Radiological Analysis of Human Hand in Terms of Artistic Anatomy

Transcription

1 ORİJİNAL ARAŞTIRMA Radiological Analysis of Human Hand in Terms of Artistic Anatomy Ali YILMAZ, MD, a Banu ALICIOĞLU, MD, b Necdet SÜT, c Enis ULUÇAM, MD, a Selman ÇIKMAZ, MD a Departments of a Anatomy, b Radiology, c Bioistatistic, Trakya University Faculty of Medicine, Edirne Ge liş Ta ri hi/re ce i ved: Ka bul Ta ri hi/ac cep ted: Ya zış ma Ad re si/cor res pon den ce: Ali YILMAZ, MD Trakya University Faculty of Medicine, Department of Anatomy, Edirne, TÜRKİYE/TURKEY ayz51@yahoo.com ABS TRACT Ob jec ti ve: The hands are one of the most cons pi cu o us parts of the body. The aim of this study was to in ves ti ga te the re la ti ons hip bet we en the bo nes that com pri se the hands and the ir aest he tic im por tan ce in terms of the Fi bo nac ci se ri es. Ma te ri al and Met hods: In this study, which was de sig ned ret ros pec ti vely, 123 di gi tal hand ro ent ge nog rams of adult pa ti ents we re re vi e wed. Each fin ger was me a su red in terms of me ta car pal, pro xi mal, midd le, and dis tal pha lan ge al lengths by using a di gi tal ca li per. The pro xi mal pha lan ge al length was sub trac ted from the sum of the lengths of the midd le and dis tal pha lan ges and the me ta car pal length was sub trac ted from sum of the lengths of the pro xi mal and midd le pha lan ges, to in ves ti ga te the con for mity to Fi bo nac ci se qu en ce. The Bland-Alt man met hod was used to eva lu a te the me a su re ments. Re sults: The re is a mat he ma ti cal harmony bet we en all fin ger bo nes in terms of the Fi bo nac ci se qu en ce. The first, se cond, and fifth me - ta car pals con form to the Fi bo nac ci se qu en ce; ho we ver the third and fo urth me ta car pals do not. Conc lu si on: It can be ea sily pro ven that all of the bo nes that form fin gers are in ac cor dan ce with the Fi bo nac ci se qu en ce. The se re sults con vin ce us that Fi bo nac ci se qu en ce can be used for the recons truc ti on of hu man hand af ter a se ri o us tra u ma or con ge ni tal ano ma li es. Key Words: Ana tomy ar tis tic; ra di og raphy; hand; fin ger pha lan ges; ant hro po metry ÖZET Amaç: El ler vü cu dun en faz la dik kat çe ken kı sım la rın dan dır. Ça lış ma mı zın ama cı eli oluş - tu ran ke mik ler ara sın da ki iliş ki yi ve Fi bo nac ci se ri si açı sın dan es te tik öne mi ni in ce le mek tir. Ge reç ve Yön tem ler: Ret ros pek tif ta sa rım da plan la nan ça lış ma mız da, 123 ye tiş kin has ta nın ön-ar ka el gra fi si in ce len di. Her bir par mak ta me ta kar pal, prok si mal, me di al ve dis tal fa lanks uzun luk la rı di - ji tal kum pas ile öl çül dü. Prok si mal fa lanks uzun luk la rı dis tal ve me di al fa lank sla rın top lam uzun - luk la rın dan, me ta kar pal le rin uzun luk la rı ise prok si mal ve me di al fa lank sla rın top lam uzun luk ların dan çı kar tı la rak Fi bo nac ci se ri si ne uy gun luk la rı araş tı rıl dı. Öl çüm so nuç la rı mız, Bland Alt man me to duy la de ğer len di ril di. Bul gu lar: Par mak la rı oluş tu ran tüm ke mik ler ara sın da ma te ma tik sel ola - rak Fi bo nac ci se ri si ile uyu mun ol du ğu nu söy le ye bi li riz. Bi rin ci, ikin ci ve be şin ci me ta kar pal ler Fi - bo nac ci se ri si ne uy gun luk gös ter mek te dir; an cak üçün cü ve dör dün cü me ta kar pal ler gös ter me - mek te dir. So nuç: İnsan eli ni oluş tu ran ke mik le ri, uzun luk la rı açı sın dan Fi bo nac ci se ri siy le iliş ki len - dir me nin müm kün ola bi le ce ği ni söy le ye bi li riz. Bu so nuç lar, in san eli nin cid di trav ma ya da kon je - ni tal ano ma li le ri nin re kons trük si yo nun da Fi bo nac ci se ri sin den fay da la nı la bi le ce ği ni or ta ya koy - mak ta dır. Anah tar Ke li me ler: Ar tis tik ana to mi; rad yog ra fi; el; par mak fa lank sla rı; an tro po met ri Turkiye Klinikleri J Med Sci 2010;30(2):690-7 Cop yright 2010 by Tür ki ye Kli nik le ri he human hand is a symbol of beauty and also an indicator of character from the perspective of its shape and function. 1 Thus, many patients not only want the surgeons to repair the function of their hands, but they also want their hands to look beautiful. 2 Throughout his- 690 Turkiye Klinikleri J Med Sci 2010;30(2)

