User:Richard Bartholomew/sandbox

This is the user sandbox of Richard Bartholomew. A user sandbox is a subpage of the user's user page. It serves as a testing spot and page development space for the user and is not an encyclopedia article. Create or edit your own sandbox here.

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Dividing a line segment[edit]

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:

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.
Draw a circle with center C and radius B. This circle intersects the hypotenuse AC at point D.
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.