Wadaraki uZvelesi TamaSia, romelsac Cveni welTaRricxvis mexuTe (zogi mkvlevari ki meore) saukuniT aTariReben.

rodesac saubaria Wadrakisa da maTematikis kavSirze , pirvel rgiSi unda ARiniSnos Wadrakis Seqmnis legenda.

Llegendis Tanaxmad, rodesac sparseTis Sahi gaecno am TamaSs, aRfrTovanda misiT da moisurva Wadrakis Semqmnelis, Tavisi qveSevrdomi brZenis dajildoeba da nebismieri survilis asruleba AaRuTqva. Sahi Zlier gaocda, roca brZenma “mokrZalebuli” ZRveni iTxova_ xorbali: mas surda Wadrakis dafis pirvel ujraze daedoT erTi marcvali, mereze _ori, mesameze _ oTxi, meoTxeze _ rva, mexuTeze Teqvsmeti da a.S yovel ujraze orjer meti marcvali vidre winaze.Sahma brZana rac SeiZleba swrafad aesrulebinaT brZenis survili, magram raoden didi iyo misi gaoceba,rodesac meore dRes samefo karis maTematikosebma moaxsenes,rom Sahs ar SeeZlo brZenis survilis dakmayofileba., radgan am raodenobis xorbali araTu Sahis beRlebSi, arame mTel msoflioSi arsebuli xorblis maragic ar ikmarebda.  ( xorblis saWiro raodenobaa geometriuli progresiis cifrTa jami)

1+2+2² +2³+2⁴+ ... +2⁶³ =2⁶⁴ --1 

Aam amocanas Tavis wignSi “wina Taobis Zeglebi” xsnida Suaazieli maTematikosi al-viruni(973-1048). Mman SeniSna, rom xorblis marcvlis raodenoba yovel KKK_ur ujraze erTiT metia wina K-1 ujraze yvela marcvlis raodenobaze da miiRo marcvlebis zusti raodenoba: 18446744073709551615 marcvali! xorblis am maragis(Tuki is iarsebebda) Sesanaxi beReli milionobiT kilometrze gadaiWimeboda.

saWadrako dafam, figurebma da maTma svlebma araerTi maTematikuri  amocanis Camoyalibebas Seuwyo xeli. maTgan erT-erTia rva lazieris amocana, romelsac dRes ganvixilavT. am amocanam miipyro sxvebTan erTad didi germaneli maTematikosis, karl fridrix gausis yuradRebac.

Ees amocana 1850 wels gadawyvita e.naukma,romelmac misi 92 amonaxsni moZebna.mxolod 24 wlis Semdeg SeZlo ingliselma maTematikosma j.gleiSerma determinatTa Teoriis gamoyenebiT eCvenebina rom amocanas sxva amonaxsni ar aqvs.

SevniSnoT, rom amocanis nebismier amonaxsnSi erTi lazieri unda idges a4 ujraze an mis Sesatyvis ujraze dafis RerZebis (4 RerZi) mimarT simetriul an centris mimarT dafis 90,180, an 270 gradausiT mobrunebiT miRebul ujraze: a5, d8, e8, h5,h4,e1,d1.

sul arsebobs 12 amonaxsni (pozicia)romelTa miReba ar SeiZleba erTmaneTisaga nsarkiseburi arekvliT, RerZebis mimarT an dafis mobrunebiT. Esenia: [1] a4, b1, c5, d8, e2, f7, g3, h6 [2]  a4, b1, c5, d8, e6, f3, g7, h2 [3]a4, b2, c5,  d8, e6, f1, g3, h7.[4]a4,b1,c7,d3,e6,f8,g1,h5. [5] a4, b2, c8, d5, e7, f1, g3,h6,[6]a4, b2, c7, d5, e1,f8, g6,h3. [7] a4,b2, c8  , d5, e7, f1 g3,h6. [8]a4,b2,c8,d6, e1, f3, g5,h7 [9] a4, b6, c1, d5, e2,f8, g3,h7. [10] a4, b7, c5, d2, e6, f1, g3, h8. [11] a4, b8,c1, d5, e7, f2, g6, h3 _ am 11 amonaxsnidan TiToeuls 7-7 oreuli aqvs. (sul 88 amonaxsni) da [12] a4, b6, c8, d2, e7, f1, g3, h5  , romelsac mxolod 3 oreuli aqvs (4 amonaxsni) – am poziciisTvis damaxasiaTebelia, rom masSi lazieri ar dgas 4X4 ganzomilebebis romelime c3-c6-f6-f3   centraluri kvadratis 16 ujridan romelimeze.

