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.
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.
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.
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
