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 currently under contract with Princeton University Press. The current versions of the modules for the (future) textbook can be found here

Recent talks

2018: Visualizing homographies: distortions (or the lack thereof) in photos shadows and art, Paideia Connections Talk, Southwestern University

2018: How to Mathematically Immerse Yourself in Art, Texas State University

2018: When Artists Become Mathematicians, Phi Beta Kappa, (En)Lightning Talks Houston

2017: Fractals in Japanese Woodblock Prints, Japan-America Society of Greater Austin Academic Lecture Series

2016: Illustrating Abstract Mathematics Through Perspective Drawing, SU Art History Program's Representations Lecture Series, Southwestern University

2016: Finding the Viewpoint at a Museum: a How-To Guide, Joint Mathematics Meetings, Seattle, WA

2015: How to Mathematically Immerse Yourself in a Work of Art, Infinite Horizons Lecture Series, Kennesaw State University, GA and Mathematics and Statistics Colloquium, Sam Houston State University, TX

minicourses and workshops

2019: upcoming 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, Factoring a homography to analyze projective distortion, accepted.

A. Crannell, M . Frantz, F. Futamura, An (isometric) view on homographies, accepted.

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

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 Horizons22 no. 2, (2014) 10-11. 

media

Southwestern Alum and Math Faculty Win Prizes for Coauthored Paper: Robert Lehr ’15 and Professor of Mathematics Fumiko Futamura receive the Carl B. Allendoerfer Award, 2018

What a Mathematician Says About “Lens Compression” in Photography, 2018

TED-Ed video lesson, The Mathematics of Sidewalk Illusions, 2017

Mathematical Moments: Making Art Work 2016

Scientific American Blog, Roots of Unity: How to Look at Art: A Mathematician's Perspective, 2016

Math in Wonderland: Southwestern professor who sees math in art brings a new dimension to the Semester in London program, 2011

Southwestern University Math Professor Receives $69,432 NSF Grant, 2011

Chicago in Nashville: Feminist artist Judy Chicago’s latest collaborative work takes shape at Vanderbilt, 2006