In this note we are interested in the rich geometry of the graph of a curve γa,b : [0, 1] → C defined as γa,b(t) = exp(2πiat) + exp(2πibt), in which a, b are two different positive integers. It turns out that the sum of only two exponentials gives already rise to intriguing graphs. We determine the symmetry group and the points of self intersection of any such graph using only elementary arguments and describe various interesting phenomena that arise in the study of graphs of sums of more than two exponentials.
|Journal||Elemente der Mathematik|
|Publication status||Published - 06 Apr 2021|