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ghl« - 7 khÂçfŸ

Ïa‰if¡ fšé -1‹ filÁ¥ Ãçéš, Ïiyfë‹ bt›ntW tot¦fisÍ© jhtu¤Â‰F¤ jhtu© mitfë‹ ntWgL© mik¥òfis¥ g‰¿Í© m¿¨Ôª. ÃwF éjéjkhd kyªfŸ, kyç‹ bt›ntW mik¥òfŸ, mitfë‹ mo¤js¤Âš <LghL, mH»a ãw¦fŸ M»ait óuzkhf¥ gç¨Jiu¡f¥g£ld. Ït‰¿š Ïiyfë‹ mo¥gil tot¦fis tiutj‰F© kyªfnshL ãwngjälš k‰W© ãu¥òjè‹ E£g¤ijÍ© f‰w¿¨njh©. Ï¥nghJ Ïa‰if¡ fšé-11‹ j‰nghija¥ Ãçéš äf MªtKŸs brašfisÍ© fhŒf¿ k‰W© fåfë‹ bt›ntW khÂçfë‹ tot¦fisÍ©, jhtu¦fŸ k‰W© ku¦fë‹ tot¦fisÍ©, jhtu¦fŸ k‰W© ku¦fis mL¤J tU© ghl¦fëY© ghª¥ngh©. 7.0 F¿¡nfhŸfŸ Ï¥ghl¤Â‹ khÂçfshš ck¡F ÏaYtJ Ïa‰if, ÏiyfŸ, kyªfŸ, fhŒf¿fŸ k‰W© fåfëš cŸs khÂçfis m¿jš e©ik¢ R‰¿ÍŸs bghUŸfŸ j‰brayhf¤ njh‹W©nghJ, m¦F ãiyahd mik¥ò ÏU¡»wJ. Ïj‹ mik¥ig¥ òç¨J bfhŸtnjhL ÃwF mjdhš, Ïj‹ jå¥g£l g©òfis¥ ghlkhf tiuf. 7.1 K‹Diu 6M© ghl¤Âš, kyªfë‹ és¡fkhd f‰wiy mil¨Ôª, Ú¦fŸ TWtJ nghš, nuh#h kyç‹ I¨J ÏjœfŸ bfh§l mik¥ghf, RU¡fkhd F¿¥òfŸ ÏU¨jd. Ï¥ghl¤Âš KGikahd bghUshf¡ fhŒf¿fŸ k‰W© fåfë‹ tiugl¦fisÍ© FW¡F¥ ÃçéY© Ú¦fŸ m¿Åª. Ïa‰ifæ‹ Ï›éj¥ bghUŸ¡ë‹ mik¥ig¢ RU¡fkhd K‹Diuæš ghª¥ngh©. vJ j‰brayhf¥ ghª¡f¥gL»wnjh nkY© Kjš ghªitænyna xG¦f‰wjhf¤ njh‹W© jhtu¦fŸ, ku¦fŸ, jhJ¡fŸ, éy¦FfŸ, kåj Ïd¦fŸ M»ait Ïašghfnt mik¥ò© cUtK© bfh§LŸsd. I¨J g¡f¦fis¡ bfh§l cUt mik¥òfŸ cæª thG© mik¥òfSl‹ ÏU¡F«nghJ, jhJ cyfnkh ÏU ko¥ò, _‹W ko¥ò, eh‹F ko¥ò k‰W© MW ko¥ò¡ bfh©l x¤j xnu Óuhd m§f mik¥ig¡ fh£L«. 7.2 Ïa‰ifæš khÂç cUt¦fŸ khÂçfŸ Ïa‰ifæ}nl mik¥ig MS»wJ. jhtu¦fëY© ku¦fëY© milahs« fhz¡Toa khÂçfshtd. 1) mséš xU gFÂahf khÂçfŸ 2) Ïiyfë‹ ÏU¥Ãl¤Âš khÂçfŸ 3) ÏiyfŸ, ÏjœfŸ, éijfŸ ngh‹wt‰¿‹ v§â¡ifæš khÂçfŸ 4) kyªfŸ, fhŒf¿fŸ, fåfŸ, éijfŸ ngh‹wt‰¿‹ cUt¤Âš khÂçfŸ Ï©khÂçfis¡ fUJ»wnghJ xU ãiyahd totæaš Ï¢braèš cŸsJ, c§ikahF©. 1


