Tactile surfaces -- feeling the limit:

Tactile Surface

In an entirely different approach to illustrating the limit concept, from the highly visual "archimedes' circle," I employed my homemade NC router to carve mathematical surfaces in hardwood. I had been experimenting with these wooden surfaces for some time, and as I was thinking about how to achieve the "perfect" surface which is exactly described by an equation, I soon realized that I needed to increase the number of rows, and decrease the size of my cutting bit. To achieve a perfect result would require an infinite number of passes, and an infinitely small bit. This is exactly what calculus is able to do.

For a first test, I used z = 1/2 cosxcosy , x from 0 to 2Pi, y from 0 to 2Pi. I milled five surfaces, using 32, 64, 128, and 256 passes-- on the fifth I "cheated" and used sand paper to "reach the limit."

Limit --movie of surface creation (2Mb)

The wooden surfaces now reside in the "Calculus Pavilion" in the Museum's Experiment Gallery: