polígonos regulares estrelados y de fantasía

7/23/2019 Polgonos Regulares Estrelados y de Fantasa

1/35

PEFAKEOEW ZNK^FHZNWNWRZNFFHBEW Q BNIHORHWH/

Ghzfew Dnzoo Yafgdnw Zeco


2/35

Izc~fhw phzh gfg~few pzachzaew q

wng~obhzaew bn pefkeoew znk~fhznw aowgzarew

no ~oh gazg~oinznogah bn zhbae geoegabe/

AWOJ 811/1:7

Geowrz~ggao knecrzagh bn pefkeoew

znk~fhznw/

AWOJ :0:/748

Bn fh izc~fh bnf znh bn ~o pefkeoe

znk~fhz hf Rneznch bn Yafgdnw/

AWOJ :0:/74:

Geowrz~ggao q gfg~few bn pefkeoew

znk~fhznw goghyew nwrznffhbew q w~w

ihorhwhw/ BNZNGDEW ZNWNZYHBEW/

PZEDAJABH W^ ZNPZEB^GGAO/

BBA/ :02/090/

Bn fh izc~fh bnf gfg~fe bnf znh bn ~o

pefkeoe znk~fhz nwrznffhbe hf Rneznch bn

Yafgdnw AA/ BNZNGDEW ZNWNZYHBEW/

PZEDAJABH W^ ZNPZEB^GGAO/

BBA/ :02/098/

GEORHGRE

Hpernch bn ~o pefkeoe znk~fhz//////////////////////////////////////////////////////////////////////////////////////////////// >

Baj~le Knecrzage x~n af~wrzh fhw bnoecaohgaeonw e wacjefekh bn nfncnorew pzachzaew q

wng~obhzaew bn fh geowrz~ggao bn few pefkeoew znk~fhznw////////////////////////////////////////////////////////// 9

Geowrz~ggao knonzhf bn ~o pefkeoe znk~fhz////////////////////////////////////////////////////////////////////////// 9

Hpfaghgao bn izc~fhw /////////////////////////////////////////////////////////////////////////////////////////////////////////////// ;

Geowrz~ggao bn fhw bayawaeonw hzcoaghw/ //////////////////////////////////////////////////////////////////////////////// 8:

Bn fh izc~fh bnf znh bn ~o pefkeoe znk~fhz hf Rneznch bn Yafgdnw/ ////////////////////////////////// 89

Geowrz~ggao q gfg~fe bn pefkeoew znk~fhznw goghyew nwrznffhbew/ /////////////////////////////////////////// 81

znh bn pefkeoew znk~fhznw nwrznffhbew/ ////////////////////////////////////////////////////////////////////////////////// 81

W~ch bn few ok~few aornzaeznw $Wa!//////////////////////////////////////////////////////////////////////////////////////////// :8

Geowrz~ggao knecrzagh bn fhw nwrznffhw/////////////////////////////////////////////////////////////////////////////// :8

Nwrznffh Pnorhkeohf/ ///////////////////////////////////////////////////////////////////////////////////////////////////////////////// ::

Pefkeoew bn ihorhwh/ ////////////////////////////////////////////////////////////////////////////////////////////////////////////// :;

Bn fh izc~fh bnf gfg~fe bnf znh bn ~o pefkeoe znk~fhz nwrznffhbe hf Rneznch bn Yafgdnw AA/ ///// :1

Rhjfh bn Af~wrzhgaeonw ////////////////////////////////////////////////////////////////////////////////////////////////////////////////// 78


4/35

Pefkeoew Znk~fhznw& Nwrznffhbew q bn Ihorhwh # Ghzfew Dnzoo Yafgdnw Zeco/

:

IZC^FHW PHZHGFG^FEW PZACHZAEW QWNGÔBHZAEW BNPEFKEOEW ZNK^FHZNW&AOWGZAREW NO ÔHGAZGÔINZNOGAH BNZHBAE GEOEGABE



5/35


7

Izc~fhw phzh gfg~few pzachzaew q wng~obhzaew bn pefkeoewznk~fhznw& aowgzarew no ~oh gazg~oinznogah bn zhbae geoegabe/

