1.
Golden Ratio:
Math or Miracle?
Sakshi Jha
#scichallenge2017

2.
Introduction
 What is the Golden Ratio: History and Meaning
 Golden Spiral
 Examples in Nature
 Applications and Uses
 Conclusion

3.
What is the GR (ϕ)
The Golden Ratio (GR) is a special number found by
dividing a line into two parts so that the longer part
divided by the smaller part is also equal to the whole
length divided by the longer part. This is represented
by the Greek Letter ϕ (Phi) and = 1.618...

4.
Why does the GR exist?
The GR is evidence of the fact that nature likes to
simplify things.
It is also evidence of the pattern and diversity
coexisting integral to evolution.
Some would argue it confirms the presence of a
Greater Being who made us all.

5.
History of the GR
 It is known that many mathematicians, scientists,
artists and architects have been fascinated by the GR.
 Pythagoras was among the mathematicians who have
done work surrounding this astonishing number as
well as Leonardo Da Vinci and astronomer Kepler.
 The Fibonacci series is also linked to the GR because
dividing 2 consecutive Fibonacci numbers eg 34/21
tends towards the GR.

6.
The Golden Spiral (GS)
In geometry, a golden spiral is: a logarithmic spiral
whose growth factor is the GR (ϕ).Therefore, a golden
spiral gets wider (or further from its origin) by a factor
of ϕ for every quarter turn it makes.

7.
Examples in Nature
 Animals
 DNA
 Human Body
 Plants
 Geographical

8.
Animals
Many animals are divided into
sections and show the GR in
their structure eg the eyes, fins
and tail of a dolphin all fall at
GR along the length of the
dolphin’s body.

9.
DNA
DNA has two grooves in its spirals with the GR
being the proportion of the major to the minor
groove

10.
Human body
The Human body
has the most
examples of the
GR eg the ratio of
the hand to the
forearm
approximates the
GR.

11.
Plants
Golden Spirals can be found
in pinecones, sunflowers,
pineapples, and many other
plants. The petals of plants
commonly grow in Fibonacci
numbers eg lillies, buttercups,
roses, daisies.

12.
Geographical
Examples of the
Golden spiral are all
around us in the shape
of the galaxies,
hurricanes and waves.

13.
Application and Use
Architecture
Music
Beauty
Art
Make Math Interesting

14.
Architecture
The application of the GR in architecture has the
following advantages:
 Brings balance and height to buildings.
 Allows for varying shapes.
 Makes buildings aesthetically pleasing.

15.
Music
The applications of GR in music are:
 Used in the timing of musical compositions eg the
climax is reached often at the ϕ(61.8%) of the song.
 Used in the design of musical instruments eg violin.
 Even Beethoven and Mozart used the GR in their
best works eg Beethoven’s fifth symphony.

16.
Beauty
The applications of the GR in beauty are:
 The most aesthetically pleasing and beautiful faces
are those that conform to the GR hence this is
applied in facial plastic surgery and cosmetic
dentistry as a guide.
 The GR method is used in the application of make-
up to look more beautiful.

17.
Art
The applications of GR in art are:
 Artists use the GR in finding the best design for
their work eg Da Vinci’s Mona Lisa follows the GR
in it’s layout.
 Using the GR is proven to make things more
aesthetically pleasing so artists often incorporate it
in their work.

18.
Make Math Interesting
 The study of the GR makes math more interesting;
students look beyond fractions and algebra and see
a hidden world of math in everyday life.
 The GR helps to put the Fibonacci sequence into
context, which is part of the curriculum, and
because it’s so intriguing they will learn more.
 The GR shows that math is all around us and in
every profession. This may persuade students to
take math in their further education.

19.
Conclusion
The GR is a truly unbelievable construct and it is amazing
how it relates to everyday life. The GR unveils a hidden
harmony in all things which is really fascinating. I think
the study of ϕ should also be included in the school
curriculum because it can show students that there is more
to math than they may think.