Expand to right
Expand to left

melika muggulu


3. sOnA saushThavamu

taruvAta manamu prAraMbhamulO tIsikonna sOnAmuggunu 90 DigrIlu tippitE dAniki aDDavarusalu nAlugu, niluvu varusalu mUDu uMTAyi (#four rows and three columns).# aTTi amarikatO sOnA chaturasrAnni sRshTiMchitE 3va chitramu (kuDivaipu, eDamavaipu reMDava chitramulOni chivaridi) labhistuMdi. dIni saushThavamu chitratalAniki laMbamugA 90DigrIla bhramaNAkshamu (#vertical four-fold axis),# chitratalamulO nAlugu 180DigrIla bhramaNAkshAlu (#four two-fold axes in the plane of the figure)# unnAyi. aMTE, raMgulu lEkuMDA 3 aDDa, 4 niluvu sOnA chitrapu saushThavamu raMgulatO 4 aDDa, 3 niluvu sOnA chaturasrAniki unnadi. iMkA konni chitrAlatO yiTTi prayOgAlanu chEsina taruvAta dIni vivaraNa arthamayinadi. adEmaMTE –

4A. pariSOdhanala sArAMSamu

  1. prAraMbha sOnA mugguku oka gIta uMTE, sOnA chaturasrAniki eppuDU reMDu gItalu uMTAyi. sumAru vaMdaku paina muggulatO chEsina prayOgAlavalana tElina sArAMSa midi. gaNitaSAstrarItyA dInini iMkA nirUpiMchalEdu.
  2. niluvu varusala saMkhya bEsigA (#odd number of columns)# uMTE, sOnA chaturasrAniki saushThavamu ekkuvagA uMTuMdi (chitratalamulO nAlugu 180 DigrIla bhramaNAkshAlu, laMbamugA 90 DigrIla bhramaNAkshamu, dIninE SAstrIyamugA 422 aMTAru).

  3. 4. dAramutO allina sOnA saushThavamu

    niluvu varusala saMkhya sari saMkhya ayitE (#even number of columns),# sOnA chaturasrAniki saushThavamu takkuva (chitratalamulO reMDu 180 DigrIla bhramaNAkshamulu, chitrAniki laMbamugA 180 DigrIla bhramaNAkshamu. dIninE SAstrIyamugA 222 (#three mutually perpendicular two-fold axes)# aMTAru.

  4. prAraMbha EkarEkhA sOnAchitrAlakU (#starting single line motifs),# sOnA chaturasrAlaku savyApasavya guNamu unnadi (#chirality). # aMTE yI muggulaku biMbapratibiMba dharmamu unnadi.


5. sOnA mUshikamu

iTTi sOnA chaturasrAlanu dArAlatO, tADulatO nirmiMchavachchunu. nailAnu dArAlatO nirmiMchina aTTi oka nA prayatnAnni 4va chitramulO chUDagalaru. EkarEkhA sOnA chitrAlatO iMkA ennO gammattulanu chEyavachchunu. oka jaMtuvu lEka manishi ityAdula AkAramulO oka sariyaina sOnA chitrAnni nirmiMchi vATini poDigistE manaku A AkAramu EkArEkhA chitramugA pariNAmamavutuMdi. vinAyakuDiki priyamaina mUshikapu Eka rEkhA chitrAnni 5va chitramulO chUDavachchunu.

4i. virahAMka-hEmachaMdra-phibanAchchi saMkhyASrENi

EDava SatAbdamulO virahAMkuDu anE oka ChaMdaSSAstraj~nuDu jIviMchADu. mAtrAvRttAlanu vivariMchETappuDu ataDu oka saMkhyASrENini viSadIkariMchADu. dAni sArAMSa mEmaMTE oka mAtranu oka vidhamugA (#I), # reMDu mAtralanu (#I –# laghuvu -oka mAtra, #U –# guruvu, reMDu mAtralu) reMDu vidhamulugA (#U, II),# mUDu mAtralanu mUDu vidhamulugA (#III, UI, IU),# nAlugu mAtralanu aidu vidhamulugA (#IIII, IIU, IUI, UII, UU),# aidu mAtralanu enimidi vidhamulugA (#UUI, UIU, IUU, UIII, IIIU, IUII, IIUI, IIIII),# ilAgE migilinavi vrAyavachchunu. 1,1,2,3,5,8,13,… dInini mAtrAmEru prastAramu aMTAru. ilATivi saMgItamulOni tALAlalO kUDA unnAyi. taruvAta hEmachaMdruDu kUDa ChaMdOnuSAsanamulO I saMkhyalanu prastAviMchADu. A taruvAta paSchima dESAlalO nEDu I saMkhyASrENini phibanAchchi sIrIs (#Fibonacci series)# aMTAru. dInini guriMchi marokappuDu pratyEka vyAsamunu vrAstAnu.


