drawing humpty dumpty in perspective
TRANSCRIPT
Drawing Humpty Dumpty in Perspective
Side Topics in Projective Geometry
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.
Axioms and non-Euclidean geometry
No parallel lines
Axioms and non-Euclidean geometry
Through the Looking GlassLewis 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
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.
with only a straight-edge…
Harmonic set
with only a straight-edge…
Harmonic set
with only a straight-edge…
Harmonic set
with only a straight-edge…
Harmonic set
with only a straight-edge…
Harmonic set
with only a straight-edge…
Harmonic set
with only a straight-edge…
Harmonic set
with only a straight-edge…
Harmonic set: Harmonics in music, C major chord
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.
Usually math inspires art.
Barbara Hepworth,Stringed Figure (Curlew) (Version 1), 1956
Richard Baker (1866-1937) Two quadratic surfaces intersecting in a twisted cubic
Henry Moore,Head, 1933
With projective geometry, art inspired math.
Gérard Desargues (1591-1661) Desargues’ Theorem
Piero della Francesca, Flagellation of Christ, 1469
Perspective drawing
Tommy Rogers, 2008
Perspective drawing
Sean Watson, 2008
Perspective drawing
Tommy Rogers, 2008
Perspective drawing
Sean Watson, 2008
Perspective drawing
Ben Sloan, 2008
Harmonic sequence and Alberti’s construction
Harmonic sequence and Alberti’s construction
Harmonic sequence and Alberti’s construction
Harmonic sequence and Alberti’s construction
Harmonic sequence and Alberti’s construction
Harmonic sequence and Alberti’s construction
Harmonic sequence and Alberti’s construction
Harmonic sequence and Alberti’s construction
Harmonic sequence and Alberti’s construction
Harmonic sequence and Alberti’s construction
Harmonic sequence and Alberti’s construction
Harmonic sequence and Alberti’s construction
Harmonic sequence and Alberti’s construction
Raphael, Marriage of the Virgin (1504)
Harmonic sequence and Alberti’s construction
Leon Battista Alberti, De pictura and Elementa picture (1518)
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