patterns in nature session1

8/14/2019 Patterns In Nature Session1

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What is

life?


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A living organism?

Old view:

Living organisms can make choices, move, react to theenvironment and reproduce

Modern view:

Life is a property of special kinds of chemicals

All living organisms have a unique chemical called DNA

Life is a special arrangement of the usual

chemical building blocks found in the physicalworld


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Deoxyribose in DNA

Ribose in RNA

Can be Adenine(A), Thymine(T),

Guanine(G), Cytosine (C)


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Life operates withinthe physicalenvironment

Life is a special arrangement of the usualchemical building blocks

The physical environment is regulated bymathematical laws of physics and chemistry

and since life exists within this physicalworld, the same laws control the organismsresponse to its genetic instructions


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Mathematics.&

patterns We dont know all the answers unlike in class!

Mathematics is a science which looks forpatterns and structure

Language for understanding natures patterns


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Patterns in Nature


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Studying cool patterns

in nature Astronomers model the patterns found in giantspiral galaxies

Physicists: movements of atoms

Biologists & Doctors try to understand the randompatterns of growth, spread of disease .

Geologists study the meandering of rivers,tortuous coastlines, and awe-inspiring mountainlandscapes.


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Patterns in nature

Many differentpatterns arise in

nature. Do we always know

what they mean ?

Or if it could havebeen otherwise?


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Also in plants


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Mathematics can be

fun! There is mathematics at every level of

life

you just need to look!

So lets do just that!


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Busy Bunnies

A newly born male-female pairstarts.

Can mate once they are 1 month old. Female produces a pair 1 month after

mating.

And so on


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Busy Bunnies


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Busy Bunnies


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Fibonacci Series

The rule for the sequence?1, 1, 2, 3, ?, ?, .

The Answer :1, 1, 2, 3, 5, 8, 13, 24,

1+ 1 = 21+ 2 = 32+ 3 = 53+ 5 = 85+ 8 = 138+ 13 = 24


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Who was Fibonacci ? Greatest European mathematician of

the middle ages

Born in Pisa, Italy, the city with the

famous Leaning Tower,~ 1175 AD

Major contributions in arithmetic,

algebra and number theory

Decimal system
http://www-groups.dcs.st-and.ac.uk/~history/Mathematicians/Fibonacci.html


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Nature and Fibonacci

White calla lily


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Euphorbia


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trillium


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Black eyed susan


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More Fibonacci

Pinecones and pineapples

Count the number of spirals.


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Spirals in a pine cone: clockwise

and anti-clockwise


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And more


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Spirals


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Spirals


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Golden Ratio

Compute the ratio of Fibonacci numbers:

2 1 =

3 2 =5 3 =

8 5 =

13 8 =21 13 =


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Another fun way to get

Golden ratio Choose any number, say x.

Find x + 1

Find 1/x

Do the above two steps over and overand over


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The Golden ratio

in nature

In Art & Architecture


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Great Wall of China

Parthenon, Greece

In Art & Architecture..

The Mona Lisa


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So why do spirals occur ?

Helps in efficient packing of seeds.

But flowers and pinecones have todeal with growing.


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Finding Golden ratio

As seeds grow older they are pushedout.


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What we learnt today

Fibonacci numbers:

Busy Bunnies

Pineapples and pinecones: # spirals

Spirals in nature

The Golden ratio

patterns in nature session1

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