The Golden Ratio

The Golden Ratio is an ancient proportion of a shorter length to a longer one. While it was employed by the Egyptians as early as second millennium B.C.E. (Before the Current Era), It was with the classical Greeks that it found its highest expression.  Jay Hambridge's stunning analysis of the Parthenon, a fifth century temple designed by Calicrates, Ictinus and Phidias and dedicated to Pallas Athena that dominates the acropolis (define) in Athens, leaves no doubt that this proportion is the motif underlying the beauty of this most beautiful edifice of human expression.
The beauty of the Golden Ratio lies in the dynamic relationship between its two parts.  The longer part dominates the pair but the shorter asserts itself against it in a delicate shifting balance.  The eye measures and compares the two distances which seem to shift in the process.  Also there is deep intellectual satisfaction in seeing an unequal, yet complementary, pair where the lesser is to the greater as the greater is to the whole.

To divide a given line into the Golden Ratio, one needs only a string and straight edge.
Let AB be any length line. Construct a perpendicular at B. Mark C at half of AB. Draw AC.  Mark D at half of AB. Measuring from A, mark S at CD. S is the division of AB into the Golden Ratio.

To extend a line AS so that it becomes the larger of the Golden Ratio pair, construct a perpendicular  at S whose height C is equal to AS. Strike an arc from the midpoint of AS thru C to B.  S is the division of AB into the Golden Ratio.
Test your sensitivity to the Golden Mean.
Dr. Knott's exhaustive page on the Fibonaci numbers and the Golden Mean.

Back
Pallas' First Day Handout. 
Macomb Community College.
Jim Pallas Homepage.

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