Mathematical patterns in nature

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1. MATHS HOLIDAY
HOMEWORK
TOPICS- MATHEMATICAL PATTERNS IN NATURE

2. NAME- ANSHUMAN SINGH
CLASS- 9‘C’
ROLL NUMBER- 5
ADMISSION NUMBER- 1068

3. ACKNOWLEDGEMENT:
•What is a Pattern in Nature?
•Mathematical Patterns in Nature
•Different mathematics pattern
•5 stunning ways we see mathematical patterns in nature

4. WHAT IS A PATTERN IN
NATURE?
The world is full of natural visual patterns, from spots on a
leopard to spirals of a fiddlehead fern. Some patterns are as
small as the molecular arrangement of crystals and as big
as the massive spiral pattern of the Milky Way Galaxy.
Patterns can be found everywhere in nature. While one
might think of patterns as uniform and regular, some
patterns appear more random yet consistent. The definition
of a pattern in nature is a consistent form, design, or
expression that is not random.
There are multiple causes of patterns in nature. Some
patterns are governed by mathematics. These are called the
“Golden Ratio”, this is a rule that describes a specific pattern
in nature. This mathematical formula is seen in spiral
patterns such as a snail’s shell or the whorls of a lily

5. SOME OF THE CAUSES OF PATTERNS IN
NATURE ARE:
•Reaction-diffusion effect: chemical interactions of pigment-forming molecules in organisms
create the spots, stripes, and other visible patterns; this is also called the turing model.
•Law of conservation of mass: predictable patterns of chemical interactions are governed by
this law of nature which states that matter is conserved but changeable in a reaction.
•Law of natural selection: patterns in the appearance and behavior of a species can change
over time due to the interaction of inheritable traits and the organism’s environment.
•Animal behavior: patterns observed in animal behavior, such as the production of
hexagons in honeycombs, are often the result of genetics and the environment.
•Laws of physics: the interaction of matter and energy create predictable patterns such as
weather patterns due to the interaction of solar energy, mass, and gravity. Planetary
motion is a predictable pattern governed by inertia, mass, and gravity. Also, weathering
patterns can create unusual rock formations such as the giant’s causeway

6. MATHEMATICAL PATTERNS IN
NATURE
Mathematics is seen in many beautiful
patterns in nature, such as in symmetry and
spirals. Both are aesthetically appealing and
proportional. Symmetry can be radial, where
the lines of symmetry intersect a central point
such as a daisy or a starfish. Bilateral
symmetry describes objects or patterns that
are equal on both sides of a dividing sector, as
seen in butterflies, mammals, and insects.

7. MATHEMATICAL PATTERNS IN
NATURE
Spirals are more mathematically complex and
varied. A spiral pattern would be described as a
circular pattern beginning at a center point and
circling around the center point as the pattern
moves outward. Examples of spirals would be a
chameleon’s tail, an aloe plant, or a nautilus
shell. There are various types of spirals; while
they look very similar, mathematically, they are
only approximately close. A logarithmic spiral,
as shown below, increases the distance of each
spiral logarithmically. In a Golden Spiral, the
increasing rectangles demonstrate Phi, or the
Golden Ratio of 1.618, based on the length versus
the width of each rectangle. Each looks very
similar, but mathematically they are slightly
different.

8. DIFFERENT MATHEMATICS
PATTERN
Waves represent the periodic distribution of
some natural medium like water, air, sound,
electromagnetic field or solid materials, etc.,
visually. The waves are coming in a pattern
called waves pattern. Sometimes the waves
come in a regular pattern. Sometimes, it
comes in an irregular pattern. This type of
pattern can see in patterns in nature.
1 Wave in water
2 Wave in Air
3 Wave in Sound

9. FIVE STUNNING WAYS WE
SEE MATHS IN THE WORLD
Have you ever stopped to look around and notice all the
amazing shapes and patterns we see in the world
around us? Mathematics forms the building blocks of
the natural world and can be seen in stunning ways.
Here are a few of my favorite examples of math in
nature, but there are many other examples as well.
1The Fibonacci Sequence
2 Fractals in nature
3 Hexagons in nature
4 Concentric Circles in Nature
5 Maths in outer space

10. 1THE FIBONACCI SEQUENCE
Named for the famous mathematician, Leonardo
Fibonacci, this number sequence is a simple, yet
profound pattern. Based on Fibonacci’s ‘rabbit
problem,’ this sequence begins with the numbers 1 and
1, and then each subsequent number is found by
adding the two previous numbers. Therefore, after 1
and 1, the next number is 2 (1+1). The next number is 3
(1+2) and then 5 (2+3) and so on What’s remarkable is
that the numbers in the sequence are often seen in
nature. A few examples include the number of spirals
in a pine cone, pineapple or seeds in a sunflower, or the
number of petals on a flower.
The numbers in this sequence also form a unique
shape known as a Fibonacci spiral, which again, we
see in nature in the form of shells and the shape of
hurricanes.

11. 2FRACTALS IN NATURE
Fractals are another intriguing mathematical
shape that we seen in nature. A fractal is a
self-similar, repeating shape, meaning the
same basic shape is seen again and again in
the shape itself.
In other words, if you were to zoom way in or
zoom way out, the same shape is seen
throughout.
Fractals make up many aspects of our world,
included the leaves of ferns, tree branches, the
branching of neurons in our brain, and
coastlines.

12. 3HEXAGONS IN NATURE
Another of nature’s geometric wonders is the
hexagon. A regular hexagon has 6 sides of equal
length, and this shape is seen again and again in the
world around us.
The most common example of nature using hexagons
is in a bee hive. Bees build their hive using a
tessellation of hexagons. But did you know that every
snowflake is also in the shape of a hexagon?
We also see hexagons in the bubbles that make up a
raft bubble. Although we usually think of bubbles as
round, when many bubbles get pushed together on
the surface of water, they take the shape of hexagons.

13. Another common shape in nature is a set of concentric
circles. Concentric means the circles all share the same
center, but have different radii. This means the circles
are all different sizes, one inside the other.
A common example is in the ripples of a pond when
something hits the surface of the water. But we also see
concentric circles in the layers of an onion and the
rings of trees that form as it grows and ages. If you
live near woods, you might go looking for a fallen tree
to count the rings, or look for an orb spider web, which
is built with nearly perfect concentric circles.
4CONCENTRIC CIRCLES IN
NATURE

14. 5MATHS IN OUTER SPACE
Moving away from planet earth, we can also see many
of these same mathematical features in outer space. For
instance, the shape of our galaxy is a Fibonacci spiral.
The planets orbit the sun on paths that are concentric.
We also see concentric circles in the rings of Saturn.
But we also see a unique symmetry in outer space that is
unique (as far as scientists can tell) and that is the
symmetry between the earth, moon and sun that makes
a solar eclipse possible.
Every two years, the moon passes between the sun and
the earth in such a way that it appears to completely
cover the sun. But how is this possible when the moon is
so much smaller than the sun? Every two years, the
moon passes between the sun and the earth in such a
way that it appears to completely cover the sun. But how
is this possible when the moon is so much smaller than
the sun?