# Engaging students: Perimeters of polygons

In my capstone class for future secondary math teachers, I ask my students to come up with ideas for engaging their students with different topics in the secondary mathematics curriculum. In other words, the point of the assignment was not to devise a full-blown lesson plan on this topic. Instead, I asked my students to think about three different ways of getting their students interested in the topic in the first place.

I plan to share some of the best of these ideas on this blog (after asking my students’ permission, of course).

This student submission comes from my former student Tiger Hersh. His topic, from Geometry: perimeters of polygons.

How has this topic appeared in pop culture?

In simulation games like ‘Farming Simulator’ and ‘Cities Skylines’ there is a need to determine the perimeter of the polygon or shape. When you first start out in the game you must keep in mind the limitations of your sandbox (which is usually in the confines of a square). This is where finding the shape of the polygon becomes very useful. When you are able to determine the boundary area of that square, you are then able to map out the land that you would wish to occupy. For Farming Simulator you can find how much space your plot of crops will take and how much space in between your fields.

In Cities Skylines (the city builder simulator) it is similar to that of Farming Simulator but instead of making separate plots of land for your crops, you are instead creating separate plots of land for living spaces, markets/businesses, and industrial spaces. The reason finding the perimeter of each type is important is so that you can create a space for them that is reasonable and does not intersect with the other districts. So it is key to having these each place separated but also given plenty of space, which would require you to find the length and width that would be appropriate to the land you have to work with and also for that place.

How can this topic be used in your students’ future courses in mathematics or science?

Once students have learned how to find the perimeter of a polygon they can use this concept and apply it to finding the distance between two points on a graph. Students may find the circumference of a circle (the perimeter of the circle) and use it on application problems that may come up in science; such as determine how far a person travels on a merry-go-round. This is then later used to determine circular motion or how fast something is going.

What interesting things can you say about the people who contributed to the discovery and/or the development of this topic?

There are many interesting people/things that contributed to this concept. One notable person is Archimedes, the greek mathematician, who around 250 B.C. used the sides of hexagons to find an approximation of pi. The method was that he would have hexagons inscribed in the circle and then double the sides of the hexagon to a 12- sided polygon, doubled the sides again to a 24 sided polygon, doubled to a 48 sided polygon, and doubled again for a 96 sided polygon. He was then able to bring the perimeter of the polygons closer and closer to the circumference of the circle. This later turned out to be what we know now today as pi.

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