MATHEMATICS IN NATURE

Go down deep enough into anything and you will find mathematics.

~ Dean Schlicter

But, it all started with “nature”

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Bilateral Symmetry

Symmetric about an axis

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Radial SymmetryRational symmetry about a fixed point

called center

Star fish

Wheel

LemonPetals of a flower

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Symmetry in Mathematics

1 × 8 + 1 = 9

12 × 8 + 2 = 98

123 × 8 + 3 = 987

1234 × 8 + 4 = 9876

12345 × 8 + 5 = 98765

123456 × 8 + 6 = 987654

1234567 × 8 + 7 = 9876543

12345678 × 8 + 8 = 98765432

123456789 × 8 + 9 = 987654321

1 × 9 + 2 = 11

12 × 9 + 3 = 111

123 × 9 + 4 = 1111

1234 × 9 + 5 = 11111

12345 × 9 + 6 = 111111

123456 × 9 + 7 = 1111111

1234567 × 9 + 8 = 11111111

12345678 × 9 + 9 = 111111111

123456789 × 9 +10 = 1111111111

1 × 1 = 1

11 × 11 = 121

111 × 111 = 12321

1111 × 1111 = 1234321

11111 × 11111 = 12345431

111111 × 111111 = 12345654321

1111111 × 1111111 = 1234567654321

11111111 × 11111111 = 13456787654321

111111111 × 111111111 = 12345678987654321

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Vitruvian Man

If you stand straight with your feet together and stretch your

arms,

Length of the outspread arms = Height of the man

The maximum width of the shoulders is a quarter of the

height of a man.

From below the chin to the top of the head is one-eighth of

the height of a man.

If you open your legs enough that your head is lowered by

one-fourteenth of your height and raise your hands enough

that your extended fingers touch the line of the top of your

head,

Space between the legs will be an equilateral triangle.

Center of extended limbs will be the navel.

Leonardo da Vinci’s Work

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Golden RatioA+B is to A as A is to BGolden Ratio = 1.61803398875…

The Last Supper

Mona Lisa

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Pi Discovered independently by first civilizations to begin

agriculture, to give a relationship between square and circle

◦Babylonians – 3.125◦Egyptians – 3.16

◦Chinese – 3◦Hebrews - 3

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Geometric Series

Bacteria such as Shewanella oneidensis multiply by doubling their population in size for every 40 minutes.

Volume occupied by N-dimensional hypercubes.

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Fibonacci Series

Sunflower

Pineapple

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Fibonacci Series

Aloe PlantNautilus shell

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Perfect ShapesEarth – Sphere – perfect shape

for minimizing the pull of the gravity to its outer edges.

Beehives – Hexagons – close packing is important to maximize the use of space

If you love nature, but not mathematics, it’s because

you love nature for what it looks like, but not for

"what it is" :-)

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May the Maths be with

you ;-)

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References

http://malini-math.blogspot.in/2010/08/maths-and-nature.html

http://www.slideshare.net/sagarian/maths-in-nature-complete

http://en.wikipedia.org/wiki/Vitruvian_Man

http://madmaths.edublogs.org/maths-in-nature-3/

http://library.thinkquest.org/trio/TTQ05063/phibeauty3.htm

http://www.utexas.edu/features/2005/math/