L'ipocicloide tricuspide: il duplice approccio di Luigi Cremona ed Eugenio Beltrami

The Hypocycloid tricuspid is one of many examples of ‘elementary problems’ that attracted great mathematicians. This allure is mostly motivated by aesthetic reasons: interpreting such term from a mathematical point of view, it means the extraordinary ability to ‘see’ with the mind’s eye the many connections, far from intuitive, among facts, theories and methods that arouse a sense of harmony in those who are able to understand them. In this paper we will emphasize how the sense of ‘mathematical beauty’ is strongly present in mathematicians of the highest level as Luigi Cremona and Eugenio Beltrami.