Patterns in Nature Slide 2 Mathematics.& patterns We dont
know all the answers unlike in class! Mathematics is a science
which looks for patterns and structure Language for understanding
natures patterns Slide 3 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. Slide 4 Patterns in nature Many
different patterns arise in nature. Do we always know what they
mean ? Slide 5 Patterns in plants Slide 6 Slide 7 Mathematics can
be fun! There is mathematics at every level of life you just need
to look! So lets do just that! Slide 8 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 Slide 9 Busy
Bunnies Slide 10 Slide 11 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 = 13 8+ 13 = 24 Slide 12
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 Slide 13 Nature and Fibonacci White calla
lily Slide 14 Nature and Fibonacci Euphorbia Slide 15 Nature and
Fibonacci trillium Slide 16 Nature and Fibonacci Black eyed susan
Slide 17 More Fibonacci Pinecones and pineapples Count the number
of spirals. Slide 18 Spirals in a pine cone: clockwise and
anti-clockwise Slide 19 And more Slide 20 Spirals Slide 21 Slide 22
Golden Ratio Compute the ratio of Fibonacci numbers: 2 1 = 3 2 = 5
3 = 8 5 = 13 8 = 21 13 = Slide 23 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 Slide 24 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
Slide 25 The Golden ratio in nature Slide 26 Great Wall of China
Parthenon, Greece In Art & Architecture.. The Mona Lisa Slide
27 What we learnt today Fibonacci numbers: Busy Bunnies Pineapples
and pinecones: # spirals Spirals in nature The Golden ratio
