User:Richard Bartholomew/sandbox

Dividing a line segment
The algorithm below produces a geometric construction that divides a line segment into two line segments. The ratio of the longer line segment's length to the shorter line segment's length is the golden ratio:
 * 1) Construct a line segment AB. Construct a line segment BC. Line segment BC is perpendicular to line segment AB. Line segment BC intersects line segment AB at point B. Line segment BC's length is half of line segment AB's length. Draw the hypotenuse AC.
 * 2) Draw a circle with center C and radius B.  This circle intersects the hypotenuse AC at point D.
 * 3) Draw a circle with center A and radius D.  This circle intersects the original line segment AB at point S.  Point S divides the original segment AB into line segments AS and SB. The ratio of line segment AS's length to line segment SB's length is the golden ratio.