Walls, Windows, and Riemann Sums

Many years ago, while I was in high school, I got my first broad view of mathematics from a beautifully illustrated book in the LIFE Science Library. One photograph from this book that has remained lodged in my mind is of the Kresge Auditorium at the Massachusetts Institute of Technology.

Kresge Auditorium (designed by Eero Saarinen), Massachusetts Institute of Technology, Cambridge, Mass.

The photo accompanies a discussion of integration (finding totals by stuffing areas bounded by curves with rectangles). The caption suggests that the nearly rectangular windows of the auditorium's glass front fills the area under the curving roof, "architecturally illustrating the technique by which calculus finds the area under a curve."

Technically, the method of using rectangles to approximate the total area under a curve is known as a Riemann sum, named for mathematician Bernhard Riemann (1826-1866).

Monona Convention Center (designed by Frank Lloyd Wright), Madison, Wisconsin.

I still can't look at a wall without, at some point, thinking of it as an integral (or Riemann sum), filling in the area between the ground (axis) and the curve defined by the roof.

Memorial Center (Mini-Dome), East Tennessee State University, Johnson City.

Reference:

Bergamini, D., and the editors of LIFE. 1963. Mathematics. Time Books.

Photos by I. Peterson