Leonardo Pisano called Fibonacci, between advanced mathematics, history of mathematics and mathematics education: three examples drawn from Liber Quadratorum

In this research, three problems faced by Leonardo Pisano, called Fibonacci, are dealt with. The main purpose is to show that history of mathematics can offer interesting material for mathematics education. The approach to the use of history of mathematics in mathematics education cannot be merely historical, but adapted to the needs of the explanations in a classroom. In the course of this paper, the meaning of such assertion will be clarified. A further purpose is a trying to explore the relations history of mathematics-mathematics education-advanced mathematics. Last, but not the least, a further aim is to offer a specific series of interesting material to the teacher in order to develop stimulating lessons. The material here expounded is conceived for pupils frequenting the third and the fourth years of the high school, but, with minor modifications, it can be adapted to the fifth year of the high school and to the initial years of the scientific faculties at the university.