Golden Section

Copyright © 2000 by Paul Niquette. All rights reserved.

Draw a line one unit long (by "unit" can be meant an inch, a foot, or you can go metric if you like). Mark a point on it. You now have two joined line segments. Call their respective lengths and 1 - .

Phi LineNow, let the point move along the line so that the following statement applies:

    The length compared to the length of the whole line exactly matches the length 1 - (the part left over) compared to length .
The value of which satisfies this relationship has received the name "ancient mean," "golden mean," and the "extreme ratio." One finds the more colorful "Golden Section" used most today.
What is the value of ?