Ivars Peterson's MathTrek
November 11, 2003
"I see geometry in everything," mathematician Thomas F. Banchoff of Brown University once remarked, as quoted in Keith Devlin's book Life by the Numbers. "When I walk down the street, I'm always fascinated by some form. I love seeing patterns; I love looking up and looking at windows and ledges and seeing the way different objects fit together, especially if you position yourself in just the right way."
I've spent many years wandering about, camera in hand, trying to capture some of these geometric wondersboth everyday sights and spectacular architectural feats.
In Washington, D.C., the National Gallery of Art's East Building, which opened to the public in 1978, features a facade that teases the eye. Designed by architect I.M. Pei, the building is a festival of vast walls, sharp edges, and surprising shapes. Walls unexpectedly meet at acute and obtuse angles rather than commonplace right angles. Perspectives change dramatically as you walk around the building.
People react viscerally to the building, which was designed to fit on an oddly shaped plot of land. There's one particularly sharp corner that has attracted a lot of attention. Over the years, so many people have felt the urge to touch the corner that the lavender-pink marble has developed a dark stain just below shoulder height where countless hands have deposited their oils.
Slim and graceful, Snelson's Needle Tower delivers a wonderful geometrical surprise when you venture underneath and look up to see a striking starlike pattern.
The photo accompanied a discussion of integration (finding totals by stuffing curves with rectangles). The caption suggested that the nearly rectangular windows of the auditorium's glass front filled the area under the curving roof, "architecturally illustrating the technique by which calculus finds the area under a curve."
And there's a lot more to see when you survey the world around you with a mathematical eye.
Copyright © 2003 by Ivars Peterson
Bergamini, D., and the editors of LIFE. 1963. Mathematics. New York: Time.
Devlin, K. 1998. Life by the Numbers. New York: Wiley.
Peterson, I. 2001. Fragments of Infinity: A Kaleidoscope of Math and Art. New York: Wiley. See http://www.isama.org/book/fragments/.
Thomas F. Banchoff has a Web page at http://www.math.brown.edu/~banchoff/.
Take a virtual tour of the National Gallery of Art's East Building at http://www.nga.gov/collection/eastarch1.htm. Information about I.M. Pei's design can be found at http://www.nga.gov/collection/20th_intro.htm.
Kenneth Snelson has a Web site at http://www.kennethsnelson.net/. Information about Snelson's Needle Tower can be found at http://hirshhorn.si.edu/collection/record.asp?Artist=Snelson&ViewMode=&Record=2.
Information about Thomas Jefferson's Monticello is available at http://www.monticello.org/gallery/index.html. Details of Jeffersonian features at the Rotunda of the University of Virginia can be found at http://www.virginia.edu/uvatours/rotunda/rotundaExplore.html.
Learn more about Edward Durrell Stone's design for the "academic podium" at the State University of New York at Albany at http://www.albany.edu/geosciences/sunyageo.html and http://www.albany.edu/about_the_university/campus_uptown.html.
Comments are welcome. Please send messages to Ivars Peterson at firstname.lastname@example.org.
A collection of Ivars Peterson's early MathTrek articles, updated and illustrated, is now available as the Mathematical Association of America (MAA) book Mathematical Treks: From Surreal Numbers to Magic Circles. See http://www.maa.org/pubs/books/mtr.html.