Pegi is a geometric tool we created to supplement a mathematical activity using large scale protractors. The protractor activity requires three people: one person holds the protractor, set at a fixed angle by two pieces of string; the other two people hold the ends of the string and stand at a fixed distance apart. The challenge is to have the protractor person move in such a way that the angle formed by the strings remains fixed, while the string people must either dole out or retract string to help maintain the angle. Teams of three people investigate how many points they can find, and what shape is formed by the points.

Pegi was created to further explore the shape created by the points, but in a way that dramatically reduces the scale and allows one to work individually, if desired. Pegi contains three components: a slotted bar, two pegs to insert in the slots, and angles of varying measures along with their supplements. All parts are made from acrylic cut on a laser cutter.

Pegi 45

One begins by selecting the distance between the pegs and inserting them in the slots of the bar (this distance is the secant), and then choosing an angle to work with. The angle slides between the two pegs, maintaining contact with both pegs . Sliding the vertex through the pegs creates a collection of points that form the same contours (ie circular arcs) found using the protractor and string.

pegi in lab

Written by Bohdan Rhodehamel
Contact Bohdan at


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