# Unit 1 Swimming Research Paper

1387 Words 6 Pages
For my mathematical exploration paper, I have decided to base it on the topic of swimming as it can be affiliated with many mathematical components. However, I was profoundly interested in determining the optimal kicking angle as it caught my recognition. As I further explored this topic, I decided to endeavour to connect a swimmer’s water movement with the quantity of water being pushed around against the flow. As a swimmer myself, I was greatly interested in determining the optimal angle to kick in order to enhance my swimming.

In swimming, kicking can be defined as the continuous up and down movement of the legs; also a way to help stabilize and mobilize your body in the water. With this knowledge, I am interested in ascertaining the relation
At first, as I was examining the image of the swimmer, I thought about determining the area between the swimmer’s legs. At first, I thought that I could relate it to the area of a triangle, but later acquired the fact that the side length and height of an isosceles triangle cannot be equivalent, which meant that the area of a triangle would not fit this image.

Figure 2

Created in Microsoft Paint

In Figure 2, I have attempted to display an isosceles triangle to put in place of the swimmer's legs. In this image, the swimmer’s legs are represented by the side length r, along with the height of the isosceles triangle being represented with h. I have noticed how the value of r and h cannot consist of equivalent values, as the shape seems to be similar to the shape of an isosceles triangle; the side lengths and height will never be the same.

Figure 3

Created in Microsoft Paint

Later on, I realized that the area between their legs can be interpreted as a minor sector, just as shown above in Figure 3; due to the fact that the length of the legs stay constant: in other words, the value of r is constant through the sector; it would be the most accurate form to represent the