The Golden Section
ILLL
Dr Shobha Bagai
University of Delhi

THE GOLDEN SECTION
He felt himself suddenly reeling back to Harvard, standing in
front of his “Symbolism in Art” class, writing his favorite
number on the chalkboard
.
1.618
……………………..
“This number PHI,” Langdon continued, “one-point-six-one-
eight, is a very important number in art. Who can tell me
why?”
……………………..
“Actually,” Langdon said, “Stettner
ʼ
s right again. PHI is
generally considered the most beautiful number in the
universe”.
……………………..
“Yes PHI,” Langdon replied. “One-point-six-one-eight. Want another example?
Measure the distance from your shoulder to your fingertips, and then divide it by the
distance from your elbow to the fingertips. PHI again. Another? Hip to floor divided by
knee to floor. PHI again. Finger joints. Toes. Spinal divisions. PHI. PHI. PHI. My
friends, each of you is a walking tribute to the Divine Proportion.”
The Da Vinci Code
by
Dan Brown
Geometry has two great treasures: one the theorem of Pythagoras; the other,
the division of a line into extreme and mean ratio. The first we may compare to
a measure of gold, the second we may name a precious jewel. – Johann Kepler
DISCOVERY OF THE GOLDEN SECTION
There are many different names for the golden section; The Golden Mean, Phi, The
Divine Section, The Golden Cut, The Golden Proportion, The Divine Proportion, and
The Golden Ratio.
The Great Pyramid of Giza built around
2560 BC is one of the earliest examples of
the use of the golden ratio. The length of
each side of the base is 756 feet, and the
height is 481 feet. So, we can find that the
ratio
of
the
base
to
height
is
756/481=1.5717.
Euclid
, the Greek mathematician wrote the
Elements
which is a collection of 13 books.
In Book 6, Proposition 30, Euclid shows how to divide a line in mean and extreme
ratio which we would call "
finding the golden section point on the line.
" Euclid used
this phrase to mean
the ratio of the smaller part of the line, to the larger part is the
SAME as the ratio of the larger part, to the whole line.
Euclid in
Elements
called
dividing a line at the ratio
0.6180399.. : 1
,
dividing a line in the extreme and mean
ratio
. This later gave rise to the name golden mean, golden ratio and even the divine
proportion.

Plato
, the Greek philosopher theorized about the Golden Ratio. He believed that if a
line were divided into two unequal segments so that the smaller segment was related
to the larger in the same way that the larger segment was related to the whole, what
would result would be a special proportional relationship.
that is,
a
+
b
a
=
a
b
, where
a
+
b
is the length of the line, then these ratios are called
the Golden ratio.
Luca Pacioli
wrote a book called
De Divina Proportione
(The Divine Proportion) in
1509. It contains drawings made by Leonardo da Vinci of the 5 Platonic solids.

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- Fall '09
- Math, The Da Vinci Code, Golden ratio, Golden Section