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Big Angles in the Park: Walking Scale Geometry – InforMath

Big Angles in the Park: Walking Scale Geometry

One of the goals of the InforMath project is to create informal mathematics activities that engage the whole body. Yes, it is true that sitting at a desk with pencil and paper doing mathematics involves the whole body, just as lying in bed at night imagining a mathematical scenario does. However, we seek to create opportunities for more overt whole body engagement in doing mathematics, whether it requires walking, dancing, arm waving, jumping , etc.

Ashley with pro and strings

To kick off the work of the Design Lab we left the friendly confines of the Tinkering Studio at the Fleet Science Center and made our way out to the fountain with our big protractors in hand. This activity requires 3 people: one person to hold the protractor, and two more people who each hold an end of the string that forms the angle. The two string holders must remain fixed; we used small cones to mark their locations in an effort to minimize any unintentional migration (see the red cones in the photo below).

Molly with pro and strings

Their primary job is to dole out and retract the string as the protractor moves. The person with the protractor tries to move in such a way that the selected angle formed by the strings remains constant. Each time a location is found that preserves the angle, a cone is set down as a marker (see the yellow cones above).


There are two main parameters that affect the system: 1) the fixed distance between the string holders (ie the distance between the two red cones above), and 2) the angle selected on the protractor. Each team of three adjusted the parameters as they saw fit, or as curiosity dictated, and then tried to find as many points, on both sides of the string holders, as they could. For each trial (ie every time we changed the angle or the distance between the string holders) we scribbled quick notes and observations, and took photos to record the collection of locations. As teams succeeded in finding points, attention began to shift towards the resulting pattern or shape formed by the locations. Was it a peanut, an hour glass, an ellipse, etc?

75 degrees

What makes this mathematical experience so much different than the experience of sitting at a desk with a pencil? Lets consider what is involved in finding a point. By design, this activity requires the cooperation of at least three people, so communication and coordination among the team is critical.

How should the protractor move to maintain the angle?

Who needs to change the tension in their string?

How should the tension be changed: increased or decreased?

Bohdan with pro and strings

To engage in these questions and respond to them requires learning to integrate the perceptual and motor. The string holder feels the tension of the string in their hand, the braid of the string tugging your skin, perhaps an urge to move away from their fixed spot as the tension increases, pulling them. Release string.

Is the angle being maintained? Peer down the string to the protractor, is the string still straight? If it’s not, what needs to be done? Should you change the tension in the string? Should the protractor move? If so, where?

If you’re holding the protractor, how should you move to find a new point? Should you look in the direction you intend to move, or try to maintain a visual of the protractor and strings? Don’t trip over your own feet! Uh oh, you feel the protractor pulling you. Is it coming from the left side or the right? Should you request more string, or move differently?

To further explore what shape is produced by the patterns, we created a small scale, desktop device, PEGI. To learn more about PEGI, click here.

Written by Bohdan Rhodehamel
Contact Bohdan at bohdanr561@yahoo.com


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