Mme-12 amonaxsnisagan magaliTad a4,b2,c8,d6, e1, f3, g5,h7 amonaxsnidan miviRoT misi oreuli. AamisaTvis SeiZleba dafis vertikalis aRmniSvneli asoebi (a,b,c,d,e,f,g,h )  SevcvaloT (1,2,3,4,5,6,7,8) cifrebiT, xolo horizontis ganmsazRvreli  (4,2,8,6,1,3,5,7) cifrebi ucvlelad davtovoT. cxadia, dafaze lazierebis ganlagebas (4,2,8,6,1,3,5,7) mimdevroba gansazRvravs.  Ggvaqvs ricxvTa Sesabamisoba

               4  2  8  6  1  3  5  7

               1  2  3  4  5  6  7  8        Tu saWadrako dafas centris mimarTulebiT 90⁰  _iT  mivabrunebT saaTis isris moZraobis sapirispiro mimarTulebiT, miviRebT (1) amonaxsnis Sesabamis erT-erT amonaxsns.

Ddafis aRniSnuli mobrunebisas a1  ujra h1 _Si gadava, h1 h8-Si h8 a8 –Si . Tu ujrebis sayovelTaod miRebul saxelwodebebs aRvadgenT, miviRebT, rom Sesabamisad yvela ujras feric Seecvleba.   imisaTvis, rom (1)is Sesabamisi amonaxsni ricxvTa mimdevrobiT CavweroT,  gadavweroT (2) Sesabamisoba.

          8 7 6 5 4 3 2 1

          3 8 4 7 1 6 2 5  saxiT. MmiRebuli meore striqoni qmnis saZiebel amonaxsns (a3,  b8, c4, d7, e1, f6, g2, h5 )

Tu saWadrako dafas kidev orjer movabrunebT 90^0_90⁰_iT, miviRebT (1) –is Sesabamis or axal amonaxsns: (24683179) da (47382516) anu

           a2,b4,c6,d8,e3,f1,g7,h9  (4)

da          a4,b7,c3,d8e2,f5,g1,h6  (5)

SeiZleba (4) pozicia (1)-dan  da (5)pozicia (3)_dan miRebuli iqnes uSualod. amisaTvis Sesabamisi (1) da (3) mimdevrobebi amovweroT SebrunebiT da yvela es ricxvi gamovakloT 9-s. miviReT (4) da (5) poziciebis gamomsaxvel mimdevrobebs.

radgan [12] amonaxsnis gamomxatveli  (46827135) mimdevrobebisa da misi Sebrunebuli (53172864)mimdevrobebis Sesabamisi ricxvebis jamia 9, am amonaxsns dafis SemobrunebiT mxolod 1 oreuli aqvs.

Ddafis centrisa da RerZebis mimarT simetriuli amonaxsnebis miReba cxadia sirTules ar warmoadgens.  saWadrako dafis mimarT[12] amonaxsnis simetriuloba ganapirobebs imas, rom mas “gardaqmnisas” mxolod ori oreuli   aqvs.

 rogorc aRvniSneT , rva lazieris Sesaxeb amocanis yoveli amonaxsni SeiZleba Caiweros ( X₁  X₂  ……...  X_{8 )} mimdevrobebi rac 1 2 3 4 5 6 7 8 cifrebis gadanacvlebaa. Aaq X saWadrako dafis im  horizontalis rigiTi nomeria, romelzedac  _uri vertikalis lazieri dgas.  radgan lazierebis arc erTi wyvili erT vertikalze ar dgas, yvela X  gansxvavebulia da radgan ori lazieri ar SeiZleba erT diagonalze idges, amitom

            l X_i -X_k   l i-k,       (k i 8)

1 –dan 8-mde ricxvebi amovweroT jer zrdadobiT, Semdeg ki klebadobiT da orive mimdevrobas qvevidan mivuweroT amave ricxvebis nebismieri gadanacvlebiT miRebuli erTi da igive mimdevrobebi da Sesabamisi ricxvebi SevkriboT. Tu miRebuli orive nakrebi