Ïitfë‹ äfΩ mo¥gil¥ òyikahd Ï¥ghl¤Â‹ vëa mik¥ghdJÏiy. kyª, fâ k‰W© ku© M»at‰iw¤ bjëthf m¿a cjλwJ. Ïitfëš Áyt‰iw¡ fh§ngh©. ghª¥gJ k£L© tiugl© m‹W v‹gijÍ© ãidéš bfhŸf. fhQjš, m¿jš, òç¨J bfhŸSjš òwF fh»j¤Âš rhjd¤Jl‹ F¿¥òfS‹ Ït‰iw bkhêbbgaª¤jš M»at‰iw ÏJ c£bfh§lJ. tiugl© tiujè‹ Âwikia m¿jèš Úª Ï¥nghJ f‰f cŸsJ kiwKfkhf cjΩ. 7.2.1 Ïjœfë‹ v§â¡if k‰W© xG¦fik¥Ãš khÂçfŸ totæaèš e‹F milahs© fhztšy (Golden) K¡»a é»j« 1:1 618 MF©. x‹W¡bfh‹W r©g¨j¥g£l totæaš mik¥ò¡fë‹ tsª¢Áæš äfΩ Á¡fdkhd é»jh¢rhu© Jšèakhdjšy. Mdhš xU gF 1:1. 618-I neh¡»¢ rhŒ¨ÂU¡»wJ. Ú¦fŸ br›tf© tiuÍkhW Tw¥g£lhš c¦fS¡F c‰rhfkhf ÏU¡F©. Ïj‹ Ús¤ÂèU¨J mfy¤Â‰fhdé»j« K¡»akhd é»jh¢rhu« Ïš äfΩ éU©g¤ j¡fJ. 5 br.Û. x 8 br.Û msΟs br›tf©, Ï›tifæš xU cjhuzkhF«. K¡»akhd é»j¤Â‹ xU ftd¤ij¡ ftU© eilKiw ~igbghdh¡ì (Fibonacci) v§fŸ MF©. Ïit v§fë‹ tçiria¡ F¿¡»wJ. ϦF x›bthU v§Q© mj‰F K‹ cŸs ÏU v§fë‹ T£L¤ bjhifahF©. ÏJ x‹w‹Ã‹ x‹whd v§fë‹ é»jkhdJ K¡»akhd é»j© M»wJ mjhtJ 1,2,3,5,8,13,21,34 ngh‹wjhF©. ~igbghdh¡ì v§fŸ k‰W© K¡»akhd é»j© M»ait jhtu Ïd¤Âš gutyhf¡ fhz¥gL»‹wd. Vw¤jhs, všyh kyªfëY©, Ïjœfë‹ v§â¡ifahdJ xU ~igbghdh¡ì v§zhF©. ~igbghdh¡ìa‰w v§fŸ mo¡fo Ïl« bgwhJ. cjhuzkhf, Áy éÂéy¡fhditahd ~óîah k‰W© fLF ngh‹w äf¢Á¿a v§â¡ifæyhd jhtu¦fŸ 4 ÏjœfŸ bfhŸ»‹wd. Áy jhtu tiffshd g£lªf¥« (bt§bzŒ¡ »§z¦fŸ) ngh‹wt‰¿‹ Ïjœfë‹ v§â¡ifia¡ F¿¥ÃL©nghJ, äfΩ £läl¥g£litahF©. Mdhš k‰witfSl‹ ruhrç v§â¡ifna bfh§l Ïjœfë‹ v©â¡ifia¡ F¿¥ÃL«nghJ, äfΫ£läl¥g£litahF©. Mdhš k‰witfSl‹ ruhrç v§â¡ifna bfh§l ÏjœfŸjh‹ ~igbghdh¡ì v©zhF«. mndfkhf e©äš bgU©ghnyhª kyçš cŸs Ïjœfë‹ v©â¡ifianah mL¡fik¥ignah ftdkhf Muha neu« vL¤J¡ bfhŸtšiy. m›thW brŒæ‹, gy éõa¦fŸ f§Q¡F¥ òy¥gL©. Kjèš, kyçš Ïjœfë‹ v§â¡ifahdJ mo¡fo ~igbghdh¡ì v§fëš x‹whF© v‹gij¡ fh§ngh©. btŸis mšèæš cŸsij¥ ngh‹W xU Ïjœ bfh§l kyªfS© (gl© 7.1) ÏU-ÏjœfŸ bfh§l , ô~nghªÃah ngh‹w kyªfS© (gl© 7.2) bghJthf¡ fhz¥gLgit m‹W. oçšèa© kyªfëš cŸsJ ngh‹w _‹W ÏjœfŸ bfh§l kyªfŸ mitfisél mÂfkhf¡ fhz¥gLgitahF© (gl© 7.3) I¨J ÏjœfŸ bfh§l kyªfŸ td¤Âš cŸsitahfΩ gæçl¥gL© kyªfshfΩ ü‰W¡ fz¡fhd tiffëš cŸsd (gl© 7.4) v£L ÏjœfŸ bfh§l kyªfŸ, I¨J ÏjœfŸ bfh§l kyªfis¥ ngh‹W bgUkséš ÏšiybaåD©, mÂf v§â¡ifæš gutyhf¤ bj‹gL© tiffëš cŸsd. (gl© 7.5) g‹_‹W (gl© 7.6), ÏUg¤Â x‹W k‰W© K¥g¤Âeh‹F Ïjœfis¡ 2


bfh§l kyªfS© (gl© 7.7) bghJthf¡ fhz¥gLgitna MF©. blŒì¡ FL©g¤ij¢ rhª¨j fªfëš bfh¤jhf cŸs kyªfë‹ btë tisa¦fŸ, ~igbghdh¡ìæ‹ Ïilélhj tçiria äfΩ bjëthf és¡F»‹wd. 13,21,34,55 mšyJ 89 M»a Ïjœfis¡ bfh§l blŒì kyªfŸ gutyhf¤ bj‹gLgitahF©. bghJthd ãy¤Âš cŸs blŒì kyªfŸ 34 ÏjœfŸ bfh§lit. Ϩãfœ¢ÁahdJ. ``mtŸ v‹id éU©ò»whŸ, mtŸ v‹id éU©géšiy`` v‹D© éisah£il éisahL©nghJ fU¤Âš bfhŸs¥gL»wJ. blŒì kyªfŸ 34 Ïjœfis¡ bfh§LŸsd vd¡ TW© nghJ m›tif ky®fis xUt® bghJ¥gilah¡F»wh®. Ï¥bghJ¥gilahd khÂçæèUªJ vªj xU jå tif blŒì kyªfS© éy» élyh©. Ï›tifæš tsª¨JŸsitia él mÂfkhf tsª¨J bfh§oU¡f neçL»wJ. mjdhš 35 ÏjœfŸ bfh§l blŒì kyªfisél 33 ÏjœfŸ bfh§lit mÂfkhf¤ bj‹gL»‹wd.

