Similarity of Parabolas - A Geometrical Perspective

The issue of similarity of parabolas can be discussed from both algebraic and geometrical perspectives. Through an algebraic lens, Kumpel (1975) examined this issue and proved the surprising fact that any two parabolas are similar. In this paper we examine the similarity of parabolas by employing geometrical considerations and suggest an approach to determine the similarity ratio. Finally, we show that in an analogy to similarity of polygons, similarity of parabolas preserves ratios of distances, and that the ratio of corresponding areas is the square of this similarity ratio.