Resumen de Ellipses of constant eccentricity

V.K. Srinivasan

• A square of side length 2a,?a> 0 is selected in the Euclidean plane. For each a> 0, two types of hexagons are constructed using the selected square. They are labelled type-1 hexagon and type-2 hexagon. For each a> 0, there are two type-1 hexagons and two type-2 hexagons. In relation to the selected square, they appear to be horizontal and vertical. The VKS ellipses circumscribe type-1 hexagons and type-2 hexagons. The construction of these two types of hexagons and the determination of the Cartesian equations of the circumscribing VKStype-1 and VKS type-2 ellipsesform the main themes for this paper. The eccentricities of these VKS type-1 ellipses and VKS type-2 ellipses are also discussed. The author hopes that the construction of the hexagons and the ellipses will be useful to students in high schools and colleges.