1. Drawing Humpty Dumpty in
Perspective
Side Topics in Projective Geometry

2. Projective Geometry…
1. is a non-Euclidean geometry based on 8
axioms, in which there are no parallel lines.
2. can be constructed with only a straight edge.
3. was inspired by the development of
Renaissance perspective.

3. Axioms and non-Euclidean geometry
 No parallel lines

4. Axioms and non-Euclidean geometry
Through the Looking Glass
Lewis Carroll
Humpty Dumpty is a
nominalist:
“Universal terms do not refer
to objective existences but are
nothing more than… verbal
utterances.”
-Martin Gardner
Annotated Alice

5. Projective Geometry…
1. Is a non-Euclidean geometry based on 8
axioms, in which there are no parallel lines.
2. can be constructed with only a straight edge.
3. was inspired by the development of
Renaissance perspective.

6. with only a straight-edge…
Harmonic set

7. with only a straight-edge…
Harmonic set

8. with only a straight-edge…
Harmonic set

9. with only a straight-edge…
Harmonic set

10. with only a straight-edge…
Harmonic set

11. with only a straight-edge…
Harmonic set

12. with only a straight-edge…
Harmonic set

13. with only a straight-edge…
Harmonic set: Harmonics in music, C major chord

14. Projective Geometry…
1. is a non-Euclidean geometry based on 8
axioms, in which there are no parallel lines.
2. can be constructed with only a straight edge.
3. was inspired by the development of
Renaissance perspective.

15. Usually math inspires art.
Richard Baker (1866-1937)
Two quadratic surfaces intersecting in a twisted cubic
Henry Moore, Barbara Hepworth,
Head, 1933 Stringed Figure (Curlew) (Version 1), 1956

16. Piero della Francesca,
Flagellation of Christ, 1469
Gérard Desargues (1591-1661)
Desargues’ Theorem
With projective geometry,
art inspired math.

17. Perspective drawing
Tommy Rogers, 2008

18. Perspective drawing
Sean Watson, 2008

19. Perspective drawing
Tommy Rogers, 2008

20. Perspective drawing
Sean Watson, 2008

21. Perspective drawing
Ben Sloan, 2008

22. Harmonic sequence and
Alberti’s construction

23. Harmonic sequence and
Alberti’s construction

24. Harmonic sequence and
Alberti’s construction

25. Harmonic sequence and
Alberti’s construction

26. Harmonic sequence and
Alberti’s construction

27. Harmonic sequence and
Alberti’s construction

28. Harmonic sequence and
Alberti’s construction

29. Harmonic sequence and
Alberti’s construction

30. Harmonic sequence and
Alberti’s construction

31. Harmonic sequence and
Alberti’s construction

32. Harmonic sequence and
Alberti’s construction

33. Harmonic sequence and
Alberti’s construction

34. Harmonic sequence and
Alberti’s construction
Raphael, Marriage of the Virgin (1504)

35. Harmonic sequence and
Alberti’s construction
Leon Battista Alberti,
De pictura and Elementa picture (1518)

36. References
• H.S.M. Coxeter, Projective Geometry
• Lewis Carroll, Through the Looking Glass
• Lewis Carroll, Symbolic Logic
• Martin Gardner, The Annotated Alice
• Sherry L. Ackerman , Behind the Looking Glass
• Angela Vierling, Mathematical Models and
Modern Art
• Annalisa Crannell, Marc Frantz, Viewpoints:
Mathematical Perspective and Fractal Geometry