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Mathematics is all around us. As we
discover more and more about our
environment and our surroundings we see
that nature can be described mathematically.
The beauty of a flower, the majesty of a tree,
even the rocks upon which we walk can
exhibit natures sense of mathematics. Here
are some basic mathematical concepts
described in nature.
Object is symmetric if it can be divided into two or
more identical pieces that are arranged in an
organized fashion. This means that an object is
symmetric if there is a transformation that moves
individual pieces of the object but doesn't change
the overall shape. There are many types of
symmetry, in this we will see:
1.Bilateral symmetry
2.Radial symmetry
3
Symmetrical arrangement, as of an organism or a body part
,
along a central axis, so that the body is divided into equivale
nt right and left halves by only one plane. There are many
examples of bilateral symmetry in nature………
4
The human face can be divided from center to get
two identical/mirrored parts.
5
Butterfly's center body divides its
two identical wings. 6
• An symmetric arrangement in which the
object can be divided into many identical
parts.
• In nature there many examples of radial
symmetry like……
7
The petals of many flowers can be divided to form
identical parts.
8
Star fish can be divided in around 10 symmetrical
parts. 9
• Parallel lines are lines in a plane which do
not meet; that is, two lines in a plane that
do not intersect or touch at any point are
said to be parallel.
• In nature there are many examples of
parallel lines, some of them are……
10
The veins of leaves never meet, so they are
parallel.
11
The strips on body of animals like Zebra and
Tiger never meet, so they are parallel.
12
These thin threads of spiders’ web never meet
each other. 13
• Shapes are different closed figure formed
with line segments and curves.
• Shapes are of two types:
–2 dimension: square, rectangle, triangle,
circle, etc.
–3 dimension: cube, cuboid, cone,
sphere, cylinder, etc.
• In nature all object are in specific shapes
like….. 14
Sections of bee hives are hexagon (5 sided
polygon)
15
All planets including earth are in the sphere
shape.
16
The mountains we see around seems
to be in cone shape. 17
• The Fibonacci sequence is a series of
numbers that follow a unique integer
sequence.
• The sequence is like:
0,1,1,2,3,5,8,13,21,36….. Did you
notice the sequence: 0, 1, 1(0+1),
2(1+1), 3(1+2), 5(2+3), 8(3+5)……….
18
In nature the
best example
of Fibonacci
sequence is
the birth
system of
rabbits.
19
This sequence was
discovered
• Patterns are link of different numbers,
colors, shapes, etc. in a particular series.
• There are different beautiful and wonderful
patterns we can discover in nature. Some
of them are……..
20
Did you notice the arrangement of leaves to
form a triangle.
21
See the black and white pattern on the zebra’s
fur.
22
Superb!!! Looking at this cool pattern I will never
like to eat this fruit and spoil the pattern. 23
Wow!!!!!!! Such a wonderful wavy arrangement
of sand made by wind. 24
This is an atom – the smallest element on
earth. See the protons, neutrons, electrons
they are spherical and their orbit is also
circular.
These are the eggs of an insect. See the
perfect sphere shape.
This beetle has a wonderful black – yellow strip
pattern and also it is bilaterally symmetrical.
These triangle shaped grass are one more
example of bilateral symmetry.
Can you notice the thorns making this cactus
radially symmetric.
This beautiful parrot with red – green – blue
pattern is also bilaterally symmetrical.
This spherical watermelon is radially symmetric
– divided by the dark green strip pattern.
Observe these spherical
planets and their oval
orbits forming a wonderful
pattern.
This spiral galaxy – milky way form an attractive
spiral pattern.
• It is truly said by Dean Schleicher,
“Go deep down enough anything, and you
will find mathematics.”
• Really mathematics ranges from the
smallest particle on earth to the universe.
35
36
37

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Book 1

  • 1.
