Area of Ovals with Constant Width

Abstract

We investigate ovals of constant width obtained from a simple closed parametric function in this paper. We measure the area
enclosed within the parametric curve and compare it relatively to the area of a correspondingly particular circle. We show that the
area of the oval approaches the area of the corresponding circle with increasing width, regardless of the number of vertices. We
prove that the area of the oval from a vertex to the next one equals the total area divided by the number of counted vertices, and the
area from a vertex to its opposite is equal to half of the total area. Bounds for the area of the oval at all possible values of
the number of vertices that satisfy the condition of convexity are derived. A correlation between a range of constant widths and
a predetermined maximum number of possible vertices for the resulting ovals is established. Theoretical findings are supported
by numerical data and accompanying figures.