6. virahAMka saushThavamu

I SrENi ekkaDekkaDa prakRtilO perugudala (#growth)# saMbhavistuMdO akkaDa kanipistuMdi. aMdukE dInini #dynamic symmetry# aMTAru. dInini phibanAchchi (#Fibonacci)# kaMTe mUDu SatAbdAlaku muMdu kanugonna virahAMkuniki gaNitaSAstramulO pEru, gauravamu labhiMchakuMDuTa SOchanIyamu. I aMkelatO sOnA muggulanu nirmiMchinappuDu nEnu oka kotta vishayAnni gamaniMchAnu. #a, b, c, d# lu nAlugu virahAMka saMkhyalaitE, #c, d#lanu aDDa, niluvu varusalugA oka EkarEkhA sOnAchitrAnni sRshTistE aMdulO marO mUDu sOnA muggulu uMTAyi. vATi aDDa niluvu varusalu #[b, c], [c, b], [a, c]. a+b=c, b+c=d# ayitE #cd = bc + cb + ac# avutuMdi. iTlu nirmiMchina virahAMkasaMkhyA chitrAlalO oka dAnini yikkaDa 6va chitramulO (paibhAgamulO 8 aDDavarusala, 13 niluvu varusala sOnA muggu; kriMdi bhAgamulO adE chitramulO 5×8, 8×5, 3×8 varusala mUDu sOnA muggulu) chUDa vachchunu. I EkarEkhAchitrAlatO sOnA chaturasrAnni nirmistE, dAniki reMDu raMgula gItalu uMTAyi.

4I. SrIvatsa chihnamu

sOnA muggulanu mugiMchE muMdu bauddhulaku pUjArhamaina pavitramaina ashTa chihnAlalO okaTaina SrIvatsa anE oka chihnAnni guriMchi yikkaDa cheppAli. reMDu aDDa varusalu, mUDu niluva varusala chukkalatO oka gItatO uMDE sOnA mugguku adanamugA paina, kiMda marO chukka peTTitE manaku SrIvatsa chihnamu labhistuMdi. TibeT bauddhamatamulO nEDu kUDa lAsAlOni AlayAlalO dInini patAkAlugA vElADadIstAru. dIninE aMtulEni muDi (#eternal knot)# aMTAru. punarapi jananaM punarapi maraNaM punarapi jananI jaTharE SayanaM anE sUktini I SrIvatsa chihnamu teluputuMdi. vishNuvu vaksha@hsthalamupai veMDrukalu yI SrIvatsAkAramulO uMTAyani kUDA aMTAru. sOnA saushThavamutO ilA ennO kotta kotta muggulanu sRshTiMchAnu, kAni vyAsapu niDivi perugutuMdani A vishayAlanu yikkaDa charchiMchaDaMlEdu.

5. mersAn saMkhyalatO muggulu


7. mersAn muggu

gaNitaSAstramulO mersAn saMkhyalu (#Mersenne numbers)# prasiddhamainavi. vITini 2#n – 1 where n is 1, 2, 3,…# anE phArmulAtO gurtiMchavachchunu. I saMkhyalu gala chukkalatO muggulanu vEya vIlavutuMdi. A vidhAnAnni 7va chitramulO telipinAnu.


8. EDu chukkala mersAn muggu

oka chinna chaturasrAniki nAlugu vaipula nAlugu chinna chaturasrAnni (chitramu #a)# chErchitE manaku (#b)# chitramu labhistuMdi. aidu (#b)# chitrAlanu okaTipaina marokaTi uMchitE (#c)# chitramu labhistuMdi. dIniki EDu chukkalu. ilAgE 15 chukkalu uMDE (#d)# chitramu, 31 chukkalu uMDE (#e)# chitrAlanu sRshTiMchavachchunu. vITini chUstE manaku #fractal patterns# j~nApakamu vastuMdi. vITiki okE gIta uMTuMdi. EDu chukkalu uMDE I mersAn muggunu 8va chitramulO chUDavachchunu.

