Patterns in Nature.

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Presentation transcript:

Patterns in Nature

Mathematics….& patterns We don’t know all the answers unlike in class! Mathematics is a science which looks for patterns and structure Language for understanding nature’s patterns

Studying cool patterns in nature Astronomers model the patterns found in giant spiral galaxies Physicists: movements of atoms Biologists & Doctors try to understand the random patterns of growth, spread of disease . Geologists study the meandering of rivers, tortuous coastlines, and awe-inspiring mountain landscapes.

Patterns in nature Many different patterns arise in nature. Do we always know what they mean ?

Patterns in plants

Mathematics can be fun! There is mathematics at every level of life… …you just need to look! So let’s do just that!

Busy Bunnies A newly born male-female pair starts. Can mate once they are 1 month old. Female produces a pair 1 month after mating. And so on…

Busy Bunnies

Busy Bunnies

Fibonacci Series The rule for the sequence? 1, 1, 2, 3, ?, ?, …. The Answer : 1, 1, 2, 3, 5, 8, 13, 24, … 1+ 1 = 2 1+ 2 = 3 2+ 3 = 5 3+ 5 = 8 5+ 8 = 13 8+ 13 = 24

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

Nature and Fibonacci White calla lily

Nature and Fibonacci Euphorbia

Nature and Fibonacci trillium

Nature and Fibonacci Black eyed susan

More Fibonacci Pinecones and pineapples… Count the number of spirals.

Spirals in a pine cone: clockwise and anti-clockwise

And more

Spirals

Spirals

Golden Ratio Compute the ratio of Fibonacci numbers: 2 ÷ 1 = 3 ÷ 2 = 5 ÷ 3 = 8 ÷ 5 = 13 ÷ 8 = 21 ÷ 13 =

Another fun way to get Golden ratio Choose any number, say x. Find x + 1 Find 1/x (reciprocal) Do the above two steps over and over and over…

Another fun way to get Golden ratio Choose any number, say x. Find x + 1 Find square root of result Do the above two steps over and over and over…

The Golden ratio in nature

In Art & Architecture.. Great Wall of China Parthenon, Greece The Mona Lisa

What we learnt today… Fibonacci numbers: Busy Bunnies Pineapples and pinecones: # spirals Spirals in nature The Golden ratio