Geometry 2012

Students from the Fall 2012 Geometry class go to the Blanton Museum in Austin, TX to analyze works in perspective.

Geometry 2012

Students from the Fall 2012 Geometry class set up a demonstration of Desargues' theorem.

MAA Minicourse 2013

Participants of our 2013 MAA Minicourse collaborate to learn projective geometry through perspective drawing.

MAA Minicourse 2013

Fumiko Futamura vogues while presenting at the 2013 Joint Math Meetings MAA Minicourse. Photo by Laura McHugh.

Math Concepts 2013

Students from the Spring 2013 Math Concepts class proudly exhibit their mathematical works of art. More pics below.

Infinite Horizons lecture 2015

I gave a talk at Kennesaw State University's Infinite Horizons lecture series on How to mathematically immerse yourself in a work of art in April 2015.

Infinite Horizons lecture 2015

Students at Kennesaw State learn how to find the viewpoint for perspective drawings.

Public lecture 2017

Fractals in Japanese Woodblock Prints lecture for Japan-America Society for Greater Austin, 2017

Mathematical Mystery Tour 2013

Students in Mathematical Concepts, Spring 2013 displayed their mathematical artwork in an exhibit in the Smith Library.

Exhibit opening, April 15, 2013

anamorphic painting

making a PVC flute using math

pinhole camera

Stellated platonic solid origami, cylinder anamorphisms

Sierpinski's tetrahedron

$dragon curve fractal quilt$

dragon curve fractal quilt

$Platonic solid snowman with fractal arms and frieze patterned scarf and n-fold symmetry snowflakes$

Platonic solid snowman with fractal arms and frieze patterned scarf and n-fold symmetry snowflakes

$drawings using wallpaper patterns, fractals and symmetry$

drawings using wallpaper patterns, fractals and symmetry

a maze in perspective

shadow projections

frieze pattern card weavings and friendship bracelets

lego impossible staircase (Penrose stairs)

$video of a fly-through inside 3D fractals$

video of a fly-through inside 3D fractals

hyperbolic crochet experiments

hyperbolic coral reef

$dragon curve fractal quilt$

$Platonic solid snowman with fractal arms and frieze patterned scarf and n-fold symmetry snowflakes$ $drawings using wallpaper patterns, fractals and symmetry$ a maze in perspective

$video of a fly-through inside 3D fractals$ hyperbolic crochet experiments

The textbook: Perspective and projective geometry

Perspective and Projective Geometry is a textbook using an inquiry-based approach designed for sophomore- and junior-level mathematics majors, developed by Annalisa Crannell, Marc Frantz and myself. The book is now published by Princeton University Press and can be found here.

minicourses and workshops

2024: MathFest workshop: Geometric puzzles and brain teasers in perspective art, presented jointly with Annalisa Crannell and Marc Frantz, MAA MathFest, Indianapolis.

2023: MAA minicourse: visualizing projective geometry through photographs and perspective drawings, presented jointly with Annalisa Crannell, MAA MathFest, Tampa.

2023: AMS Professional Enhancement Program (PEP): visualizing projective geometry through photographs and perspective drawings, presented jointly with Annalisa Crannell, Joint Mathematics Meetings, Boston.

2021: MAA Virtual Programming minicourse: gaining perspective on geometry: IBL activities that use art in projective geometry, presented jointly with Annalisa Crannell and Marc Frantz

2019: MAA minicourse #6: visualizing projective geometry through photographs and perspective drawings, presented jointly with Annalisa Crannell and Marc Frantz, MAA MathFest, Cincinnati.

2018: MAA minicourse #4: visualizing projective geometry through photographs and perspective drawings, presented jointly with Annalisa Crannell and Marc Frantz, MAA MathFest, Denver.

2018: Learning station on hyperbolic crochet coral reefs, Hot Science, Cool Talks, Environmental Science Institute, UT Austin.

2017: MAA minicourse #4: visualizing projective geometry through photographs and perspective drawings, to be presented jointly with Annalisa Crannell and Marc Frantz, MAA MathFest, Chicago.

2016: MAA minicourse #2: visualizing projective geometry through photographs and perspective drawings, presented jointly with Annalisa Crannell and Marc Frantz, MAA MathFest, Columbus.

2016: learning session: drawing shadows with Desargues, Operation: Math Girls (OMG) conference, Sam Houston State University

2015: seminar teaching workshop: seeing the abstract: visual thinking for engaged learning, funded by Dr. Lawrence Musgrove’s Visual Thinking for Engaged Learning grant funded by the Presidential Innovation Grants Initiative

2014: MAA minicourse #14: visualizing projective geometry through photographs and perspective drawings, presented jointly with Annalisa Crannell and Marc Frantz, Joint Mathematics Meetings, Baltimore

2013: MAA minicourse #5: visualizing projective geometry through photographs and perspective drawings, presented jointly with Annalisa Crannell and Marc Frantz, Joint Mathematics Meetings, San Diego (pic)

PUBLICATIONS on math & Art

A. Crannell, M. Frantz, F. Futamura, Perspective and Projective Geometry, Princeton University Press, 2019.

A. Crannell, M . Frantz, F. Futamura, An (isometric) view on homographies, J Geometry and Graphics, 23 no. 1 (2019) 65-83.

A. Crannell, M. Frantz, F. Futamura, Factoring a homography to analyze projective distortion, J Math Imaging Vis, 61 no. 7 (2019) 967-989.

F. Futamura, R. Lehr, A new perspective on finding the viewpoint, Mathematics Magazine, 90 no. 4 (2017) pp. 267-277.

Student research with Robert Lehr, class of 2015

Recipient for the 2018 MAA Carl B. Allendoerfer Award for expository excellence of papers published in Mathematics Magazine in 2017.

A. Crannell, M. Frantz, F. Futamura, The Image of a Square, Amer. Math. Monthly, 124 no. 2, (2017) pp. 99-115.

A. Crannell, M. Frantz, F. Futamura, The Cross ratio as a parameter for Dürer's solid (Party game for a 500th anniversary) J. Math. Arts, 8 (2014), no. 3-4, 111--119. (on the shortlist of four papers considered for the 2016 JMA Outstanding Paper Award)

A. Crannell, M. Frantz, F. Futamura, Dürer: Disguise, Distance, Disagreements, and Diagonals! Math Horizons, 22 no. 2, (2014) 10-11.

Reprinted in: The Best Writing on Mathematics 2015, Princeton University Press, 2015.