A full PPT on assignment mathematics patterns in nature thank you

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 naturalvisualpatterns,fromspots ona
leopard to spirals of a fiddlehead fern. Some patterns are as
small as the moleculararrangement ofcrystals and as big
as the massive spiralpatternof the Milky Way Galaxy.
Patterns canbe found everywhereinnature. While one
might think of patterns as uniformand regular, some
patterns appear more randomyet consistent. The definition
of a patternin nature is a consistent form, design, or
expressionthat is not random.
There are multiple causes ofpatterns in nature. Some
patterns are governedby mathematics. These are called the
“GoldenRatio”, this is a rule that describes a specific pattern
in nature. This mathematicalformula is seenin spiral
patterns suchas a snail’s shell or the whorls of a lily

5. SOME OF THE CAUSES OF PATTERNS IN
NATURE ARE:
• Reaction-diffusioneffect:chemicalinteractions ofpigment-formingmolecules in organisms
create the spots, stripes, and other visible patterns;this is also called the turingmodel.
• Law of conservationofmass:predictable patternsofchemical interactions are governed by
this law of nature whichstates that matter is conservedbut changeable in a reaction.
• Law of naturalselection:patternsinthe appearance and behavior ofa species can change
over time due to the interactionofinheritable traits and the organism’s environment.
• Animal behavior:patterns observedin animal behavior, suchas the productionof
hexagons in honeycombs, are oftenthe result of genetics and the environment.
• Laws of physics:the interactionofmatter and energy create predictable patternssuchas
weather patterns due to the interactionofsolar energy, mass,and gravity. Planetary
motionis a predictable patterngoverned by inertia, mass, and gravity.Also, weathering
patterns cancreate unusualrockformations suchas 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 describesobjects or patterns that
are equal on both sides of a dividingsector, as
seen in butterflies, mammals, and insects.

7. MATHEMATICAL PATTERNS IN
NATURE
Spirals are more mathematically complexand
varied. A spiralpatternwould be described as a
circular patternbeginning at a center point and
circling around the center point as the pattern
moves outward. Examples of spirals would be a
chameleon’s tail, analoe plant, or a nautilus
shell. There are various types ofspirals;while
they look very similar, mathematically, theyare
only approximately close. Alogarithmicspiral,
as shownbelow, increases the distance ofeach
spiral logarithmically. Ina Golden Spiral, the
increasingrectangles demonstratePhi, or the
GoldenRatio of 1.618, based on the length versus
the width of eachrectangle. Eachlooks very
similar, but mathematically they are slightly
different.

8. DIFFERENT MATHEMATICS
PATTERN
Waves representthe periodic distributionof
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 lookaround and notice all the
amazingshapes and patterns we see in the world
around us?Mathematics forms the building blocks of
the naturalworld and canbe seenin 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 ConcentricCircles in Nature
5 Maths in outer space

10. 1THE FIBONACCI SEQUENCE
Named for the famous mathematician, Leonardo
Fibonacci, this number sequenceis a simple, yet
profound pattern. Based onFibonacci’s ‘rabbit
problem,’this sequencebegins withthe numbers 1 and
1, and theneach subsequent number is found by
addingthe 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 sequenceare oftenseenin
nature. Afew 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 forma unique
shape known as a Fibonacci spiral, which again, we
see in nature inthe 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 geometricwonders is the
hexagon. A regular hexagonhas 6 sides of equal
length, and this shape is seenagainand again in the
world around us.
The most commonexample of nature usinghexagons
is in a bee hive. Bees build their hive using a
tessellationofhexagons. 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. Althoughwe usually think of bubbles as
round, whenmany bubbles get pushed togetheron
the surface of water, they take the shape of hexagons.

13. Another commonshape in nature is a set of concentric
circles. Concentricmeans 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
somethinghits the surface ofthe water. But we also see
concentriccircles in the layers ofan onion and the
rings of trees that formas 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 concentriccircles.
4CONCENTRIC CIRCLES IN
NATURE

14. 5MATHS IN OUTER SPACE
Moving away fromplanet earth, we canalso see many
of these same mathematicalfeatures inouter space. For
instance, the shape of ourgalaxy is a Fibonacci spiral.
The planets orbit the sun on paths that are concentric.
We also see concentriccircles in the rings of Saturn.
But we also see a unique symmetryinouter space that is
unique (as far as scientists cantell) and that is the
symmetry betweenthe earth, moonand sunthat makes
a solar eclipse possible.
Every two years, the moonpasses betweenthe sunand
the earthin sucha way that it appears to completely
cover the sun. But how is this possible whenthe moonis
so much smaller thanthe sun?Every two years, the
moonpasses betweenthe sunand the earthin sucha
way that it appears to completely cover the sun. But how
is this possible whenthe moonis so much smaller than
the sun?