Dalla retta di Simson-Wallace all’ipocicloide tricuspide.Storia di un soggetto elementare che ha affascinato celebri matematici

[automatically translated] The hypocycloid tricuspid is a well-known curve of the fourth order, and third-class in the course of a couple of centuries has intrigued many mathematicians of the caliber of Steiner, Cremona, Beltrami, Cesàro, Fréchet, Schröter, Clebsch, Battaglini, Laguerre, Cayley , wanting to name only the most famous. This interest is connected with various aspects of mathematics: a. his generation as the envelope of the line of Simson-Wallace, whose story itself is intriguing; b. its link with the circle of Feuerbach, which, in turn, has an interesting history; c. the fact that it can get as quadric reversal of a circle and then the close connection with the origins of the birational transformations. It is therefore no wonder that the hypocycloid with three cusps has obtained great popularity among mathematicians in the second half of the nineteenth century.