transformation from orthogonal circle to unit circle (PDF)
  18. Curvature of circle obtained by Mobius transformation of real line (PDF)
  19. Concentric and isometric circles under Mobius transformation

    (i-ii) (PDF)

    (iii) (PDF)

  20. The most general Mobius transformation of the unit disc to itself (PDF)
  21. The Mobius transformation that is the most general rotation of the Riemann sphere (PDF)
  22. Hyperbola maps to lemniscate under complex inversion (PDF)
  23. Complex inversion is involutory and therefore elliptic (PDF)
  24. Most general mapping from UHP to unit disc (PDF)
  25. Most general mapping from UHP to UHP (PDF)
  26. Most general mapping from the unit disc to the unit disc (PDF)
  27. Validating criteria for elliptic, parabolic, and hyperbolic MTs (p. 180) (PDF)
Notes

  1. Notes and [Exercises] in text (PDF)

Last modified on October 30, 2021.

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

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