Fig.7.1 One petalled flower of White Calla Lily

Fig.7.2 Two petalled flower of Euphorbia

Fig. 7.3 Three petalled flower of Trillium

Fig. 7.4 Five petalled flower of Columbine

gl« 7.1 x‰iw Ïjœbfh§l

Fig. 7.5 Eight petalled flower of Bloodroot

Fig. 7.6 Thirteen petalled flower of Black-eyed Susan

Fig. 7.7 A flower of Shasta Daisy with twenty one petals

btŸis¡ fhšyh mšè kyª 3


gl« 7.2 ÏU-ÏjœfŸ bfh§l ô~nghªÃah kyª gl« 7.3 _éjœ bfh§l £oçšèa© kyª gl« 7.4 I¨J Ïjœ bfh§l bfhy©ig‹ kyª gl« 7.5 v£L ÏjœfŸ bfh§l ¥s£%£ kyª gl« 7.6 g‹_‹W ÏjœfŸ bfh§l Nr‹ kyª gl© 7.7 ÏUg¤Âx‹W ÏjœfŸ bfh§l õh«lh blŒì kyª 7.2.2 Ïiyfë‹ v§â¡if k‰W© xG¦fik¡f¥g£l khÂçfŸ ~igbghdh¡ì v§fë‹ r©g¨jK© jhtu¦fS© Ïjœfë‹ v§â¡ifia¡ f£L¥gL¤jéšiy. gl¦fŸ 7.8-7.12, vëikahd jhtukhd «Ü«tª£o‹ éõa¢ RU¡f¤Â‹ tiugl¦fshF©. òÂa¡ FU¤JfŸ bghJthf¤ j©oèUªJ Ïiyæ‹ fQéèU¨J tsª»wJ. (gl© 7.8) Ï¡fQ¡fë}nl gL¡if¡ nfhLfŸ tiu¨jhš, fhz¡Toa jhtu¤Â‹ ts®¢Áia¡ f©l¿ayh« (gl« 7.9) ika¤ j©L, g¡fth£L¡ »isfis x›bthU ãiyæ‹ bjhl¡f¤Âš c§lh¡F»wJ. ËtU© »isfŸ mt‰¿‹ ÏU ãiyfë‹ nghJ© m¥gona ÏU¨J, Ëò òÂa g¡fth£L¡ »isfis x›bthU ËbjhlU© ãiyæ‹ bjhl¡f¤ÂY© cUth¡F»wJ. všyh¡ »isfS¡F© Ïnj ãa Ãunah»¡f¥gL»wJ. Ï©khÂçæ‹ K‹nd‰w¤ÂèU¨J ~igbghdh¡ìæ‹ jå¤j‹ik thŒ¨j Áukkhd Kašfë‹ tsª¢Á ãiy ÃuÂgè¡»wJ. gy v§â¡ifæš »isfŸ K‹nd‰w¤Â‹ v¨ãiyæY© ~igbghdh¡ì v§zhf ÏU¥gš (gl© 7.10) «Ü«tª£lhš, Ïj‹ tsª»w éj© fh£Áah¡f¥gL»wJ. vëa ku¤Â‹ tsª¢ÁiaÍ© bfhŸ»wJ. x›bthU tsª¢Áæ‹ ãiyÍ© xU tUl fhy© Úo¡»wJ. (gl¦fŸ 7.1, 7.12)

Fig. 7.8

Fig. 7.9

Fig. 7.11

Fig. 7.10

Fig. 7.12

Figs. 7.8 – 7.12 Pattern of branching in Sneezewort plant

4


gl¦fŸ 7.8 - 7.12 «Ü«tª£ jhtu¤Âš »isahF© «Ü«tª£ ku¤Â‹ fU¤J¢ RU¡f¤Â‹ khÂç tiugl© m¤jhtu© j£ilahf cŸsjhf¡ fh£l¥gL»wJ. ~igbghdh¡ì v§fis¡ bfh§L bršY© tsª¢Áia ÏJ és¡F»wJ. Mdhš, bgU©ghyhd jhtu¦fë‹ g§òfis m䜤 éL»wJ. m¦F mL¤jL¤JŸs Ïiyfnsh FU¤Jfnsh mL¤jL¤j ãiyfë‹ tsª¢ÁÍl‹, ika¤ j§il¢ R‰¿Y© tisaäL»‹wd. j§o‹ ÑGŸs Ïiyæš xU òŸëæš xU jå Ïiy ÏU¡F© (gl© 7.13) Ï›éiy¡F ``0`` vd v§â£lhš (gl© 7.14), j§oš Ïiyfis, Mu©Ã¤J¡ bfh§oU¡F©, neuhf nkYŸs Ïiytiu T£Lf, bghJthf eh© milÍ© v§zhdJ ~igbghdh¡ì v§ tçiræ‹ x‹whf ÏU¡F©. (gl© 7.15)

