MathDB

2

Part of 1993 Flanders Math Olympiad

Problems(1)

jeweler

Source: flanders '93/2

9/27/2005
A jeweler covers the diagonal of a unit square with small golden squares in the following way: - the sides of all squares are parallel to the sides of the unit square - for each neighbour is their sidelength either half or double of that square (squares are neighbour if they share a vertex) - each midpoint of a square has distance to the vertex of the unit square equal to 12,14,18,...\dfrac12, \dfrac14, \dfrac18, ... of the diagonal. (so real length: ×2\times \sqrt2) - all midpoints are on the diagonal (a) What is the side length of the middle square? (b) What is the total gold-plated area? http://www.mathlinks.ro/Forum/album_pic.php?pic_id=281
geometry