No knonzhf& fh geowrz~ggao bn ~o pefkeoe znk~fhz znx~anzn bnf zhbae bn fhgazg~oinznogah x~n fe gazg~owgzajn= geoegabe nwrn zhbae z& pebncew ~oaynzwhfa|hzizc~fhw bn gfg~few bnf znh& bnf pnzcnrze& bn few fhbew& fh hpernch q bn few ok~fewx~n fe iezcho/

Bnoecaohbew pez

Bacnowao bn ~o fhbe bn ~o pefkeoe znk~fhz/

Izc~fh


8/35


9

Baj~le Knecrzage x~n af~wrzh fhw bnoecaohgaeonw e wacjefekh bn nfncnorewpzachzaew q wng~obhzaew bn fh geowrz~ggao bn few pefkeoew znk~fhznw/

Geowrz~ggao knonzhf bn ~o pefkeoe znk~fhz

Nlncpfe< Geowrz~ggao bn ~o ^obngkeoe $pefkeoe bn 88 fhbew& af~wrzhgao/ 8!/

Af~wrzhgao 8


9/35


;

Hpfaghgao bn izc~fhw

Nlncpfe 8< Hpfaghgao bn fh izc~fh bnf znh bn pefkeoew znk~fhznw/

Gfg~fe bnf znh bn ~o ~obngkeoe znk~fhz aowgzare no ~oh gazg~oinznogah bn zhbae

8:gc/

BHREW&>:o

790wno wno

o

& f~nke&

7907:&;: 0&>209

88wno wno

Hpfaghobe fh izc~fh knonzhf wn ranon&> 822 0&>209

2:4&8>>:

oH z wno ~

H gc

H gc

Z< Nf znh bn nwrn ~obngkeoe nw bn :2:4&8>>:gc /


10/35


4

Nlncpfe :< Hpfaghgao bn fh izc~fh bnf pnzcnrze bn pefkeoew znk~fhznw/

Dhffhz nf pnzcnrze bn ~o pefkeoe znk~fhz bn :9 fhbew n aowgzare no ~oh gazg~oinznogahbn 80 c/ bn bacnrze/

BHREW /z c

790

840 840: 9&1:7 0&8:0>:9

wno wno wno wnoo o

Znncpfh|hobe no fh izc~fh knonzhf bnf pnzcnrze :9 0&8:0>

:90 0&8:0>

78&77

P z o wno c

P c

P c

P c

Z< Nf pnzcnrze bnf pefkeoe nw bn 78&77c /


11/35


1

Nlncpfe 7< Hpfaghgao bn fh izc~fh bacnowao bn few fhbew bn ~o pefkeoe znk~fhz/

G~ore cabn ~o fhbe bn ~o dnprkeoe znk~fhz aowgzare no ~oh gazg~oinznogah bn 4 gcbn zhbae5

BHREW & ;827 0& 27744; ;

wno wno wno wnoo

Hpfaghgao bn fh izc~fh knonzhf8& 2:4>;: 4

:

89 0&27744

9&12:04

F z wno gc

F wno gc

F gc

F gc

Z< nf fhzke bn ~o fhbe bn nwrn dnprkeoe nw bn 9&12:04gc /


12/35


80

Nlncpfe 2< Hpfaghgao bn fh izc~fh hpernch bn ~o pefkeoe znk~fhz/

Nf gfg~fe bnf hpernch * * bn ~o pefkeoe znk~fhz gezznwpeobn hf zhbae bn fh

gazg~oinznogah aowgzarh no nf pefkeoe/ Hbncw gezznwpeobn h fh pnzpnobag~fhz bnwbn

nf gnorze h g~hfx~anzh bn few fhbew bn ~o pefkeoe znk~fhz/

G~f nw fh hpernch bn ~o bngkeoe znk~fhz aowgzare no ~oh gazg~oinznogah bn :0 gcbn zhbae5

Hpfaghobe fh izc~fh knonzhf2

z gc

gco

gc

gc

gc

gc

Z< Fh hpernch bn nwrn pefkeoe nw bn81&;>2gc / bn fhzke/


13/35


88

GEOWRZ^GGAOKNECRZAGH BNPEFKEOEW ZNK^FHZNW/



14/35


8:

Geowrz~ggao bn fhw bayawaeonw hzcoaghw/

8/ Rzh|hz nlnw ghzrnwahoew no nf pfhoe& w~ aornzwnggao nw nf gnorze bn fhgazg~oinznogah x~n gazg~owgzajn hf pefkeoe bn zhbae z $Af~wrzhgao :!

