Maths and Nature for Layman

8/4/2019 Maths and Nature for Layman

http://slidepdf.com/reader/full/maths-and-nature-for-layman 1/175



Patterns, Nature, & Math

Are They Interconnected?

Mrs. Christi Wilson

Greenbrier Middle School

Maths of nature



•“If people do not believe

that mathematics is simple,it is only because they do

not realize how complicated life is “

(John Von Neumann)



Tree Trunk Mushroom

Plants

Granite Fossils

Minerals

Butterfly Tiger

Animals

Waves Dew

Water

"Natural" Patterns



Natural beauties







Natural Intelligence

• Some Insects can performs

complicated Tasks which is

beyond Human beings.

• Unknowingly they apply quite

advance mathematics.





spider’s web



spider’s web



spider’s web



spider’s web



spider’s web



Spider’s web is 25 times stronger than

the same thickness steel wire





• Termites air-conditioned

mound with chimney.

• It is an EngineeringMarvel.

•

Up to 30 feet high.• CO2 /O2 balance .











S

http://www.abc.net.au/science/photos/mathsinnature/photo5.htm

http://www.abc.net.au/science/photos/mathsinnature/photo5.htm



Square

pattern

Non Useful

empty space



Non Useful

empty space

Hexagonal pattern



Hexagonal packing

Fibonacci Numbers



Fibonacci Numbers

Nature has it’s own Number

System called Fibonacci

number system which is

applicable to all those

things which take birthand grow primarily and

almost all aspects of life



Fibonacci “ Leonardo Da vinci”

http://images.google.com/imgres?imgurl=http://www.math.ethz.ch/fibonacci/fibonacci.jpg/image&imgrefurl=http://www.math.ethz.ch/fibonacci/Eroeffnung&h=268&w=220&sz=13&hl=en&start=1&tbnid=MjZIlG3_mgGOXM:&tbnh=113&tbnw=93&prev=/images%3Fq%3Dfibonacci%26svnum%3D10%26hl%3Den%26lr%3D



Role of Fibonacci numbers

• Trees , Plants, leaves, flowers, stems

• Bee Hive, spider’s web • Human Body

• Various insects an Animals• music, art, Culture, and Science

• Business, Ads, and share market

St t ith i f bbit



Start with one pair of rabbits

Rules of growth

1. Every new born pair becomes adult in

one month.

2. Every adult pair after one month givesbirth to one pair every month.

3. No rabbit dies.

population of rabbits after one year = ?



Modelization of a population

• First month

• Secod month

• Sixth month

• third month

• Fourth month

• Fifth month

Adult pairs Young pairs

Sequence: 1, 1, 2, 3, 5, 8, … Fn+1= Fn + Fn-1







Month Pairs of Rabbits

1 1

2 1

3 2

4 3

5 5



Fibonacci Series

• The rule for the sequence?

1, 1, 2, 3, ?, ?, ….

• The Answer :1, 1, 2, 3, 5, 8, 13, 21, …

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

Fibonacci’s Rabbit Colony



Fibonacci s Rabbit Colony

1 1 2 3 5 8 13 2134

55

89

144

0

20

40

60

80

100

120

140

160

J a n u a r y

F e b r u a r y

M a r c h

A p r i l

M a y

J u n e

J u l y

A u g u s t

S e p t e m b e r

O c t o b e r

N o v e m b e r

D e c e m b e r

Pairs of Rabbits



New born tender



‘sneezewort’

One

One

Two

Three

Five

Eight

New born ---- tenderAdult ---- strongGives birth ----branches out

http://ccins.camosun.bc.ca/~jbritton/fibslide/fib12.gif






1 1 2 3 5 8 13 21 34 55




1, 1 ,2 ,3 ,5 ,8 ,13 ,21 ,34 ,55 ,…

1/1, 2/1, 3/2, 5/3, 8/5, 13/8…

1, 2, 1.5, 1.666, 1.6, 1.625, …

Golden ratio

phi = 1.6180339887…



Phi = 1 6180339887



Phi = 1.6180339887…

• Golden ratio

• Golden mean

• Golden section

• Fibonacci ratio

• Divine Ratio

• Sacred ratio



<>



Golden Spiral manipulative

http://nlvm.usu.edu/en/nav/frames_asid_133_g_3_t_1.html?open=instructions

http://nlvm.usu.edu/en/nav/frames_asid_133_g_3_t_1.html?open=instructions





(Sh ll)



(Shell)





The human feotus develops along the lines of a Fibonacci spiral



Sheep



Sheep







Galaxies

Sea Shell



A low pressure area over Iceland showsan approximately logarithmic spiral pattern

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

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

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

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



Spirals in the Galaxy



p y







Rose petals





Sunflower with 34 petals



Sunflower with 34 petals

1 13



Flowers!1

2

3

5

8

13

21

white calla lilyeuphorbia trillium

http://ccins.camosun.bc.ca/~jbritton/fibslide/fib03.jpg



white calla lily

bloodroot black-eyed susan

daisy family

13, 21, 34, 55

or 89 petals

Leaf arrangements










g









Leaves, petals and



, p

seeds arranegment

0·382x360 = 137·5°

222.5/137.5 =Φ

= 1.618



• In a 120 0 arrangement like a fan,

4th one would hide the first leaf

Leaf arrangements



g• If we look down on a plant, the leaves are

often arranged so that leaves above do nothide leaves below.

• Each gets a good share of the sunlight and

catches the most rain to channel down to theroots as it runs down the leaf to the stem.

• Insects can collect pollens easily.

Why does nature like using Phi in so many plants?



• Although hexagonal symmetry is

the best packing for circular seeds,

it doesn't answer the question of

how leaves should be arranged

round a stem or how to pack

flower-heads with seeds that grow in size.














Fi di G ld i



Finding Golden ratio

• As seeds grow older they are pushedout.



Left to right: A sunflower picture from The Algorithmic Beauty of Plants , P.

Prusinkiewicz. A cactus by C. Smith. Another Cactus by C. Smith and M.Fuhrer.





http://www.forbes.com/asap/2000/1127/162.html












Pine cones pa[na kaona













Banana Apple

In vegetable?









5

Red

Spirals

8

Blue

Spirals







1 1.618

WHOLE

WHOLE = LARGE = GOLDEN MEAN

LARGE SMALL





Human Hand



Human Hand



DNA



DNA









• Dr. StephenMarquardt, a former



q ,plastic surgeon, hasused the goldensection, thatenigmatic numberthat has long stood for

beauty, and some of its relatives to make amask that he claims isthe most beautiful

shape a human facecan have.



http://www.mathematicianspictures.com/sp_Golden_Mean.htm



http://www.mathematicianspictures.com/sp_Golden_Mean.htm



Leonardo Da Vinci, Mona















स धम समभा



Symbol

Musical instruments are often based

http://www.sathyasai.org/



on phi

Musical scales are based on

Fibonacci numbers;



Fibonacci numbers;

piano keyboard scale of 13

keys has 8 white keys and 5black keys, split into groups of

3 and 2.

• 13 notes separate each octave of 8 notes in a scale,

of which the 5th and 3rd notes create the basic

foundation of all chords, and are based on whole

tone which is 2 steps from the root tone, that is

the 1st note of the scale.

Golden mean gauge

http://www.goldenmeangauge.co.uk/



gaaolDna Anaupat maapI

http://www.goldenmeangauge.co.uk/

















The Bagdad City Gate



Dome ofSt. Paul:London,England



Windson Castle































Golden Caliper



Advertisement

ART

rchitecture

MUSIC



http://www.nestle.ca/en/Products/Browse_by_Category/Chocolates/kit_kat_4_finger.htm

http://www.trekbikes.com/bikes/2003/mountain/fuel90.jsp



Human expectations occurin a ratio that approaches Phi

http://www.surrey.ac.uk/Alumni/credit_card/

http://www.nestle.ca/en/Products/Browse_by_Category/Chocolates/kit_kat_4_finger.htm

http://www.trekbikes.com/bikes/2003/mountain/fuel90.jsp



•

our brains are hardwired to find Fibonacciprogressions naturally pleasing.

• Changes in stock prices largely reflect human

opinions, valuations andexpectations. Humans exhibit positive and

negative evaluations of the opinions they hold

in a ratio that approaches phi, with 61.8%positive and 38.2% negative.

• Used to predicting stock market behaviour.

Shape of Universe



http://home.aanet.com.au/robertw/Stella.html



Rings of Saturn







Further classic subdivisions of the rectanglealign perfectly with major architectural features



Further classic subdivisions of the rectangle align perfectly with major architectural features of the structure.

align perfectly with major architectural featuresof the structure.

Egyptians in the design of the pyramids,





•The CN Tower in Toronto,the tallest tower.



•The ratio of observationdeck at 342 meters to thetotal height of 553.33 is0.618, the reciprocal of Phi!

Notre Dame in Paris







http://evolutionoftruth.com/div/nature.htm

http://evolutionoftruth.com/div/face.htm

http://evolutionoftruth.com/div/hand.htm





http://evolutionoftruth.com/div/nature2.htm



























http://www.mathematicianspictures.com/PHI_GOLDEN_RATIO_GOLDEN_MEAN/Phi_Golden_Ratio_Golden_Mean.htm



2

http://www.mathematicianspictures.com/PHI_GOLDEN_RATIO_GOLDEN_MEAN/Phi_Golden_Ratio_Golden_Mean.htm



8 5

2

1





Phi as repeated square root



Phi as continued fraction



Fibonacci numbers define key points in human aging

Huma

n Age

Development Stage

Key Attributes



0 Gestation Conception

1 Newborn Birth

1 Infant Walking, vocalizing

2 Toddler Talking, expressing, imitating

3 Toddler Self image and control, toilet training

5 Early child Formal education begins

8 Mid child Age of reason, knowing of right and wrong

13 Adolescent Thinking, puberty, sexual maturation and drive

21 Youngadult

Full physical growth, adult in society, educationcomplete, beginning career, financial

responsibility, eligible for voting34 Mid adult Refinement of adult skills, parenting role

55 Elder adult Fulfillment of adult skills, serving, retirement beginswith eligibility for Medicare, Social Security

89 Completion Insight and wisdom into life

Surely it is logical to conclude



that the connections exist

because nature, mathematicsand the human mind, with its

subtle sense of beauty, have onesupreme link— they are all the

created products of God, theMaster Designer - Russel Grigg



Date post:	07-Apr-2018
Category:	Documents
Upload:	amarnath-murthy
View:	222 times
Download:	0 times

Maths and Nature for Layman

Documents