Function Grinder

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Function Grinder
Organ Function Grinder.jpg
On display at National Museum of Mathematics
Type Hands-on
Topics Functions, music


A musical interactive box reminiscent of an old fashioned organ grinder at a circus midway. Three dials, a crank, and tickets with numbers on them invite the visitor to explore.

Activities and user interaction

Grab a ticket with an x value of your choice, then set the three dials to create your function. Put your ticket into the input slot and start cranking. Each step of the function transforms your number, and each mathematical transformation is represented by a corresponding, custom musical treatment. Can you hear the transformations in the music, too? Your ticket emerges at the other end, now printed with the entire equation

Mathematical background

A "function" is one of the most fundamental concepts in mathematics. Functions transform each input value (called "x" in this exhibit) to some output value (called "y" here). The functions computed by this organ grinder are each composed of three simpler functions, illustrating how in complicated things can often be broken down into simpler building blocks. Does the order in which you enter the three simple functions matter?

History and museology

The Organ Function Grinder was part of the original suite of exhibits of the Math Midway, a travelling exhibit which was the beta test for the permanent exhibits at MoMath. Copies of this exhibit are installed in Singapore and Brazil.