Fig. 7.13

Fig. 7.14

Fig. 7.15

Fig. 7.16

Fig. 7.17

Figs. 7.13 – 7.18 Arrangement of leaves on the stem (Phyllotaxy) in the Sneezewort plant

gl« 7.13

gl« 7.14

gl« 7.15

gl« 7.16

gl« 7.17

gl« 7.18

gl¦fŸ 7.13 - 7.18 «Ü«tª£ jhtu¤Â‹ j§oš (~igšnyhlh¡ì) Ïiyfë‹ mL¡fik¥ò kWgoÍ© j§oš brayh‰Wifæš, v¤jid jlitfŸ eh© j§il¢ R‰W»nwh© 8 Leaves vd v©Qnth«. (gl« 7.16) Ϫj v©Q« bghJthf, v§ tçiria¡ bfhŸ»wJ. (gl© 5 Revolutions 7.17) Ïiyfë‹ mL¡fik¥ò, ÃwF é»jh¢rhu¤Âš F¿¥Ãl¥gL»wJ. e© khÂç¤ PHYLLOTAXY: 5/8 jhtu¤Âš cŸs Ïiyfë‹ v§â¡ifahdJ 8 MF©. k‰W© R‰¿‹ Fig. 7.18 v©â¡if 5 MF«. Ϥjhtu«, ~igšnyhlh¡ì 5/8-I¡ bfh©ljhf¡ Tw¥gL»wJ. x›bthU tifÍ© mj‹ ~igšnyhlh¡ìædhnyna tªâ¡f¥gL»wJ. bgU«ghY« v¥bghGJ« fz¡»l¥gL« é»j¥ bghU¤jkhdJ, ~igbghdh¡ì tçiræ‹ bjhlª¢Áahd mšyJ x‹Wé£l x‹¿‹ Kiwfshf mik»wJ. (gl© 7.18)

5


gl« 7.19 »isfŸ, ÏiyfŸ k‰W© éijfë‹ (~igšnyhlh¡ì)æ‹ xG¦fik¥Ãš ~igbghdh¡ì v§fŸ mo¡fo fhz¥gL»wJ. jhtu¤ij eh© nkèU¨J f§lhš (gl© 7.19) ÏiyfŸ neçilahd x‹w‹nkš x‹whf mL¡f¥g£oU¥gšiy, Mdhš Nça‹ k‰W© kiH¡F btë¡fh£L© tifæš ey‹fU mik¨ÂU¡F©. xU ÏiyæèU¨J k‰wj‰F, j§oš eh© R‰W v§â¡if¡ fhQ©nghJ© Ïiyfë‹ v§â¡ifia nehf nkYŸs Mu©Ã¤J¡ Fig. 7.19 bfh©oU¡F« Ïiy tiu T£L«, nghJkhd v§â¡ifÍ© ~igbghdh¡ìæš cŸsJ. x›bthU ÂiræY© ÂU©òtj‹ v§â¡ifÍ© Ïiyfë‹ T£L¤ bjhifÍ© bghJthf, _‹W bjhlª¢Áahd ~igbghdh¡ì v©fshf ÏU¡F«. 7.2.3 ó¦bfh¤Âš ÁW jå¤jå kyªfŸ éijfŸ k‰W© fåfë‹ khÂç brÂYl‹ m‹dhÁ¡ fhŒfë‹ mik¥òfŸ khÂçfŸ (gl© 7.20-7.23), Nçafh¨Â¥ ó¡fë‹ éij mik¥òfŸ k‰W© m‹dhÁ¥ gH¤Â‹nkš btë¤jŸëa gFÂfS© (gl© 7.28- 7.32) ntWgLjiy él vijnaD« bfh§LŸnsh©. m‹dhÁ¡ fhæ‹ éij bfh§LŸs bršfŸ, c§ikæš ÂU¤Âaik¡f¥g£l ÏiyfŸ, x‹W nrª¨J Ús© - FW»a¤ j§Ll‹ Ïizªjit. c§ikahd ÏiyfŸ k‰W© ÏJ ngh‹wt‰Wl‹ ~igšnyhlh¡ì ÏU¥gJ nghš, ϦF eh© fhzéšiy. v¥gonah, »isæš nrª¡f¥g£oU¥gÂèU¨J e© ftd¤ij¡ ftu¡Toa xG¦fik¥òfëš nk‰ R‰whf¢ bršY© RUŸ btë¥òwkhf tsª»wij eh© f§LbfhŸs Ko»wJ. (gl© 7.21) Ϩj m‹dhÁ¡ fhæ‹ gl¤Âš, v£L RUŸ tisa¦fŸ, fhæ‹ nk‰òwkhf¡ fofhu KŸ Âiræš VWtjhf¤ bj‹gL©nghJ (gl© 7.22) g‹_‹W RUŸfŸ nkY© br¦F¤jhf fofhu KŸ vª Âiræš nknyWtij¡ fhzyh«.(gl« 7.23)

Fig. 7.20

Fig. 7.21

6


Fig. 7.22

Fig. 7.23

Figs. 7.20 – 7.23 The pattern of arrangement of scales patterns in a pine cone

gl« 7.22

gl« 7.23

gl¦fŸ 7.20-7.23 m‹dhÁ¡ fhæš xG¦fik¡f¥g£LŸs brš tot¦fë‹ khÂç beU¡fkhf ml¡» mik¡f¥g£l T£lik¥Ãš äf¢ Á¿a ó¡fŸ, blŒì kyç‹ FGéš Ïl© bg‰¿U¥gJ (gl© 7.24) bgU©ghY© ÏU gçkhz mik¥Ãš m‰òj¤ij¡ fhzyh©. fofhu KŸë‹ vªÂiræš ÏUg¤Â x‹W© (gl¦fŸ 7.25-7.27) k‰W© K¥g¤Â eh‹F rktª¡fkhd mšyJ rk msΡ nfhz© bfh§l RUŸfis¡ fhzyh©. v¨j blŒì kyçY©, fofhu KŸ bršY© ÂiræY© fofhuKŸ bršY© vªÂiræY© bršY© RUŸfë‹ bjhlª mik¥ò, bghJthf¤ bjhlª¨jh‰ nghYŸs ~igbghdh¡ì tçir v©fis¡ bfh©oU¡F«.