:/ Wanobe o nf ocnze bn fhbew bn ~o pefkeoe znk~fhz& wn w~jbayabn nf bacnrze8 :

q q no o fhbew ak~hfnw $Af~wrzhgao 7!/ Nw geoynoanorn ningr~hz ~oh rzhwfhgao

phzhfnfh bn ~oh w~jbayawao rnorhrayh no ~o zhqe g~qe ezakno no8

q &

pzeqngrobefe h ~o p~ore geoynoanorn | no fhw o phzrnw ak~hfnw x~n

znpznwnorho few fhbew bnf pefkeoe $Af~wrzhgao 2!/

Wa nf pefkeoe nw ~o egrkeoe/ Rzhwfhgao phzhfnfh eprhrayh

Af~wrzhgao :

Af~wrzhgao 7 Af~wrzhgao 2


15/35


87

F~nke rzhwfhbhz nwrew p~orew no fh w~jbayawao bnf zhqe hf bacnrze pez8 :

q q

rzhwfhgao phzhfnfh/

7/

Dhganobe gnorze no 8q q geo zhbae 8 :q q wn rzh|h ~o hzge x~n aornzwngrh hf nln tno

8i q

:i & wanobe hbncw rhoknorn h fh gazg~oinznogah/ Wn znparn fh epnzhgao

dhganobe gnorze no:

q geo nf cawce zhbae8 :

q q n aornzwngrhobe few p~orew8

i q

:i bnf nln t q rhoknorn h fh gazg~oinznogah no

8q $Af~wrzhgao >!/

2/ No fh Af~wrzhgao >wn znpznwnorhz ~o nonkeoe phzh nogeorzhz few p~orew x~nznpznwnorho few yzragnw bnf pefkeoe& wn rzh|hzo zhqew bnwbn few iegew

8i q :i

x~n aornzwngrho h few p~orew phznw e acphznw bnf bacnrze 8 :q q gezrhobe h fh

gazg~oinznogah/

Nwrew p~orew weo few yzragnw bnf pefkeoe x~n iezchzo w~w fhbew q nwrew fhfonh pefakeohf/ H& J& G& o $Af~wrzhgao 9!/ Nwrh geowrz~ggao knecrzaghznpznwnorh ~o dnprkeoe/

Af~wrzhgao >< Nwrn nw nf ele knecrzage bn few pefkeoew znk~fhznw/


16/35


82

Geowrz~azncew ~o pefkeoe znk~fhz bn 84 fhbew/ W~ bacnowao pzaogaphf nw fhnoynzkhb~zh bnf zhbae z bn fh gazg~oinznogah x~n aowgzajn hf pefkeoe& wa z32&> gc/

Af~wrzhgao 9

Af~wrzhgao ;


17/35


8>

BN FH IZC^FH BNF ZNHBN ^O PEFKEOE ZNK^FHZHF RNEZNCH BN YAFGDNW/



18/35


89

Bn fh izc~fh bnf znh bn ~o pefkeoe znk~fhz hf Rneznch bnYafgdnw/

Daprnwaw

Nf znh bn ~o pefkeoe znk~fhz aowgzare no fh gazg~oinznogah bn zhbae z nw ak~hf hfwncapzeb~gre bnf ocnze bn fhbew o pez nf g~hbzhbe bnf zhbae q pez nf wnoe bnfok~fe bnlhbe pez fh hjnzr~zh hok~fhz norzn few zhbaew x~n wn pzeqngrho no bewyzragnw geowng~rayew bnf pefkeoe/

Rnwaw:

:

:o zH wno ~

Bncewrzhgao

A/ Pewr~fhbe< Rebe pefkeoe znk~fhz nwr geoiezchbe pez rhorew rzaok~fewawwgnfnw geokz~nornw gece ocnzew bn fhbew ranon nf pefkeoe& g~qe yzragngeco nw nf gnorze bnf pefkeoe/

AA/ Wn bniaon hf znh bnf rzaok~fe gece nfwncapzeb~gre bn bew fhbew pez nf wnoebnf ok~fe gecpznobabe pez nwrewfhbew/h/ Few fhbew bn nwrew rzaok~few

awwgnfnw weo nf zhbae bn fhgazg~oinznogah x~n few gazg~owgzajn/

j/ Wnko AA8

:HJEH hj wno & wa h q j3z& wn ranon

:

