math 121 (day 7)rhammack/math121/lectures/math121lecture7.pdfsidewalk drawings by julian beever....

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MATH 121 (Day 7) The Anamorphic Image Richard Hammack: www.people.vcu.edu/rhammack/Math121/

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Page 1: MATH 121 (Day 7)rhammack/Math121/Lectures/MATH121Lecture7.pdfSidewalk Drawings by Julian Beever. Floor Drawings by Kurt Wenner. Vancouver, British Columbia, 2010. Created Date: 9/12/2013

MATH 121

(Day 7)

The Anamorphic Image

Richard Hammack:

www.people.vcu.edu/∼rhammack/Math121/

Page 2: MATH 121 (Day 7)rhammack/Math121/Lectures/MATH121Lecture7.pdfSidewalk Drawings by Julian Beever. Floor Drawings by Kurt Wenner. Vancouver, British Columbia, 2010. Created Date: 9/12/2013

Thomas Eakins, 1872

Page 3: MATH 121 (Day 7)rhammack/Math121/Lectures/MATH121Lecture7.pdfSidewalk Drawings by Julian Beever. Floor Drawings by Kurt Wenner. Vancouver, British Columbia, 2010. Created Date: 9/12/2013

Thomas Eakins, 1872

Page 4: MATH 121 (Day 7)rhammack/Math121/Lectures/MATH121Lecture7.pdfSidewalk Drawings by Julian Beever. Floor Drawings by Kurt Wenner. Vancouver, British Columbia, 2010. Created Date: 9/12/2013

David Hockney, acrylic on canvas, 1971

Page 5: MATH 121 (Day 7)rhammack/Math121/Lectures/MATH121Lecture7.pdfSidewalk Drawings by Julian Beever. Floor Drawings by Kurt Wenner. Vancouver, British Columbia, 2010. Created Date: 9/12/2013

David Hockney, acrylic on canvas, 1971

Page 6: MATH 121 (Day 7)rhammack/Math121/Lectures/MATH121Lecture7.pdfSidewalk Drawings by Julian Beever. Floor Drawings by Kurt Wenner. Vancouver, British Columbia, 2010. Created Date: 9/12/2013

David Hockney, etching and aquatint, 1974

Page 7: MATH 121 (Day 7)rhammack/Math121/Lectures/MATH121Lecture7.pdfSidewalk Drawings by Julian Beever. Floor Drawings by Kurt Wenner. Vancouver, British Columbia, 2010. Created Date: 9/12/2013

David Hockney

Page 8: MATH 121 (Day 7)rhammack/Math121/Lectures/MATH121Lecture7.pdfSidewalk Drawings by Julian Beever. Floor Drawings by Kurt Wenner. Vancouver, British Columbia, 2010. Created Date: 9/12/2013

William Hogarth, c. 1740

M.C. Escher, lithograph, 1955

Page 9: MATH 121 (Day 7)rhammack/Math121/Lectures/MATH121Lecture7.pdfSidewalk Drawings by Julian Beever. Floor Drawings by Kurt Wenner. Vancouver, British Columbia, 2010. Created Date: 9/12/2013

William Hogarth, c. 1740 M.C. Escher, lithograph, 1955

Page 10: MATH 121 (Day 7)rhammack/Math121/Lectures/MATH121Lecture7.pdfSidewalk Drawings by Julian Beever. Floor Drawings by Kurt Wenner. Vancouver, British Columbia, 2010. Created Date: 9/12/2013

Hans Holbein the Younger, The Ambassadors, 1533

Camera obscura

Page 11: MATH 121 (Day 7)rhammack/Math121/Lectures/MATH121Lecture7.pdfSidewalk Drawings by Julian Beever. Floor Drawings by Kurt Wenner. Vancouver, British Columbia, 2010. Created Date: 9/12/2013

Hans Holbein the Younger, The Ambassadors, 1533

Camera obscura

Page 12: MATH 121 (Day 7)rhammack/Math121/Lectures/MATH121Lecture7.pdfSidewalk Drawings by Julian Beever. Floor Drawings by Kurt Wenner. Vancouver, British Columbia, 2010. Created Date: 9/12/2013