Fig. 7.24

Fig. 7.26

Fig. 7.25

Fig. 7.27

Figs. 7.24 – 7.27 Arrangement of florets in a flower of Daisy

7


gl« 7.24

gl« 7.25

gl« 7.26

gl« 7.27

gl¦fŸ 7.24-7.27 blŒì kyçš Á¿a ó¡fë‹ mik¥ò RUŸfëY© m‹dhÁ¥gH¤Â‹ bršfŸ (gl© 7.28) k‰W©, mitfŸ fuLKulhf mWnfhz tot¤Âš ÏU¥gjhš, _‹W bjëthd RUŸfë‹ tçirfis¡ fh§ghŒ. 5 RUŸbfh§l xU tçir c£FêÎ nfhz¤Âš ty¥òwkhf nknyW© nghJ (gl© 7.30), 8 RUŸfŸ bfh§l Ïu§lhtJ tçir äfΩ br¦F¤jhf ÏlJòw© nknyW»wJ. (gl© 7.31) 13 RUŸfŸ bfh§l _‹‰htJ tçir äfΩ br¦F¤jhf tyJòw© nknyW»wJ (gl© 7.32)

Fig. 7.28

Fig. 7.29

Fig. 7.30

Fig. 7.31

Fig. 7.32

Figs. 7.28 – 7.32 The pattern of arrangement of scales in a pineapple fruit

gl¦fŸ 7.28-7.32 m‹dhÁ¥ gH¤Âš xG¦fik¡f¥g£l mL¡» mik¡f¥g£l khÂç M¥ÃŸ kyªfŸ I¨J Ïjœfis¡ bfh§lJ, I¨nfhz¥ gŸs¦fŸ gH¤Â‹ moæš fhz¥gL»wJ. fåia¥ gFÂahf bt£L©nghJ e£r¤Âu toéš éijfis btë¥gL¤J »wJ. (gl« 7.34) Fibonacci numbers in plant sections

Bananas have 3

Apples have 5 8


gl« 7.33 thiH¥gH© k‰W© M¥ÃŸ fåfë‹ FW¡F¥ gF 7.2.4 fhŒ, få khÂçfŸ fhè~¥st® xU rhjhuz fhè~¥stª btë¡nfh£oš bgU©ghY© I¦nfhzkhf ÏU¡»wJ. ftdkhf¥ ghª¡ifæš, ika¥òŸëia¡ fhzyh©. m¦F óé‹ ÏjœfŸ äfΩ Á¿ajhf cŸsd. kWgoÍ© fhQ©nghJ m¢Á¿a ó¡fŸ Ï©ika¤ij¢ R‰¿ ÏU ÂirfëY© RUshf mik¡f¥g£oU¥gij¡ fhzyh©. nuhkbd«¡ ¥u¡nfhè/fhè~¥stª ghª¥gj‰F© Rit¥gj‰F© ¥u¡nfhè k‰W© fhè~¥stç‹ Ïil¥g£l fy¥ghf ÏU¡F©. Ïu§Lnk br¦F¤jhd Eåia¡ bfh§litahfΩ xnu khÂçahfΩ ÏU¡F© Mdhš KGtJkhfnt FW»a FU¤J¡fis¡ bfh©lit. Ϩj¢ Á¿a¥ ó mik¥ò RUŸfis¥ ghª¥gj‰F Rygkh¡F»wJ. bt§il¡fhæ‹ tot¤ij ghª¤J m¿¨ÂU¡»Öuh? ÏJ I¨J g¡f tot¤ij¡ bfh§lJ. mjdhš thiH¡fhÍ© m›thnw cŸsJ. c§ikæš, thiHæ‹ FW¡F¥ gFÂæš ika¤Âš K¥gFÂfis¡ bfh§lJ mjhtJ 3 ÃçÎfŸ (gl© 7.33) ftdkhf¥ ghª¤jhš, R‰¿Y© mÂf mséš cjhuz¦fŸ ÏU¡F«. c©ikahfnt Ïitfis¡ fh©Ã¥gJ« és¡FtJ« äfΫ MªtKŸsjhŒ ÏU¡F©nghJ, Ïš Áy MuhŒ¢Áfis Ïizajs¤Âš nk‰bfhŸs c¦fS¡F¤ bjçé¥gJ jFÂahdnj. ϦF neu© mDkÂ¥gijél Úª nkY© mÂf brŒÂfisÍ© gl¦fisÍ© f§L m¿ayh©. K‹ò F¿¥Ã£lJnghš, Ϩj m¿jyhdJ, tiugl© tiutš kiwKfkhf¤jh‹ c¦fS¡F cjΩ. £lkhd btë všiy¡ nfhLfis tiutj‰FŸ K‹ò Úª xnu neh¡f¤njhL ghl¤Â‰FŸshd mik¥ig tiutJ K¡»a¥ ga‹ghlhf ÏU¡F©. jâ¡if¡ nfŸéfŸ 1) Ïa‰ifæš milahs© fhztšy khÂçfŸ vit? vit? 2) K¡»akhd é»j© v‹gJ v‹d? mJ V‹ m›thW miH¡f¥gL»wJ? 3) vit ~igbghdh¡ì v§fŸ? 4) kyªfëš ~igbghdh¡ì eilKiw¡F cjhuz¦fŸ juΩ. 5) fhŒf¿fëY© fåfëY© ~igbghdh¡ì eilKiwæ‹ rh£Áfis v¦F fh©»Ö®? 6) mo¤js <Lgh£o‹ ÏU bt›ntW éj¦fŸ ahit? fhŒf¿fŸ k‰W© fåfë‹ vL¤J¡fh£LfnshL F¿¥ÃLf. 7) Xçjœ k‰W© <çjœ kyªfŸ x›bth‹¿Y© xU cjhuz© jUf. 8) bt¿¿l¦fis¥ óª¤Â brŒf. i) é»jkhf Ïiyfë‹ mL¡fik¥ò btë¥gL¤JtJ m¤jhtu¤Â‹ tifahf ----------- vd miH¡f¥gL»wJ. cjhuzkhf, «Ü«tª£ jhtu¤Âš Ïiyfë‹ v§â¡if-------MF©. nkY© R‰¿‹ v§â¡if------ MF«. Ϥjhtu« --------- 5/8-I bfh©ljhf¡ Tw¥gL»wJ. ii) m‹dhÁ¡ fhæ‹ gl¤Âš, v£L------- fhæ‹ ------- Mf ------Âiræš VWtjhf¤ bj‹gL©nghJ, g‹_‹W ----9