8

:H z wno

HE j z

JE h z

Af~wrzhgao 4


19/35


8;

AA/ Nf pefkeoe znk~fhz ranon o rzaok~few awwgnfnw geokz~nornw& pez fe rhore


20/35


84

GEOWRZ^GGAO Q GFG^FEBN PEFKEOEW ZNK^FHZNWGOGHYEW NWRZNFFHBEW/



21/35


81

Geowrz~ggao q gfg~fe bn pefkeoew znk~fhznw goghyew nwrznffhbew/

Nwrew pefkeoew ranono p~orhw nwrznffhbhw q geokz~nornw x~n nwro aowgzarhw no ~ohgazg~oinznogah bn zhbae Z& nwrhw gezznwpeobno h ok~few hg~rok~few/ Few ok~fewejr~wok~few nwro gazg~owgzarew h ~oh gazg~oinznogah cnoez bn zhbae z q nwgeogorzagh h fh chqez/

No fh pzacnzh phzrn bnf rzhjhle bn pefkeoew znk~fhznw nwrznffhbew wn geowabnzh nfzhbae Z nf bejfn bnf zhbae cnoez z q nw fh zh|o bn pewrnzkhz hf pefkeoe nwrznffhbebn rznw p~orhw& p~nw hf ~whz Z3:z wn ejwnzyh ~o rzaok~fe nx~afrnze/ Hf iaohf wngeowabnzh nwrn pefkeoe phzh Z ?:z/

znh bn pefkeoew znk~fhznw nwrznffhbew/

Nwrew pefkeoew nwro iezchbew pez rzhpn|eabnw wacrzagew e bnfreabnw beobn w~wbahkeohfnw weo< bahkeohf chqez i& x~n nw nf zhbae Z bn fh gazg~oinznogah q fhbahkeohf n nw ~o fhbe bnf pefkeoe znk~fhz aowgzare no fh gazg~oinznogah

cnoez/* * ::

n F z wno

& beobn z nw nf zhbae bn fh gazg~oinznogah cnoez q

Af~wrzhgao 1


22/35


:0

790

:

:wno wno

o

& izc~fh x~n wn nog~norzh bnrhffhbh no nf aoiezcn O 811/1:7 bn fh

Pzepanbhb Aornfngr~hf/

^o pefkeoe nwrznffhbe ranon o fhbew& fe x~n wakoaiagh x~n ranon:

op~orhw no w~

nwrznffh/

Nf znh bn nwrn pefkeoe nw ak~hf hf znh bn ~o bnfreabn:

n wno

Af~wrzhgao 88< IKDAL nw ~o pnorkeoe znk~fhz/


25/35


:7

790

840: 79: >

wno wno wno wnoo

79 0&>4;4wno & f~nke : 8&> 0&>4;4n

8& ;972n gc

Hpfaghobe fh iezc~fh

:88& ;972 7 80 87& ::>

2H gc gc gc

znh bnf pefkeoe nwrznffh pnorhkeohf nw bn :87& ::>gc

Fh w~ch bn few ok~few aornzaeznw * *aW nwr bhbe pez 840 $ :!aW o & wa 80o fhbew& wn

ranon gc q z 3:&> gc

Nwrznffh dnprhkeohf

Beobn Z3 >&9 gc q z 3 :&4 gc/

Af~wrzhgao 8:

Af~wrzhgao 87


27/35


:>

:

:

:

:

/

8

2

8 :&:> 7 92

20&>

2

80/8:>

Bnwhzzeffe

H n i o ~

H gc

H gc

H gc

Nwrznffh egrhkeohf

Phzh nwrn phz bn nlncpfew rzhjhlhcew few pefkeoew znk~fhznw goghyew beobn :Z z

h! Nwrznffh bn rznw p~orhw Z?:z< Fonhw wnkcnorhbhw e bn p~orew wefe weo

zninznogahfnw


28/35


:9

Z< Nf znh x~n g~jzn nwrh nwrznffh nw bn :80&8:>gc

G~ore cabn fh w~ch bn w~w ok~few aornzaeznw aW bn nwrn pefkeoe nwrznffhbe5

840 $ :!aW o & wa 9o fhbew

840 2aW

;:0aW

j! Pefkeoe nwrznffh bnghkeohf/

G~f nw nf znh bn nwrh nwrznffh bnghkeohf5

Bnc~wrznfe< ::7&8;>H gc /

G~ore cnbaz fh w~ch bn w~w ok~few aornzaeznw5

Bnc~wrznfe< 7:20 nw w~ aW /

Af~wrzhgao 89< Pefkeoe znk~fhz goghye beobn :Z z # Pefkeoe nwrznffh bnghkeohf >Z gc q 8&>z gc


