This week I gave my “I am a mathematician” talk to the students at Rosedale. My main goal was to show them two aspects of mathematics; abstraction and reduction. Below is a presentation I created to help illustrate my points.
The first slide is a circle, one of the most well recognized geometric objects. The students were able to tell me this was a circle, but when asked what a circle was, many (if not all) described a circle as a round thing with no edges. Of course many objects that are not circles satisfy this description; i.e. spheres, ovals, ellipses, etc. After a discussion with the students I was able to convince them that a circle is the set of points equidistant from a particular point. The students seemed to realize that a circle is just an idea, not a physical object.
Next I had the students pretend that distance did not exist. In this scenario, there was no difference between a circle and an oval. Likewise, a coffee cup and a donut is “the same” object. These ideas demonstrated what is meant by abstraction.
The last slide is the seven bridges of Koenisberg. This is a great example of how mathematicians can reduce a complex problem to a simpler one. The students seemed very engaged in trying to find a solution to the problem. When I showed them why it was not possible, the students where able to change the problem to make it possible.