I have always been a person of many interests. But from early childhood, throughout my academic life and subsequent professional career, two pursuits have decidedly and consistently been foremost among them: primarily, music (violin performance, study, and teaching in particular); and secondarily, mathematics.
For quite a number of years, my interest in math found an outlet in a related field: computer programming. I have owned two Commodore computers, which, unlike today’s PCs, Macs, iPhones, etc., provided a platform that made writing and running programs (code) an easy and natural process—at least for users like me who knew the BASIC computer language!
At some point I ran across a book with some prewritten BASIC programs and purchased it. One program that particularly struck my fancy was called CURVE: it allowed one to input a set of ordered pairs of coordinates, and would then return coefficients for each term of the polynomial of best fit of whatever degree the user specified.
So I wondered what polynomial function might have a graph that looked like a violin! A function, per se, wouldn’t do it, of course, but by laying the violin on its side, I could generate a graph of half of it, then take advantage of the instrument’s inherent bilateral symmetry and reflect the generated points to “close the deal.”
But how to get the individual points? A visual artist could simply draw the outline of a violin on a sheet of graph paper. But my artistry (if any) was musical. I had to be resourceful! So I looked around and found that I had a little plastic pencil sharpener, a few inches long, in the shape of a violin. (Never mind that it was purple.) I proceeded to place the sharpener sideways on a sheet of graph paper and trace the outline of half of it. Then, using the “violin”’s axis of symmetry as my x-axis, I read off the coordinates of, I think, 32 points along the penciled path.
I copied the aforementioned CURVE program into my Commodore 64, then entered the points. I used a program of my own devising, called GRAPH PRINTER, to see what the resulting curve looked like. It took a few attempts to find the optimum degree for my polynomial; I ultimately settled on 12.
Some years later, when I had an iMac with a built-in app called “Grapher,” I was able to get a nice-looking multicolored graph on the screen. Since Grapher could graph multiple functions on the same set of axes, I was able to input both my half-violin function and its reflection (with the signs of all the terms reversed). I then took a screenshot, created a link to it on my homepage, uploaded it to the web, and voilà: violin!