iii)

iv)

nkY« br§F¤jhf ------, -------- Âiræš nknyWtij¡ fhzyh«. v¨j blŒì kyçY©, fofhu KŸ bršY© ÂiræY©, fofhu KŸë‹ vª ÂiræY© bršY© -------bjhl® mik¥ò, bghJthf¤ bjhlª¨jh‰nghYŸs --------. tçir v©fis¡ bfh©oU¡F«. M¥ÃŸ k‰W© thiH¥ gH¤Â‹ FW¡F¥ gFÂfë‹ gŸskhf cŸsitfë‹ mik¥Ãš ~igbghdh¡ì v§fshtJ Kiwna ------ k‰W© ------- MF«.

7.3 fhŒf¿fŸ k‰W© fåfë‹ ãwK© mo¤js¤Âš <LghL©. fhŒf¿fŸ k‰W© fåæ‹ ãw¦fŸ, xU F¿¥Ãl¤j¡f g§ghF©. xU gH¤Âš gy ãw¦fŸ ÏU¡fyh©. Áy rka¦fëš x‹W nrª¨jitahfΩ ÏU¡fyh©. vL¤J¡¡h£lhf xU kh©gH© mšyJ xU M¥ÃŸ gH©. gH¦fŸ ngh‹nw fhŒf¿fë‹ K¡»a m¦fkhf mj‹ mo¤js <LghL cŸsJ. fhŒf¿fë‹ g§òfis m¿a ÏJ äfΩ K¡»akhF©. mo¤js¤Âš <LgLjš ÏU tiffshf ÏU¡fyh©. f§zhš fhQ© js¥gu¥Ã‹ <LghL v‹gJ fåæ‹ njhè‹ m¦fkhF© k‰W© fåæ‹ nkš bkšèa¡ щWfshfnth, ãw¥óršfshfnth bt›ntW ãw¦fëš bj‹gLgitahF«. Ï›tif¤js¦fëš <LghlhdJ bjhLtjhš czu¡Toait. få mšyJ fhŒf¿æ‹ mo¥gil tot¤J¡F Ït‰¿‹ mik¥Ãš K¥gçkhz© nrª¡f¥gL»wJ. _‹W bt›ntW tif¡ fhŒf¿fis vL¤J¡ bfhŸsΩ. cjuhzkhf f¤jç¡fhŒ mšyJ Riu¡fhŒ mšyJ j¡fhë¥gH¦fŸ bt§il¡fhŒ mšyJ Õ‹« mšyJ njhnyhL g£lh⥠gU¥òfŸ ÏiyfSl‹ fhè~¥stª mšyJ K£il¡nfh« mšyJ KŸs¦». f¤jç¡fhnah Riu¡fhnah fd¥gçkhz© ä¡f fhŒf¿fshF©. Õ‹n[h njYl‹ g£lhânah Ú§L FW»ia. fhë~¥stnuh KŸs¦»nah fd¥gçkhzkhditna nkY© j§Lfnsh Ïiyfnsh mitfSl‹ cŸsd. xU (set) T‰¿‹ KGikahd k‰W© FW¡F¥ gFÂæ‹ tiugl¤ij étu¦fSl‹ vGJnfhyhš tiuf. fhŒf¿fŸ bjëthd mo¤js¤Â‹ <LghL© ãwK© bfh§lit. fhè~¥stçš cŸsJ nghš, mo¤js <LghL nghJkhd cWÂÍl‹ mJnt tot© bfhŸ»wJ. fhŒf¿fSl‹ ngh‹W, gH¦fë‹ mo¤js¤Âš <LghL xU K¡»a m¦fkhF©. fåæ‹ g§Ãid¡ bfhL¥gj‰F ÏJ äf K¡»akhF«. fåæ‹ g§Ãš Úª m¿¨jij Ïj‹ btë¡nfh£L mik¥ò k‰W© Ïj‹ mo¤js <LghL k‰w mid¤ijÍ© ãwngjälè‹ têna ckJ MŒ¨j¿jš ÃuÂgè¡f nt§L©. fåia¡ f‰w¿¨j Ëò KGtJkhd fåiaÍ© mj‹ FW¡F¥ gFÂiaÍ© Úª t§z¦fë£nlh és©gu¤Â‰¡hd tªz¦fë£nlh tiuf. 10


