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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/