Can any definition of triangle be considered the best one?

This paper deals with an important item in Mathematics Education: mathematical definitions. In particular it focuses on the definition of a triangle, an only seemingly “simple” mathematical object. In order to do this, we discuss the main following points: 1) the distinction between the formal mathematical concept of definition and the use of this word in classroom practice; 2) some specific problems concerning geometry, along with a comparison of many different definitions of a triangle and of different curricular choices; 3) a possible impact of modern technologies on the definition of triangle. Finally, we emphasize the necessity for a teacher to employ a balanced mix of intuition and formalism both in compulsory and in upper school.