29/35


:;

Pefkeoew bn ihorhwh/

Wn dho rzhjhlhbe pefkeoew znk~fhznw

aowgzarew no ~oh gazg~oinznogah bn zhbaegeoegabe& aowgzarew no PzepanbhbAornfngr~hf$o 811/1:7= :0:/748 q:0:/74:!& f~nke wn dh rzhjhlhbe geopefkeoew znk~fhznw nwrznffhbew aowgzarewno ~oh gazg~oinznogah bn zhbae Z qgazg~owgzare h ~oh wnk~obh gazg~oinznogahcnoez q geogorzagh h fh pzacnzh bn zhbaez/

Hkznkhzncew ~o hgparn zninzabe hpefkeoew bn ihorhwh& nwrew weo rzhjhlewhzrwragew x~n georanono rznw e cwgazg~oinznogahw geogorzaghw/ Few yzragnwx~n iezcho nwrew pefkeoew aornzwngrho hfew hzgew bn fh gazg~oinznogahgeoiezchobe ghbh delh bnf pefkeoe& wnnorznkho rznw nlncpfew bn geowrz~ggaobn pefkeoew bn ihorhwh/

Af~wrzhgao 8;

Af~wrzhgao 84

Af~wrzhgao 81


30/35


:4

BN FH IZC^FH BNFGF^FE BNF ZNH BN ^OPEFKEOE ZNK^FHZNWRZNFFHBE HF RNEZNCHBNF YAFGDNW AA/



31/35


:1

Bn fh izc~fh bnf gfg~fe bnf znh bn ~o pefkeoe znk~fhz nwrznffhbehf Rneznch bn Yafgdnw AA/

Daprnwaw

Nf znh bn ~o pefkeoe znk~fhz nwrznffhbe aowgzare no gazg~oinznogahw geogorzaghw bnzhbaew Z fh chqez q z fh cnoez& nx~ayhfn h ~o g~hzre bnf znh bnf rzhpn |eabnwacrzage bn bahkeohfnw n q i pez nf ocnze bn fhbew bnf pefkeoe/

Rnwaw

Bncewrzhgao

A/ Pewr~fhbe< Rebe pefkeoe znk~fhz nwrznffhbe nwr geoiezchbe pez rzhpn|eabnwwacrzagew g~qe yzragn geco nw nf gnorze bnf pefkeoe/

AA/ Pewr~fhbe< Rebe pefkeoe znk~fhz nwrznffhbe ranon rhorew rzhpn|eabnwwacrzagew q geokz~nornw gece p~orhw bn nwrznffh x~n fe iezcho/

h/ Wn bniaon gece znh bn ~o rzhpn|eabn wacrzage hf wnca pzeb~gre bn w~wbahkeohfnw n q i& f~nke :

:

n iH ~

:8 $ !2

H n i o ~

HJED nw ~o rzhpn|eabnwacrzage g~qhw

bahkeohfnw weo n q i/

i nw nf zhbae Z bn fh

gazg~oinznogah chqez/

n nw nf fhbe F bnf

pefkeoe znk~fhz aowgzare

no fh gazg~oinznogah

cnoez/

Af~wrzhgao :0


32/35


70

j/ Wa o nw nf ocnze bn fhbew bnf pefkeoe&:

ownzo fhw p~orhw bn nwrznffh

x~n geoiezcho few rzhpn|eabnw e bnfreabnw/

g/ znh bnf pefkeoe nwrznffhbe

Af~wrzhgao 8> UUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUU :>

Af~wrzhgao 89 UUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUU :9

Af~wrzhgao 8; UUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUU :;

Af~wrzhgao 84 UUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUU :;

Af~wrzhgao 81 UUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUU :;

Af~wrzhgao :0 UUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUU :1
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7:


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polígonos regulares estrelados y de fantasía

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