ÏU bt›ntW t§z¤Â‹ rhjz¤Âš, ckJ MŒ¨J m¿jyhdJ, v›thW Ï¢rhjd© ga‹gL¤j¥gL»wJ v‹gijÍ© k‰W© xnu bghUë‹ gil¥Ãš v›thW ÏitfŸ njh‹W»‹wd v‹gijÍ© ck¡F¡ fh©Ã¡F«. brŒKiw _‹W bt›ntW tif¡ fhŒf¿fis KGikahfΩ mt‰¿‹ FW¡F¥ gFÂfSlD© vGJnfhyhY© ngdhédhY© tiu¨J f‰w¿f. ãwngjK© ÏLf. fhŒf¿fis¡ fU¥ÃY© btŸisæY© f‰w¿f ãw ngjälyhš tªzäLf. 7.4 gæ‰ÁfŸ 7.4.1 tF¥ò¥ gæ‰ÁfŸ _‹W bt›ntW éj¡ fåfis¡ f‰w¿f, vGJnfhYlD©, ik¥ ngdhÎlD© ãwngjälYl‹ tªzäLjèY© Úª njª¨bjL¤J tif. cjhuzkhf: M¥ÃŸ mšyJ Ãs©« mšyJ ngç¡fhŒ mšyJ bgªç. kh©gH¦fŸ mšyJ Kyh©gH¦fŸ mšyJ thiH¥gH¦fŸ Âuh£ir¥ gH¦fŸ mšyJ m‹dhÁ¥ gH© xU KGikahd bjhF¥igÍ© FW¡F¥ gFÂæ‹ tiugl¦fisÍ© étu¦fSl‹ vGJnfhyhš tiuf. Ϥjlit t§z vGJnfhšfënyh khÎ tªz¦fënyh Úª brayh‰wyh©. vGJnfhè‹ fç¥bghUis¥ ga‹gL¤j nt§lh©. c©Kila tiugl¤Â‹ v¥gFÂiaÍ© mê¡f têæšiy v‹gij ãidéš bfhŸf. v¥gonah, Ï¥nghJ Ú¦fŸ, e‹F RygbkdΫ j‹d©Ã¡ifÍlD©, tisÎfŸ k‰W© mik¥òfŸ tiujèš ãidÎ bfhŸs nt§L©. bghUë‹ mik¥ò g‰¿Í© jF¨jthW f‰wèY© m¿jèY© k‰W© fh»j¤Âš khÂç tiugl¦fshf Ïitfis kh‰¿aik¥gÂY© v§z© bfhŸs nt§L©. 7.4.2 Å£L¥ gæ‰ÁfŸ i) k‰w ÏU fhŒf¿fis KGtJkhfΩ Ïitfë‹ FW¡F¥ ÃçÎfSlD© vGJnfhš k‰W© ngdhédhY© k‰W© ãwngjälyhš t®zä£L« tiuf. ii) ntW ÏU fåfis KGikahfΩ mitfë‹ FW¡F¥ ÃçÎfnshL©, t§z vGJnfhšfŸ, ik¥ngdh k‰W© 㪠tªz¦fis étu¦fSlD© ãwngjä£L© f‰w¿a¥ ga‹gL¤Â tiuf. fåæ‹ Fz¤Âš Ú m¿¨jij Ïj‹ btë¡ nfh£L mik¥ò k‰W© Ïj‹ mo¤js <LghL, k‰w mid¤ijÍ© ãwngjälè‹ Cnl ckJ MŒ¨j¿jš ÃuÂgè¡f nt§L©. fåia m¿¨j Ëò KGtJkhd fåiaÍ© mj‹ FW¡F¥ ÃçitÍ© Úª bfh§l tªz¦fë£nlh, és©gu¤Â‰¡hd t®z§fë£nlh tiuf. ÏU bt›ntW ãw rhjd¤Âš ckJ MŒ¨j¿jyhdJ v›thW Ϩj rhjd© ga‹gL¤j¥gL»wJ v‹gijÍ© k‰W© xnu bghUë‹ gil¥Ãš v›thW ÏitfŸ njh‹W»‹wd v‹gijÍ© ck¡F¡ fh©Ã¡F«. 11


