The Function Box

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The Big Picture

As told by Andy Long:

Clifford A. Long, 1931-2002
Clifford A. Long, 1931-2002

The "Function Box" was the brain child of my dad, Clifford Long, a mathematics professor at Bowling Green State University. He dreamed of a function box, a machine for dynamically producing surfaces of functions of two variables. He was big on what are now known as manipulatives: for example, he built a large wooden hyperbolic paraboloid to use in multivariate calculus, because he knew that lots of students have trouble visualizing surfaces (e.g. those projected onto a screen). But this was an extremely time-consuming and energy-intensive process: he wanted something computer-controlled, that would allow him to dynamically produce such surfaces.

Years ago I bought him the toy PinPressions, which illustrates the idea, only backwards:


Honest Abe as a matrix
Honest Abe as a matrix
Abe as a function
Abe as a function

Suppose we're interested in the function represented by the height of Abe Lincoln's face above a table: you could take a reading of the surface using pinpressions; if the pins were all wired, we could read off the coordinates (as a matrix), and then create a function to interpolate those values. This is an example of rapid prototyping.

We want to operate in the reverse sense, however: suppose that we have a formula and seek a graphical representation of the surface corresponding to the function. We simply sample the function, and raise the pins to the corresponding heights, as a graphical representation of the function.


Ken Townsley, with Michael and Dan Glier
Ken Townsley, with Michael and Dan Glier
Phil Schmidt and Kirsty Fleming, supporters of the project
Phil Schmidt and Kirsty Fleming, supporters of the project
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