Hans Holbein the Younger, The Ambassadors, 1533

Anamorphosis

Page 13: MATH 121 (Day 7)rhammack/Math121/Lectures/MATH121Lecture7.pdfSidewalk Drawings by Julian Beever. Floor Drawings by Kurt Wenner. Vancouver, British Columbia, 2010. Created Date: 9/12/2013

Hans Holbein the Younger, The Ambassadors, 1533

Anamorphosis

Page 14: MATH 121 (Day 7)rhammack/Math121/Lectures/MATH121Lecture7.pdfSidewalk Drawings by Julian Beever. Floor Drawings by Kurt Wenner. Vancouver, British Columbia, 2010. Created Date: 9/12/2013

How to make an anamorphosis

A

B C

D A′

B′

V

D′

C ′

Page 15: MATH 121 (Day 7)rhammack/Math121/Lectures/MATH121Lecture7.pdfSidewalk Drawings by Julian Beever. Floor Drawings by Kurt Wenner. Vancouver, British Columbia, 2010. Created Date: 9/12/2013

How to make an anamorphosis

A

B C

D

A′

B′

V

D′

C ′

Page 16: MATH 121 (Day 7)rhammack/Math121/Lectures/MATH121Lecture7.pdfSidewalk Drawings by Julian Beever. Floor Drawings by Kurt Wenner. Vancouver, British Columbia, 2010. Created Date: 9/12/2013

How to make an anamorphosis

A

B C

D A′

B′

V

D′

C ′

Page 17: MATH 121 (Day 7)rhammack/Math121/Lectures/MATH121Lecture7.pdfSidewalk Drawings by Julian Beever. Floor Drawings by Kurt Wenner. Vancouver, British Columbia, 2010. Created Date: 9/12/2013

How to make an anamorphosis

A

B C

D A′

B′

V

D′

C ′

Page 18: MATH 121 (Day 7)rhammack/Math121/Lectures/MATH121Lecture7.pdfSidewalk Drawings by Julian Beever. Floor Drawings by Kurt Wenner. Vancouver, British Columbia, 2010. Created Date: 9/12/2013

How to make an anamorphosis

A

B C

D A′

B′

V

D′

C ′

Page 19: MATH 121 (Day 7)rhammack/Math121/Lectures/MATH121Lecture7.pdfSidewalk Drawings by Julian Beever. Floor Drawings by Kurt Wenner. Vancouver, British Columbia, 2010. Created Date: 9/12/2013

How to make an anamorphosis

A

B C

D A′

B′

V

D′

C ′

Page 20: MATH 121 (Day 7)rhammack/Math121/Lectures/MATH121Lecture7.pdfSidewalk Drawings by Julian Beever. Floor Drawings by Kurt Wenner. Vancouver, British Columbia, 2010. Created Date: 9/12/2013

How to make an anamorphosis

A

B C

D A′

B′

V

D′

C ′

Page 21: MATH 121 (Day 7)rhammack/Math121/Lectures/MATH121Lecture7.pdfSidewalk Drawings by Julian Beever. Floor Drawings by Kurt Wenner. Vancouver, British Columbia, 2010. Created Date: 9/12/2013

How to make an anamorphosis

A

B C

D A′

B′

V

D′

C ′

Page 22: MATH 121 (Day 7)rhammack/Math121/Lectures/MATH121Lecture7.pdfSidewalk Drawings by Julian Beever. Floor Drawings by Kurt Wenner. Vancouver, British Columbia, 2010. Created Date: 9/12/2013

How to make an anamorphosis

A

B C

D A′

B′

V

D′

C ′

Page 23: MATH 121 (Day 7)rhammack/Math121/Lectures/MATH121Lecture7.pdfSidewalk Drawings by Julian Beever. Floor Drawings by Kurt Wenner. Vancouver, British Columbia, 2010. Created Date: 9/12/2013

How to make an anamorphosis

A

B C

D A′

B′

V

D′

C ′

Page 24: MATH 121 (Day 7)rhammack/Math121/Lectures/MATH121Lecture7.pdfSidewalk Drawings by Julian Beever. Floor Drawings by Kurt Wenner. Vancouver, British Columbia, 2010. Created Date: 9/12/2013

How to make an anamorphosis

A

B C

D A′

B′

V

D′

C ′

Page 25: MATH 121 (Day 7)rhammack/Math121/Lectures/MATH121Lecture7.pdfSidewalk Drawings by Julian Beever. Floor Drawings by Kurt Wenner. Vancouver, British Columbia, 2010. Created Date: 9/12/2013

How to make an anamorphosis

A

B C

D A′

B′

V

D′

C ′

Page 26: MATH 121 (Day 7)rhammack/Math121/Lectures/MATH121Lecture7.pdfSidewalk Drawings by Julian Beever. Floor Drawings by Kurt Wenner. Vancouver, British Columbia, 2010. Created Date: 9/12/2013

How to make an anamorphosis

A

B C

D A′

B′

V

D′

C ′

Page 27: MATH 121 (Day 7)rhammack/Math121/Lectures/MATH121Lecture7.pdfSidewalk Drawings by Julian Beever. Floor Drawings by Kurt Wenner. Vancouver, British Columbia, 2010. Created Date: 9/12/2013

How to make an anamorphosis

A

B C

D A′

B′

V

D′

C ′

Page 28: MATH 121 (Day 7)rhammack/Math121/Lectures/MATH121Lecture7.pdfSidewalk Drawings by Julian Beever. Floor Drawings by Kurt Wenner. Vancouver, British Columbia, 2010. Created Date: 9/12/2013

How to make an anamorphosis

A

B C

D A′

B′

V

D′

C ′

Page 29: MATH 121 (Day 7)rhammack/Math121/Lectures/MATH121Lecture7.pdfSidewalk Drawings by Julian Beever. Floor Drawings by Kurt Wenner. Vancouver, British Columbia, 2010. Created Date: 9/12/2013

How to make an anamorphosis

A

B C

D A′

B′

V

D′

C ′

Page 30: MATH 121 (Day 7)rhammack/Math121/Lectures/MATH121Lecture7.pdfSidewalk Drawings by Julian Beever. Floor Drawings by Kurt Wenner. Vancouver, British Columbia, 2010. Created Date: 9/12/2013

Leonardo da Vinci, c. 1505

Page 31: MATH 121 (Day 7)rhammack/Math121/Lectures/MATH121Lecture7.pdfSidewalk Drawings by Julian Beever. Floor Drawings by Kurt Wenner. Vancouver, British Columbia, 2010. Created Date: 9/12/2013

Erhard Schon, c.1531-4

Page 32: MATH 121 (Day 7)rhammack/Math121/Lectures/MATH121Lecture7.pdfSidewalk Drawings by Julian Beever. Floor Drawings by Kurt Wenner. Vancouver, British Columbia, 2010. Created Date: 9/12/2013

Guillaume Scrots, 1546King Edward VI

Page 33: MATH 121 (Day 7)rhammack/Math121/Lectures/MATH121Lecture7.pdfSidewalk Drawings by Julian Beever. Floor Drawings by Kurt Wenner. Vancouver, British Columbia, 2010. Created Date: 9/12/2013
Page 34: MATH 121 (Day 7)rhammack/Math121/Lectures/MATH121Lecture7.pdfSidewalk Drawings by Julian Beever. Floor Drawings by Kurt Wenner. Vancouver, British Columbia, 2010. Created Date: 9/12/2013

Istvan Orosz (1997)

Page 35: MATH 121 (Day 7)rhammack/Math121/Lectures/MATH121Lecture7.pdfSidewalk Drawings by Julian Beever. Floor Drawings by Kurt Wenner. Vancouver, British Columbia, 2010. Created Date: 9/12/2013

