drawing humpty dumpty in perspective

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