Dividing A Line Segment
The following algorithm produces a geometric construction that divides a line segment into two line segments where the ratio of the longer to the shorter line segment is the golden ratio:
- Having a line segment AB, construct a perpendicular BC at point B, with BC half the length of AB. Draw the hypotenuse AC.
- Draw a circle with center C and radius BC. This circle intersects the hypotenuse AC at point D.
- Draw a circle with center A and radius AD. This circle intersects the original line segment AB at point S. Point S divides the original segment AB into line segments AS and SB with lengths in the golden ratio.
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