Starting with the vertices P1 (0, 1), P2 (1, 1), P3 (1, 0), P4 (0, 0) of a square, we construct further points as shown in the figure: P5 is the midpoint of P1 P2, P6 is the midpoint of P2P3, P7 is the midpoint of P3 P4, and so on. The polygonal spiral P1P2P3 P4P5P6P7 . . . path approaches a point P inside the square.
(a) If the coordinates of Pn are (xn, yn) show that ½ xn+ xn+1 + xn+2 + xn+3 = 2 and find a similar equation for the y-coordinates.
(b) Find the coordinates of P.