Locus

Mathematics teacher, you are in trouble if you introduce a circle by defining it as 'the locus of all points equidistant from a central point', unless your class consisted of specially selected geniuses. The term locus itself is rather abstract. To imagine a circle, which consists of a continuous line in the form of a loop, in terms of points may even be more nightmarish. No doubt mathematically, a circle is defined that way, but we have to bear in mind the reality in the classroom, at least the command of the English language among the students, their standard of mathematics and their ability to form a mental picture based on the definition.

I would like to suggest an interesting story to help students to understand a circle in terms of focus. Without delving much into further technicality and suffice to say that by considering the footprints of the goat described in the following story as moving points, I am sure mathematics teachers can proceed further to fill in the gaps and incorporate the complete story into the mathematical lesson in the class.

One day a goat was loosely tied to a pole a day ahead of a big feast. That night the goat tried to escape to save its own life. Since it was very dark, the goat could not see at all. The goat thought for a while (assuming this goat was very intelligent) and decided the run in such a way that the rope was always tight. By this way, the goat thought it could get as far from the pole as possible and possibly escape from the would-be butcher, whoever he was. It ran and ran the whole night and unknowingly, it was actually running in a circle. It is not difficult to imagine this with the aid of a diagram. As the goat ran repeatedly in a circle, the impact of its soles with the ground have created a circular trench. So if we imagine the footprints of the goat as points and the circular trench represents the locus of a circle.

With a little imagination, it is not difficult to create stories for various loci like a straight line, parabola, ellipse, and so on. It is interesting to try the story-telling method, exciting to find that the students enjoy the lesson and satisfying to learn that they can understand the concepts better.