Istvan Orosz (1997)

Page 36: MATH 121 (Day 7)rhammack/Math121/Lectures/MATH121Lecture7.pdfSidewalk Drawings by Julian Beever. Floor Drawings by Kurt Wenner. Vancouver, British Columbia, 2010. Created Date: 9/12/2013

Istvan Orosz (1997)

Page 37: MATH 121 (Day 7)rhammack/Math121/Lectures/MATH121Lecture7.pdfSidewalk Drawings by Julian Beever. Floor Drawings by Kurt Wenner. Vancouver, British Columbia, 2010. Created Date: 9/12/2013

Istvan Orosz (1981)

Page 38: MATH 121 (Day 7)rhammack/Math121/Lectures/MATH121Lecture7.pdfSidewalk Drawings by Julian Beever. Floor Drawings by Kurt Wenner. Vancouver, British Columbia, 2010. Created Date: 9/12/2013

Istvan Orosz (1981)

Page 39: MATH 121 (Day 7)rhammack/Math121/Lectures/MATH121Lecture7.pdfSidewalk Drawings by Julian Beever. Floor Drawings by Kurt Wenner. Vancouver, British Columbia, 2010. Created Date: 9/12/2013

Chuck Close, Anamorphic Self Portrait, 2007

Page 40: MATH 121 (Day 7)rhammack/Math121/Lectures/MATH121Lecture7.pdfSidewalk Drawings by Julian Beever. Floor Drawings by Kurt Wenner. Vancouver, British Columbia, 2010. Created Date: 9/12/2013
Page 41: MATH 121 (Day 7)rhammack/Math121/Lectures/MATH121Lecture7.pdfSidewalk Drawings by Julian Beever. Floor Drawings by Kurt Wenner. Vancouver, British Columbia, 2010. Created Date: 9/12/2013
Page 42: MATH 121 (Day 7)rhammack/Math121/Lectures/MATH121Lecture7.pdfSidewalk Drawings by Julian Beever. Floor Drawings by Kurt Wenner. Vancouver, British Columbia, 2010. Created Date: 9/12/2013

HOAXHOAX

HOAXHOAX

Page 43: MATH 121 (Day 7)rhammack/Math121/Lectures/MATH121Lecture7.pdfSidewalk Drawings by Julian Beever. Floor Drawings by Kurt Wenner. Vancouver, British Columbia, 2010. Created Date: 9/12/2013

HOAXHOAX

HOAXHOAX

Page 44: MATH 121 (Day 7)rhammack/Math121/Lectures/MATH121Lecture7.pdfSidewalk Drawings by Julian Beever. Floor Drawings by Kurt Wenner. Vancouver, British Columbia, 2010. Created Date: 9/12/2013

HOAXHOAX

HOAXHOAX

Page 45: MATH 121 (Day 7)rhammack/Math121/Lectures/MATH121Lecture7.pdfSidewalk Drawings by Julian Beever. Floor Drawings by Kurt Wenner. Vancouver, British Columbia, 2010. Created Date: 9/12/2013

HOAXHOAX

HOAXHOAX

Page 46: MATH 121 (Day 7)rhammack/Math121/Lectures/MATH121Lecture7.pdfSidewalk Drawings by Julian Beever. Floor Drawings by Kurt Wenner. Vancouver, British Columbia, 2010. Created Date: 9/12/2013

HOAX

HOAX

HOAXHOAX

Page 47: MATH 121 (Day 7)rhammack/Math121/Lectures/MATH121Lecture7.pdfSidewalk Drawings by Julian Beever. Floor Drawings by Kurt Wenner. Vancouver, British Columbia, 2010. Created Date: 9/12/2013

HOAXHOAX

HOAXHOAX

Page 48: MATH 121 (Day 7)rhammack/Math121/Lectures/MATH121Lecture7.pdfSidewalk Drawings by Julian Beever. Floor Drawings by Kurt Wenner. Vancouver, British Columbia, 2010. Created Date: 9/12/2013