  • 2. Mathematics is all around us. As we discover more and more about our environment and our surroundings we see that nature can be described mathematically. The beauty of a flower, the majesty of a tree, even the rocks upon which we walk can exhibit natures sense of mathematics. Here are some basic mathematical concepts described in nature.
  • 3. Object is symmetric if it can be divided into two or more identical pieces that are arranged in an organized fashion. This means that an object is symmetric if there is a transformation that moves individual pieces of the object but doesn't change the overall shape. There are many types of symmetry, in this we will see: 1.Bilateral symmetry 2.Radial symmetry 3
  • 4. Symmetrical arrangement, as of an organism or a body part , along a central axis, so that the body is divided into equivale nt right and left halves by only one plane. There are many examples of bilateral symmetry in nature……… 4
  • 5. The human face can be divided from center to get two identical/mirrored parts. 5
  • 6. Butterfly's center body divides its two identical wings. 6
  • 7. • An symmetric arrangement in which the object can be divided into many identical parts. • In nature there many examples of radial symmetry like…… 7
  • 8. The petals of many flowers can be divided to form identical parts. 8
  • 9. Star fish can be divided in around 10 symmetrical parts. 9
  • 10. • Parallel lines are lines in a plane which do not meet; that is, two lines in a plane that do not intersect or touch at any point are said to be parallel. • In nature there are many examples of parallel lines, some of them are…… 10
  • 11. The veins of leaves never meet, so they are parallel. 11
  • 12. The strips on body of animals like Zebra and Tiger never meet, so they are parallel. 12
  • 13. These thin threads of spiders’ web never meet each other. 13
  • 14. • Shapes are different closed figure formed with line segments and curves. • Shapes are of two types: –2 dimension: square, rectangle, triangle, circle, etc. –3 dimension: cube, cuboid, cone, sphere, cylinder, etc. • In nature all object are in specific shapes like….. 14
  • 15. Sections of bee hives are hexagon (5 sided polygon) 15
  • 16. All planets including earth are in the sphere shape. 16
  • 17. The mountains we see around seems to be in cone shape. 17
  • 18. • The Fibonacci sequence is a series of numbers that follow a unique integer sequence. • The sequence is like: 0,1,1,2,3,5,8,13,21,36….. Did you notice the sequence: 0, 1, 1(0+1), 2(1+1), 3(1+2), 5(2+3), 8(3+5)………. 18
  • 19. In nature the best example of Fibonacci sequence is the birth system of rabbits. 19 This sequence was discovered
  • 20. • Patterns are link of different numbers, colors, shapes, etc. in a particular series. • There are different beautiful and wonderful patterns we can discover in nature. Some of them are…….. 20
  • 21. Did you notice the arrangement of leaves to form a triangle. 21
  • 22. See the black and white pattern on the zebra’s fur. 22
  • 23. Superb!!! Looking at this cool pattern I will never like to eat this fruit and spoil the pattern. 23
  • 24. Wow!!!!!!! Such a wonderful wavy arrangement of sand made by wind. 24
  • 25.
  • 26. This is an atom – the smallest element on earth. See the protons, neutrons, electrons they are spherical and their orbit is also circular.
  • 27. These are the eggs of an insect. See the perfect sphere shape.
  • 28. This beetle has a wonderful black – yellow strip pattern and also it is bilaterally symmetrical.
  • 29. These triangle shaped grass are one more example of bilateral symmetry.
  • 30. Can you notice the thorns making this cactus radially symmetric.
  • 31. This beautiful parrot with red – green – blue pattern is also bilaterally symmetrical.
  • 32. This spherical watermelon is radially symmetric – divided by the dark green strip pattern.
  • 33. Observe these spherical planets and their oval orbits forming a wonderful pattern.
  • 34. This spiral galaxy – milky way form an attractive spiral pattern.
  • 35. • It is truly said by Dean Schleicher, “Go deep down enough anything, and you will find mathematics.” • Really mathematics ranges from the smallest particle on earth to the universe. 35
  • 36. 36
  • 37. 37