6. nakshatrAkAra bahubhuji

SAstrIya siddhAMtAlapaina AdhArapaDina mari konni muggulu nakshatrAkAra bahubhujiki (#Star Polygon)# cheMdinavi. udAharaNaku oka ashTabhujAnni tIsikoMdAmu (chitramu 9#a).# pakkapakkana uMDE konalu (agrAlu) kalupabaDDAyi yiMdulO. dIniki shlAphlI chihnamu (#Schläfli symbol) ’8/1′. # chitramu 9#b# lO idE ashTabhujini reMDu reMDu agrAlaku kalupagA vachchina AkAramu chUpabaDinadi. I AkRti reMDu gItalatO nakshatrAkAramulO unnadi. dIni shlAphlI chihnamu ’8/2′. chitramu 9#c# lO mUDu mUDu konalu kalupabaDDAyi, alA chEstE okE gItatO oka nakshatrAkAramu vachchinadi. idi aMdarikI parichitamaina muggu.


9. bahubhuji muggu

iTTi muggunu mAtRkagA tIsikoni oka baMdhakavitvamunu kUDa nEnu kaumudilO prachuriMchina muggulapai vyAsamulO vrAsinAnu. chitramu 9#d, 9e, 9f# lalO hRdayAkAramulO uMDE oka asaMpUrNa dIrghavRttamu (#incomplete ellipse) 8/1, 8/2, 8/3# nakshatrAkRtulaku saripOyE kONAlatO nirmiMchabaDinavi. vITini oka vidhamaina hRdayakamalAlu ani cheppavachchunu. chitramu 9#g# lO chitramu 9#b# vale chekkabaDina haMpIlOni oka staMbhamupaina uMDE SilpAnni chUpAnu. chitramu 9#h# lO chitramu 9#f# vale nailAnu dAramutO nEnu allina oka amarikanu chUpAnu. ilAgE paMchabhujiki (5/1) 5/2 nakshatramu, shaDbhujiki (6/1) reMDu gItalatO 6/2 #Star of David,# saptabhujiki (7/1) 7/2, 7/3 AkRtulu labhistAyi.

7. muDula siddhAMtamu


10. muDi saMkhyala muggu

melika muggulalOni muDulu muDula siddhAMtamunu (#knot theory)# anusaristAyi. muggulO reMDu gItalu ekkaDa okadAni kiMda marokaTi pOtuMdO, A biMduvunu saMdhi sthAnamu (#crossover point)# aMTAmu. nEnu muMdu vivariMchina sOnA muggulO, #r# aDDa varusalu, #c# niluvu varusalu uMTE, dAniki (#r-1) (c-1) – 1# saMdhi sthAnamulu uMTAyi. udAharaNaku, 6 aDDa varusalu, 5 niluvu varusalu uMTE, manaku 19 saMdhisthAnAlu uMTAyi. prati saMdhi sthAnapu saMkhyaku ennO chitrAlanu manamu vrAyavachchunu. mUDu, nAlugu saMdhi sthAnAlaku oka chitramu, aidu saMdhi sthAnAlaku 2 chitrAlu, AriMTiki mUDu, EDiMTiki EDu, enimidiki 21, tommidiki 49, ilA perugutU pOtuMdi I saMkhya. adIkAka, gIta (lEka dAramu) eppuDU vaMkara lEkuMDA uMDAlani lEdu. alA vaMkaraTiMkara gItalatO oka pratyEkamaina muDi saMkhyatO manamu mana Uhaku tOchinaTlu chitrAlanu sRshTiMchavachchunu. alA sRshTiMchina oka chitrAnni 10va chitramulO chUDavachchunu.

8. nAgabaMdhamu

melika muggulalO mukhyamaina oka muggu nAgamaMDalamu. dIninE nAgabaMdhamu ani kUDa aMTAru. tamiLanADulO kAvErI nadItIramulO karUru paTTaNamulO paSupatISvaruni guDi okaTi unnadi. idi sumAru padava SatAbdapu kAlamu nATidi. I AlayastaMbhAlapaina konni apurUpamaina nAgamaMDalAlu unnAyi. padamUDava SatAbdapu uttarArdhamulO hOyasala rAjulu maisUru samIpamulO sOmanAthapura dEvAlayAnni nirmiMchAru. I Alayapu paikappulO nAgamaMDalamu(5va chitramu) okaTi vuMdi. tirukkaDaiyUru amRtaghaTESvarAlayamulO kUDa oka sarpabaMdha SilAphalakamu galadu.

migitA pEjIlu: 1 2 3
#    
   
Print Friendly