Tactile surfaces -- feeling
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
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
--movie of surface creation (2Mb)
The wooden surfaces now reside in the "Calculus Pavilion"
in the Museum's Experiment Gallery: