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Origina

lStory

TheFascinatingFibo

naccis,autho

r:Sh

onaliC

hinn

iah.

illustrator:

HariK

umar

Nair.Pu

blishe

dby

Pratha

mBo

oks,

https://storyw

eaver.org.in/stories/561

9-the-fascinating-fib

onaccis

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mBo

oks.Re

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theoriginalstory.©Th

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TheFascinatingFibo

naccis

Shon

aliC

hinn

iah

HariK

umar

Nair

letsread

asia.org

growup!

26

Num

bers.Weuse

themeveryday.To

count,measure,callfriends

onthe

phoneand

evento

findoutw

hatsomething

costs.

Butdidyou

knowyou

canalso

usenum

bersto

createpatterns

-geometricalshapes,

rangolidesigns,andmore?

Did

youknow

number

patternscan

beseen

within

patternsin

nature?

1

Awordof

caution:

Althou

ghthereareman

yexam

ples

inna

ture

that

seem

tofollow

theFibo

naccip

attern,the

rearealso

man

yexam

ples

inna

ture

that

dono

t-likefour

leaved

clovers,or

flowerswith

4pe

tals.

Wha

t’sintriguing

,tho

ugh,

isho

woftenthese

Fibo

nacciN

umbe

rsdo

appe

arin

nature.S

ofar,scientistsha

ven’tfigured

outW

HYna

ture

seem

sto

love

Fibo

naccin

umbe

rsso

much.

Maybe

YOUcanfin

dthean

swer

whe

nyou

25

Butfirst,w

hatisa’Num

berPa

ttern’?

ANum

berPa

tternisasequ

ence

ofnu

mbe

rswhe

reeach

numbe

risconn

ectedto

the

previous

onein

ONEspecificway.

Take

thisvery

simplenu

mbe

rpa

ttern:

0,1,2,

3,4...How

iseach

numbe

rin

thissequ

ence

conn

ectedto

theon

ebe

fore

it?Well,every

numbe

rin

thissequ

ence

istheprevious

numbe

rwith

1AD

DED

toit.

Here’san

othe

rnu

mbe

rpa

ttern:

14,12,10

,

2

24

8,6...Eachnum

berin

thissequence

isthe

previousnum

berwith

2SU

BTRACTEDfrom

it.

3

Itispo

ssiblethat

Fibo

naccicam

eacross

Hem

acha

ndra’ssequ

ence

during

histravels,

butsince

hewas

thefirston

eto

introd

uceit

toEu

rope

,the

senu

mbe

rsbe

camekn

ownto

theworld

astheFibo

nacciSeq

uence.

23

Now

foraslightlymoretricky

pattern:

0,1,

3,6,10

,15...How

does

thissequ

ence

work?

Let’s

see.

0+1=11+2=33+3=66+4=10

10+5=

15 Doyouseethepa

tternhe

re?Wha

twillthe

next

numbe

rin

thissequ

ence

be?

Yes,21

,becau

se15

+6=21

.

4

ABRIEF

HISTO

RYTo

endthis

excitingtale

ofFibonacciNum

bers,let’stouch

brieflyupon

thehistory

oftheFibonacciN

umber

Sequence.

Inthe

11thcentury

(almost1000

yearsago),

aJain

scholarand

monk

calledHem

achandra,who

livedin

present-dayGujarat,discovered

aninteresting

mathem

aticalpatternwhile

studyingpoetry

andmusic.H

ewas

lookingatthe

number

ofdifferentways

inwhich

youcould

combine

’long’and’short’sounds

inmusic

tocreate

differentrhythmicpatterns.

Around100

yearslater,an

Italianmathem

aticiancalled

LeonardoFibonacci(c.1170

-c.1250)-wrote

aboutthevery

samemathem

aticalpatternin

hisbook

LiberAbaci,or

’BookofCalculation’

in1202.Fibonaccitravelled

extensivelyalong

theMediterranean

coast,meeting

merchants

fromthe

Eastandfinding

outabouthowthey

didmathem

atics.

22

Now

,let’stake

the’num

berpattern’w

ejust

discussed:1,3,6,10,15...,andsee

ifwecan

createa’SH

APEpattern’from

it.

Wecan!W

enow

havea’shape

pattern’oftriangles

thatgetbiggerand

biggeras

we

increasethe

number

ofdotsaccording

toour

number

pattern!

Anum

berpattern

hasbecom

eashape

pattern!

5

Even

larger

structures

likehu

rrican

esan

deven

somega

laxies

seem

tofollowthe

Fibo

nacciSpiralp

attern.

Fascinating,

isn’tit?

21

Ifyoufoun

dthat

interesting,

it’stim

eyouwereintrod

uced

toabe

autiful

numbe

rsequ

ence

calledtheFibo

nacci(or

Hem

acha

ndra)Seq

uenceof

numbe

rs.T

heFibo

nacciSeq

uenceof

numbe

rsgo

eslikethis:

0,1,1,2,3,5,8,13

,21,34

...

Canyoufin

dthepa

tternthat

conn

ectsthese

numbe

rs?Yes!Everynu

mbe

rin

theFibo

nacci

Sequ

ence

isthesum

ofthetw

onu

mbe

rsbe

fore

it!Like

this.

6

...eveneggs

(seehow

thisspiralgoes

theother

way

(anti-clockwise)as

compared

tothe

clockwise

spiralonpage

14?)!

20

0+1=11+1

=22+1

=33+2

=55+3

=88+5

=13

13+8=21

21+13=34

Gotit?

Good.N

owfor

theREALLY

interestingpart-linking

thisnum

berpattern

topatterns

innature.

7

...snailshe

lls

19

Thenu

mbe

rof

petalsflo

wersha

veareoften

linkedto

Fibo

naccin

umbe

rs!C

anyouthinkof

flowerswith

1,3an

d5pe

tals?(The

seareall

Fibo

naccin

umbe

rs.)Herearesomeexam

ples

tohe

lpyoualon

g.1pe

tal-1.

Anthurium;

2.Ca

llalilies3pe

tals-2

.Bou

gainvillea;3.

Clovers5pe

tals-4

.Tem

pletree;5.H

ibiscus;

6.Jasm

ine

8

Ofcourse

itdoes!

Youcan

seethe

Fibonaccispiralinseashells

(althoughyou

mighthave

totw

istyourhead

aroundabitto

seethe

exactspiralpatternof

theprevious

page)...

18

Flowers

with

2petals

arenotvery

common.

TheCrow

nofThorns,w

hichyou

seehere,is

oneexam

ple.

Flowers

with

4petals

(4isNOTaFibonacci

number)are

alsorare.Countthe

petalsof

flowers

thatyoucom

eacross

andsee

foryourself!

9

Here’stheFibo

nacciSpiralw

ithon

emoregrid

-212

-ad

dedto

ouroriginalfig

ure.

Seeho

wthespiralcontinue

s?Doe

sthespiral

look

familiar?

17

Themostinterestin

gflo

wer

ofall,whe

rethe

Fibo

nacciseq

uenceisconcerne

d,istheda

isy.

Differen

tdaisy

speciesha

ve13

,21,or

34pe

tals-w

hich

areallFibon

acciNum

bers!

10

Now

takethe

samecurved

linethrough

eachofthe

othergrids,from

smallestto

biggest,from

cornerto

oppositecorner,ending

with

the13

squaredgrid.W

hatwegetis

alovely

spiralpattern.

Whatis

thelink

between

thisspiralpattern

createdby

squaredFibonaccinum

bers,andnature?

Well,the

exactsameFibonacciSpiral

canbe

foundin

nature!Where?

Let’ssee,

shallwe?

16

Thereare

evenmore

complex

andstunning

patternsin

naturethatappear

tobe

basedon

theFibonaccinum

bers.

Ifyouare

willing

todo

alittle

math,you

cansee

itforyourself.Shallw

etry

itout?Now

,whatw

ouldwegetifw

esquared*

eachof

thenum

bersin

theFibonaccisequence?

FibonacciSequence:1,1,2,3,5,8,13,etc.Ifw

e’squared’each

ofthesenum

bers,we

would

get:

11

Now

,let’spu

shallthe

gridswe’ve

draw

nso

fartowards

each

othe

r,an

darrang

ethem

like

inthepicture.

Don

e?Now

draw

asm

ooth

curved

linefrom

onecorner

ofthesm

allestgrid

toits

oppo

site

end,

asshow

nin

thefig

ure.

15

1x1=1Sq

uaredor

12=12x2=2Sq

uared

or22

=43x3=3Sq

uaredor

32=95x5=5

Squa

redor

52=25

8x8=8Sq

uaredor

82=

6413

x13

=13

Squa

redor

132=16

9

SotheFibo

nacciSeq

uenceSq

uared:

1-4

-9-

25-6

4-1

69-e

tc.

*Whe

nyoumultip

lyanu

mbe

rby

itself,the

numbe

ris’sq

uared’.

12

Similarly,32is

drawnas

3squares

acrossand

3squares

down.Again,w

eknow

that32=9,

andthere

are9squares

inthe

grid.

52isdraw

nas

5squares

acrossand

5squares

down,m

akingagrid

with

25squares,82as

8squares

acrossand

8squares

down,m

akinga

gridwith

64squares,132squared

isdraw

nas

agrid

with

169squares,and

soon.

14

Now

,justlikeweconverted

anum

berpattern

intoashape

patternwith

thetriangles

before,let’s

tryto

converttheFibonacciSequence

Squaredinto

ashape

pattern.Let’stry

toDRAW

12,22,32andso

on.

12iseasy

enough-itis

justonesquare.

22isdraw

nlike

this-2

squaresacross

and2

squaresdow

n.

Weknow

that22=4,and

thereare

4squares

inthe

figure(wecallthis

figurea’grid’).

13