... adapted from Polya [br][br]The challenge is inscribe a square in a triangle - two vertices of the [br]square should lie on the base of the triangle.[br][br]You can vary the triangle by dragging the RED dots.[br]You can vary the inscribed rectangle by dragging the GREEN dot.[br][br]Can you think of a way to use the mean value theorem to show that[br]this can be done? Can it always be done?[br][br]Can you inscribe a cube in a tetrahedron - with one face of the cube[br]lying on base of the tetrahedron ?[br][br][i][b][color=#ff0000]What other questions [could,would] you ask of your students?[/color][/b][/i]