gahal chauras kode

gahal chauras kode haah ganiteey varganmadhye vidyarthyanna bhaumitik aakadyambaddal tark karnyas madat karnyasathi vaparla jaanara eka optical bhram aahe; kinwa tyaeivaji tyanna aakadyancha vapar karoon tark karnyas shikavanyasathi navhe tarr keval majkurache varnan aanee bhoomitiche svayamsiddha shabd vaparnyasathi. tyat thodya vegalya sanrachananmadhye samaan aakarachya done mandani darshavilya aahet. pratyekane 13x5 ujavya koneey trikon tayar keela aahe, parantu tyat 1x1 chhidra aahe.
upay.
kodichi gurukilli hii aahe qee 13x5 "trikon" paiki konatahi kharokhar trikon nahee, kinwa jarr asel tarr too kharokhar 13x5 nasel, kaaran hypotenews asey disanare vakalele aahe. tulana shabdant, manvi dolhyala teey tase disu shakate, taree 'hypotenews' eka susangat utaar thevat nahee. 
dilelya ghatak bhaganmadhun kharaa 13×5 trikon tayar keela jaau shakat nahee. chaar aakruti (pivalya, laal, nilya aanee hiravya aakarachya) ekoon 32 ekake kshetrafalachya aahet. aakadyanpasun tayar jhalele spasht trikon 13 ekake rund aanee 5 ekake unch aahet, tyamule asey disate qee kshetra "s" = = 32.5 ekake asave. tathapi, nilya trikonache gunottar 5:2 (= 2.5) aahe, tarr laal trikonache gunottar 8:3 (± 2.667) aahe, tyamule pratyek aakrutitil spasht sanyukt hypotenews pratyakshat vakalela aahe. vakalelya hypotenuges, pahili aakruti pratyakshat ektrit 32 ekake vyapate, tarr dusari aakruti 33 vyapate, jyat 'gahal' chauras samavisht aahe.
vakanyache praman andaje ekak (1.245364267 °) aahe, jeey kodechya aakrutivar pahane katheen aahe aanee graphik mhanoon chitrit kele gele aahe. khalchya pratimetil laal aanee nila trikon jethe midatat tyaa grid binduchi nond ghya (ektrit aakrutichya ujavya bajula 5 chauras aanee khalchya davya davya done ekak varr) aanee tyachi tulana tulana aakrutivaril tyach binduparyant qaraa; kadaa varchya pratimetil khunachya kinchit khalee aahe, parantu khalchya bajus tyatoon jaate. donhi aakadyanmadhun hypotenus aachchhadit kelyane agadi eka grid chauras kshetrasah (pikche pramey 0 aanee hairssp; + −1 = 1 dete) eka atishay patal samantar chaturbhuj (chaar laal thipkyanni darshavilele) tayar hote, tyamule 'gahal' kshetra.
tattva.
martin gardnerchya matey, yaa vishisht kodicha shodh newyork shaharatil haushi jadugar paul curry yane 1953 madhye lavala hota. tathapi, vichhedan virodhabhas heey tattva 16 vya shatkachya suruvatipasun dnyat aahe. 
kodichya bhaganchi purnank parimane (2,3,5,8,13) hii kramakrami fibonachi sankhya aahet, jee "patal samantar chaturbhuj" madheel achook ekak kshetrakade netat.
itar anek bhaumitik vichhedan kodee fibonachi anukramachya kahee sopya gunadharmanvar aadharit aahet.
samaan kodee.
samm lloydcha buddhibal puttle virodhabhas 8×8 chaurasanchya done punarrachana darshavito. mothya" punarrachanemadhye (ujavikadil pratimetil 5 × 13 aayatakruti), aakrutinmadhil antaramadhye ektrit ekak chauras tyanchya chauras antar samakakshanpeksha adhik kshetra asate, jyamule eka bhram nirman hoto qee tethil aakruti mool chauras aakrutipeksha jaast jaaga ghetat. lahan" punarrachanemadhye (5 × 13 aayatakrutichya khalicha aakar), pratyek chaturbhujala tribhujala tyachya varchya/khalchya kathasathi ardhya ekkachya kshetrafalachya aadhare greed resheshi sanrekhit karane aavashyak aahe, parinami eka ekak chauras kshetramadhye ekoon nuksan hote.
mitsunobu matsuyamacha 'virodhabhas' chaar sarvasamaveshak chaturbhuj aanee eka lahan chauras vaparato, jeey eka motha chauras tayar karatat. jevha chaturbhuj tyanchya kendrambhovati firavale jaatat tevha teey lahan chaurasachi jaaga bharatat, jaree aakrutiche ekoon kshetrafal aparivartit disate. naveen mothya chaurasanchi bajoo mool chaurasapeksha thodi lahan aahe yaa vastusthitidvare spasht virodhabhas spasht keela jaato. jarr "θ" haah pratyek chaturbhujatil done viruddha bajunmadhil coone asel, tarr donhi kshetranche gunottar seek 2 "θ" dware dile jaate. θ" = 5° sathee, heey andaje 1.00765 aahe, jeey sumare 0.8% chya farkashi sambandhit aahe.
gayab honare kode haah eka yantrik optical bhram aahe joou kodeche kahee bhag firavale jaatat tevha vishisht vastuchi vegvegali sankhya darshavito.