HOAXHOAX

HOAX

HOAX

Page 49: MATH 121 (Day 7)rhammack/Math121/Lectures/MATH121Lecture7.pdfSidewalk Drawings by Julian Beever. Floor Drawings by Kurt Wenner. Vancouver, British Columbia, 2010. Created Date: 9/12/2013

HOAXHOAX

HOAXHOAX

Page 50: MATH 121 (Day 7)rhammack/Math121/Lectures/MATH121Lecture7.pdfSidewalk Drawings by Julian Beever. Floor Drawings by Kurt Wenner. Vancouver, British Columbia, 2010. Created Date: 9/12/2013

Sidewalk Drawings by Julian Beever

Page 51: MATH 121 (Day 7)rhammack/Math121/Lectures/MATH121Lecture7.pdfSidewalk Drawings by Julian Beever. Floor Drawings by Kurt Wenner. Vancouver, British Columbia, 2010. Created Date: 9/12/2013
Page 52: MATH 121 (Day 7)rhammack/Math121/Lectures/MATH121Lecture7.pdfSidewalk Drawings by Julian Beever. Floor Drawings by Kurt Wenner. Vancouver, British Columbia, 2010. Created Date: 9/12/2013
Page 53: MATH 121 (Day 7)rhammack/Math121/Lectures/MATH121Lecture7.pdfSidewalk Drawings by Julian Beever. Floor Drawings by Kurt Wenner. Vancouver, British Columbia, 2010. Created Date: 9/12/2013
Page 54: MATH 121 (Day 7)rhammack/Math121/Lectures/MATH121Lecture7.pdfSidewalk Drawings by Julian Beever. Floor Drawings by Kurt Wenner. Vancouver, British Columbia, 2010. Created Date: 9/12/2013
Page 55: MATH 121 (Day 7)rhammack/Math121/Lectures/MATH121Lecture7.pdfSidewalk Drawings by Julian Beever. Floor Drawings by Kurt Wenner. Vancouver, British Columbia, 2010. Created Date: 9/12/2013
Page 56: MATH 121 (Day 7)rhammack/Math121/Lectures/MATH121Lecture7.pdfSidewalk Drawings by Julian Beever. Floor Drawings by Kurt Wenner. Vancouver, British Columbia, 2010. Created Date: 9/12/2013
Page 57: MATH 121 (Day 7)rhammack/Math121/Lectures/MATH121Lecture7.pdfSidewalk Drawings by Julian Beever. Floor Drawings by Kurt Wenner. Vancouver, British Columbia, 2010. Created Date: 9/12/2013
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Page 59: MATH 121 (Day 7)rhammack/Math121/Lectures/MATH121Lecture7.pdfSidewalk Drawings by Julian Beever. Floor Drawings by Kurt Wenner. Vancouver, British Columbia, 2010. Created Date: 9/12/2013
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Page 68: MATH 121 (Day 7)rhammack/Math121/Lectures/MATH121Lecture7.pdfSidewalk Drawings by Julian Beever. Floor Drawings by Kurt Wenner. Vancouver, British Columbia, 2010. Created Date: 9/12/2013

Floor Drawings by Kurt Wenner

Page 69: MATH 121 (Day 7)rhammack/Math121/Lectures/MATH121Lecture7.pdfSidewalk Drawings by Julian Beever. Floor Drawings by Kurt Wenner. Vancouver, British Columbia, 2010. Created Date: 9/12/2013
Page 70: MATH 121 (Day 7)rhammack/Math121/Lectures/MATH121Lecture7.pdfSidewalk Drawings by Julian Beever. Floor Drawings by Kurt Wenner. Vancouver, British Columbia, 2010. Created Date: 9/12/2013
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Vancouver, British Columbia, 2010

Page 75: MATH 121 (Day 7)rhammack/Math121/Lectures/MATH121Lecture7.pdfSidewalk Drawings by Julian Beever. Floor Drawings by Kurt Wenner. Vancouver, British Columbia, 2010. Created Date: 9/12/2013