THE IMPORTANCE OF BEING MEAN

Many historical loci can be obtained through approaches that differ from classic methods built on their own pure description as loci. Aim of this work is to show how various algebraic curves can be obtained as the locus for particular midpoints, and how the consideration of the latter can give rise to a succession of homotheties, namely, contractions or dilations, of the original curve. What is important to underline is that points generating a locus possess the particular property of being midpoints of other pairs of points, or segments, stemming from a particular configurations of points and lines. This is illustrated here, by various examples.