I am a function

Exhibit

I am a function
On display at	Mathematikum
Type	Hands-on
Topics	Functions

I am a function is a hands-on exhibit on display at Mathematikum.

Description

A screen is presented on top of a wooden stand, with a long carpet in front of it. As we walk on the carpet towards the screen, a sensor measures the distance between the stand and us. The screen shows a fixed (white) graph of a function, and as we move on the carpet a new (yellow) graph of our distance vs time is drawn. The aim is to come to the given graph as close as possible. The carpet has markings showing the distance to the stand. A button next to the screen allows to reset the exhibit and a new white function graph appears.

Activities and user interaction

The screen is non-touch, and it becomes obvious that the only button is a reset. The users immediately realize that the yellow graph is related to their position by means of some sensor. The height of the curve is the distance to the stand, which can be compared with the carpet markings. Moving forwards towards the stand makes the function decrease, while moving backwards makes the graph rise. All didactical aspects of a function can be experienced: the values at a certain point (where do I have to start?), the variational aspect (do I have to walk slow or fast, and in which direction?), the function as a whole (could I repeat my walk without looking on the screen?)

The fact that all these mathematical aspects are experienced but not verbalized (minima, maxima, slope, etc.) keeps the activity fun and playful, while the visitor is conscious of the mathematical ideas. Visitors of all ages do it with pleasure, others can observe it.

Additional activities may be doing that looking away from the screen, with the help of a friend that gives instructions, or trying to trick the machine to draw a discontinuity.

Mathematical background

All aspects of a function (slope, extrema etc.) may be discussed/experienced in this exhibit.

History and museology

The idea of this exhibit can be traced back to the Texas Instruments calculator-based ranger (CBR), a sonic motion detector sold for TI-82 and other calculators with the package “Ranger” around 1997. There are many copies and versions of this exhibit in the world.

Resources

Cf. with the catalog(s) of Mathematikum,

• Learning Math with Interactive Experiments. 45 Experiments from Mathematikum. Giessen, 2016.
• Beutelspacher, A., Wie man in eine Seifenblase schlüpft, C. H. Beck, Munich, 2015. ISBN 978 3 406 68135 6. (in German)