INTRODUCTION
The heart of Mathematics is more than just numbers, numbers which many
supposed to be meaningless and uninteresting.
Many of us gone for a beach trips or did
mountain climbing perhaps and noticed in awe the world around us.
The different shapes
we see around us, the hues of the sky from sunrise to sunset, the clouds transforming from
stratus to cumulus, the contour of the rainbow in the horizon are all beautiful because of
harmony and pattern. The degree of changing hues of color has to be of exact measurement
to appear pleasing and harmonious to the human eye.
We can see patterns everywhere either in school or in our house, even in ourselves,
we just need to learn how to notice them.
And we need to study patterns because
Mathematics is a study of patterns.
That is one reason why those who use patterns to
analyze and solve problems often find success.
Because it seeks to discover relationships and
connections between seemingly unrelated bits of information.
If we count the number of
petals of most flowers, notice that they are either of one petal, two petals, three petals, five
or eight.
This sequence of numbers from the set (1,2,3,5,8,13…) whose pattern was
discovered by Fibonacci.
While the German mathematician and astronomer Johannes Kepler (known for his
laws of planetary motion) observed that dividing a Fibonacci Number by the number
immediately before it in the order of sequence yields a quotient approximately equal to
1.618.
This amazing ratio is denoted by
φ
called the Golden Ratio.
The Golden Ratio is
so Fascinating that proportions of the human body such as the face follows the so called
Divine Proportion.
The closer the proportion of the body parts to the Golden ratio, the more
aesthetically pleasing and beautiful the body is.
Many painters, including the famous
1

Leonardo Da Vinci were so fascinated with the Golden Ratio that they used it in their works
of art.
LEARNING OBJECTIVES:
At the end of this lesson, the students will learn about the different Patterns in
Nature and how patterns help us to solve different problems. This will also give them an
information about Fibonacci Sequence and the idea behind it and its relationship to the
different patterns in nature.
The students will encounter the “The Golden Ratio”, they will
understand how it is derived, where to use it and how the Fibonacci sequence related to
Golden Ratio. The listeners will gain knowledge about the concept behind the Golden
Rectangle, how it is constructed and how it is related to the Golden Ratio. And this topic will
give an idea to the student about the meaning of Golden Spiral, how it forms inside the
Golden Rectangle and where it is usually seen.
TOPIC DISCUSSION
Patterns and Numbers in Nature
Patterns are regular, repeated, or recurring forms or design. Studying patterns help
students in identifying relationships and finding logical connections to form generalizations
and make predictions.
Mathematics is sometimes called the “Science of Pattern”, that is any

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- Summer '19
- Hsieh
- The Da Vinci Code, Fibonacci number, Golden ratio, golden rectangle