7.5 bjhF¤jik¤jš Ïa‰ifæ‹ Áy m‰òj¦fis Ï¥ghl© btë¥gL¤J»wJ. nkY© c§ikia V‰W¡ bfhŸs¡ f£lha¥gL¤J»wJ. Ïa‰iria MŒ¨J m¿jèš bjhlª¨J brštjhš nkY© nkYkhd kªkkhf ek¡F ÏJ btëtU»wJ. bt›ntW tiffshd jhtu¦fŸ k‰W© ku¦fë‹ mik¥ig¤ jGéÍŸs khÂçfis¥ g‰¿ eh© m¿¨J tUtjhš Ï¥ghl© Ïa‰ifæ‹ tiugl¤ij tiujèš gu¨j Ïl¤ij¤ Âw¡»wJ. v¥goahæD© tisÎfŸ k‰W© mik¥òfŸ tiujèš e‹F trÂahfΩ, j‹d©Ã¡ifÍlD© ÏU¡f nt§L©. bghUS¡F¤ jF¨jthW f‰wèY© m¿jèY©, mik¥ò¥ g‰¿Í© fh»j¤Âš khÂç tiugl¦fshf Ïitfis kh‰¿aik¥gÂY© Á¨Â¡f nt§L©. Ï¥ghl¤Â‹ K¡»akhd m©r¦fshtd. jhtu¦fëY© ku¦fëY© milahs© fhz¡Toa khÂçfŸ msé‰F¤ jF¨j khÂçfŸ Ïiyfë‹ khÂçfŸ ÏiyfŸ, ÏjœfŸ, éijfŸ ngh‹wt‰¿‹ v§â¡ifæš khÂçfŸ kyªfŸ, fhŒfŸ, fåfŸ, éijfŸ ngh‹wt‰¿‹ tot¤Âš khÂçfŸ. 7.6 jâ¡if¡ nfŸéfS¡fhd éilfŸ ÑœfhQ© tifëš milahs© fhz¡Toa khÂçfŸ Ïa‰ifæš cŸsd. msé‰F V‰w khÂçfŸ Ïiyfë‹ khÂçfŸ ÏiyfŸ, ÏjœfŸ, éijfŸ ngh‹wt‰¿‹ v§â¡ifæš khÂçfŸ kyªfŸ, fhŒfŸ, fåfŸ, éijfŸ ngh‹wt‰¿‹ tot¤Âš khÂçfŸ. totæaèš e‹F milahs© fhztšy K¡»akhd é»jkhf 1:1.618 cŸsJ. x‹W¡ bfh‹W r©g¨j¥g£l totæaš mik¥òfë‹ tsª¢Áæš äfΩ Á¡fdkhd é»jkhf ÏJ x¥ò¡ bfhŸs¥gL»wJ. K¡»akhd é»j¤Â‹ xU ftd¤ij¡ ftU© eilKiw. ~igbghdh¡ì v§fŸ MF©. Ïit v§fë‹ tçiria¡ F¿¡»wJ. Ϧf x›bthU v§Q© mj‰F K‹ cŸs ÏU v§fë‹ T£L¤ bjhifahF©, k‰W© ÏU x‹w‹Ã‹ x‹‰hd v§fë‹ é»jkhdJ K¡»akhd é»j© M»wJ. mjhtJ 1, 2, 3, 5, 8, 13, 21, 34 ngh‹wjhF©. Ït‰¿‹ Ïjœfë‹ v§ cjhuzkhf 3 ÏjœfŸ bfh§l xU £çšèa© kyª, 5 ÏjœfŸ bfh§l xU £bl©gš kyª (¢r©gh), 13 ÏjœfŸ bfh§l xU blŒì kyª, ÏJ ngh‹wt‰¿Y©, NÝaf¨Â¥ óé‹ ik¤Âš éijfë‹ xG¦fhd mik¥ò fofhuKŸ bršY© vªÂiræš 21 k‰W© fofhuKŸ bršY© Âiræš 34 RUŸfëY© kyªfë‹ ~igbghdh¡ì eilKiwia¡ fhzyh«. fhŒf¿fëY© fåfëY© ~igbghdh¡ì v§ bj‹gL»wJ. Ït‰¿‹ btë¥òw mik¥Ãš, cjhuzkhf 5 g¡f¦fŸ bfh§l bt§il¡fhŒ. nkY© Ït‰¿‹ FW¡F¥ gFÂæš cjhuzkhf 3 ÃçÎfŸ bfh§l thiH¡fhŒ k‰W© 5 ÃçÎfŸ bfh§l M¥ÃŸ. ÏU bt›ntW éj¦fëš mo¤js¤Â‹ <LghlhdJ: f§zhš fhQ© js¤Â‹ <LghL, M¥ÃŸ gH¦fŸ, kh©gH¦fŸ, jªóõ⥠gH¦fŸ, òly¦fhŒ, Õª¡f¦fhŒ¥ ngh‹w g‰¿ VW© fhŒfŸ ngh‹wt‰¿š fhz¥gL»wJ. bjh£L 12


czU© mo¤js<LghL bfh§lit, MuŠR¥ gH¦fŸ, m‹dhÁ¥gH©, ghf‰fhŒ, fhè~¥stª ngh‹wt‰¿š fhz¥gL»wJ. btŸis¡ fšyh mšè kyª xU Ïjœ bfh§lJ k‰W© ô~nghªÃah, ÏU ÏjœfŸ bfh©lJ. bt‰¿l¦fis ãu¥òf 7.7 ÏW édh¡fŸ 1) xU kyçš Ïjœfë‹ v§fëY© xG¦fik¥ÃYkhd khÂçfis¥ gçªJiu¡fΫ. 2) Áy fhŒf¿fis¡ f‰w¿¨J KGtJkhdJ©, FW¡Fth»Y© Úª tªzä£L mšyJ girÍŸs¡ »nuah‹ ga‹gL¤Â tiugl¦fŸ tiuf. 3) m‹dhÁ¡ fhŒ k‰W© m‹dhÁ¥ gH¤Â‹ xG¦fhf mL¡»aik¡f¥g£l khÂçia¤ jUf. 4) ~igšnyhlh¡ìæ‹ Ïašig cjhuz¤Jl‹ étç¡fΩ 5) ÏU fåfis KGtJkhfΩ mt‰¿‹ FW¡F¥ gFÂfSl‹ t§z vGJnfhšfŸ, tiugläL© ngdh k‰W© Úª tªz¦fis¥ ga‹gL¤Â étu¦fSlD© ãwngjälèdhY© tiugl¦fŸ tiuf. 7.8 jftš F¿¥òfS© nk‰nfhŸfS©. 1) 2) 3) 4)

bgaª bjçaéšiy. 2006 tiuglälY¡F© tªzäLtj‰Fkhd KGikailªj¤ Jizt‹ ¡th§l© ÃçRç¥ò, y§l‹. J§âf‹,o.1987 ckJ Á¤Âuäliy K‹nd‰¿¡ bfhŸ ~ngh«blç‹ fiy¢ nrit, Ï‹¡, fè~nghªåah. ~ngh«blª, lòŸÍ 1997 giræLgitfë‹ fiy, thš£nlª ~ngh«£blª ÃuRç¥ò, Ï‹¡, fè~nghªåah ¥nghbtš, lòŸÍ v~¥ 1997 cæ%£lKŸs tiugl¤Â‹ fiy thš£blª ~ngh«blª ÃuRç¥ò, Ï‹¡, fè~ngh®åah.

13

Lesson 7  

7.2 Ïa‰ifæš khÂç cUt¦fŸ khÂçfŸ Ïa‰ifæ}nl mik¥ig MS»wJ. jhtu¦fëY© ku¦fëY© milahs« fhz¡Toa khÂçfshtd. 1) mséš xU gFÂahf khÂçfŸ 2) Ïiyfë‹ ÏU¥Ãl...

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