The Division of Plane Figures: Historical Background, Diachronic Approach and Mathematical Solutions
Résumé
The cutting or division of plane figures is an important chapter in mathematics since Antiquity, both in practice (division of inheritance, decoration among others) and for the concepts developed. Several works in the history of mathematics have given insight into this importance, the nature of the problems and the different solving methods. This chapter proposes, in a diachronic approach, a historical and mathematical study of a selection of problems of division of plane figures taken from Medieval Arabic and Latin texts up to textbooks published for mathematics education throughout the 19th century. We show in particular the genealogy of the problems and the different mathematical solving approaches. We highlight geometrical (constructions), computational, algebraic or even analytical methods focusing on the division of a triangle. Finally, we also raise the question of their use in today’s mathematical education by considering various ways of exploitation.