On the maximal inflation of two squares - Thierry Gensane and Philippe Ryckelynck We consider two non-overlapping congruent squares q_1, q_2 and the homothetic congruent squares q_1^k, q_2^k obtained from two similitudes centered at the centers of the squares. We study the supremum of the ratios of these similitudes for which q_1^k, q_2^k are non-overlapping. This yields a function \psi =\psi (q_1,q_2) for which the squares q_1^\psi, q_2^\psi} are non-overlapping although their boundaries intersect. When the squares q_1 and q_2 are not parallel, we give a 8-step construction using straight edge and compass of the intersection q_1^\psi \cap q_2^\psi and we obtain two formulas for \psi. We also give an angular characterization of a vertex which belongs to q_1^\psi \cap q_2^\psi. ✪ ✪ ✪ ✪ ✪ Link tải tài liệu: LINK TẢI TÀI LIỆU Theo LTTK Education