2 Anatomy tory, many ar tists and phi lo sop hers se arc hed for a ma gi cal mat he ma ti cal for mu la that co uld exp la in be a uty; the se arch en ded in a for mu la cal led the gol den me an. 3,4 Alt ho ugh the re is no writ ten do c- u ment abo ut the ori gin of this nu me ri cal va lu e, the re are many re fe ren ces to it thro ug ho ut history. 5,6 The gol den me an is ge ne rally at tri bu ted to Pytha go ras and Pla to, but it is al so tho ught to be con nec ted to lo ga rith mic and equ i an gu lar spi rals and the Fi bo nac ci se qu en ce. 7,8 The Fi bo nac ci se qu en ce was first des cri bed by Le o nar do Pi sa no Bi gol lo (al so known as Fi bo nac ci) in his bo ok Li ber Aba ci pub lis hed in With this bo ok, Fi bo nac ci tri ed to in tro du ce the nu me - ra ti on de ci mal that al so inc lu des ze ro to the in tel - lec tu ally dor mant Eu ro pe. In the last sec ti on of his bo ok, he put for ward a ridd le-li ke prob lem abo ut the rep ro duc ti on of rab bits in a con fi ned are a. This ridd le, which was li ke a prob lem, po ints out an arith me ti cal se qu en ce, re sul ting in a par ti cu lar ra - ti o. Each new num ber in the se ri es was simply the sum of two be fo re it (1, 1, 2, 3, 5, 8, 13...). The ra - ti o of two suc ces si ve num bers ap pro xi ma tes a 1.62 con ti nu ing va lu e (1; 2; 1.5; 1.60; 1.625; ). Af ter the first twel ve num bers, this nu me ri cal va - lu e can be fi xed to when the num bers are ro - un ded up. 5,9 This ir ra ti o nal va lu e is al ter na tely cal led the gol den me a n, gol den ra ti o, gol den sec ti o n or Fi bo nac ci se qu en ce, and is used in many works of arc hi tec tu re, mu sic, art and sculp tu re However the se num bers and ra ti os se e med to be used by ar tists in tu i ti vely. Le o nar do da Vin ci, ho - we ver, used the se va lu es de li be ra tely in his ex pe ri - ments. For examp le, he de sig ned the dra wing of Lu ca Pa ci o li s bo ok The Di vi na Pro por ti o ne, in which the re was a pro fi le sho wing the gol den me - an of the hu man fa ce. At the be gin ning of twen ti - eth cen tury, Le Cor bu si er men ti o ned the pro por ti ons of the hu man body, in his study known as Mo du lar. 4,10 To day, in the me di cal fi eld, as well as in ana - tomy, the re are many cli ni cal branc hes such as plas tic re cons truc ti ve and est he ti cal sur gery which con si der the hu man body as an ar tis tic ob ject. Ho - we ver, cur rent stu di es mostly de al with the fa ce Yılmaz et al and ha ve neg lec ted the ot her parts of the body. However, li ke the fa ce, the hands at tract the most at ten ti on and are dif fi cult to hi de. The aim of this study is to in ves ti ga te the re la - ti on bet we en the bo nes that form the hands and the Fi bo nac ci se qu en ce. We pre sent the exis ten ce of such a ra ti o ba sed on sci en ti fic da ta in the est - he ti cal vi ew of the hu man body. MATERIAL AND METHODS Pos te ro an te ri or ra di og rams of the hands of pa ti ents who had app li ed to Trak ya Uni ver sity Me di cal Scho ol Hos pi tal bet we en Feb ru ary 1 and March 25 of 2008 we re exa mi ned. All X-rays we re exa mi ned by an ex pe ri en ced musc le-ske le ton ra di o lo gist and an ana to mist at a ge ne ral-pur po se Poly star Si e mens work sta ti on. Ca ses in whom bo ne de ve lop ment had not be en comp le ted, patients with con ge ni tal and de ve lop men tal dyspla si a, me ta bo lic ill nes ses that af fect bo nes, tra u ma tic de for ma ti ons, sur gi cal ope ra ti ons, or un sa tis fac tory ra di og rams we re not ta ken in to con si de ra ti on. Me a su re ments we re perfor med in ra di og rams of 123 pa ti ents (66 ma les, 57 fe ma les) with a me an age of 47,80±14,99. Alt ho ugh this study was de sig ned ret ros pec ti - vely, et hi cal ap pro val was ob ta i ned from the lo cal Et hi cal Re vi ew Com mit te e of the Fa culty of Me di - ci ne. The re a son for plan ning a ret ros pec ti ve study was to avo id ne ed less ra di a ti on ex po su re to the pati ents. To ha ve mo re ac cu ra te me a su re ments and to cla rify the ana to mi cal struc tu res bet ter, the shots we re en lar ged. Me ta car pal (first me ta car pal [mc1], se cond me ta car pal [mc2], third me ta car pal [mc3], fo urth me ta car pal [mc4], fifth me ta car pal [mc5]), pro xi mal pha lan ge al (pro xi mal pha lanx of the thumb [pp1], pro xi mal pha lanx of the in dex fin ger [pp2], pro xi mal pha lanx of the midd le fin ger [pp3], pro xi mal pha lanx of the ring fin ger [pp4], pro xi mal pha lanx of the litt le fin ger [pp5]), midd le pha lan - ge al (midd le pha lanx of the in dex fin ger [mp2], midd le pha lanx of the midd le fin ger [mp3], midd - le pha lanx of the ring fin ger [mp4], midd le pha lanx of the litt le fin ger [mp5]), and dis tal pha lan ge al (dis tal pha lanx of the thumb [dp1], dis tal pha lanx Turkiye Klinikleri J Med Sci 2010;30(2) 691

3 Yılmaz ve ark. of the in dex fin ger [dp2], dis tal pha lanx of the midd le fin ger [dp3], dis tal pha lanx of the ring fin ger [dp4], dis tal pha lanx of the litt le fin ger [dp5]) lengths we re me a su red bet we en the dis tal and pro - xi mal tips of the me ta car pals and pha lan ges by using di gi tal ca li per. The dif fe ren ces bet we en pro xi mal pha lan ge al lengths (pp2, pp3, pp4, pp5) and the sum of the distal and midd le pha lan ge al lengths of each fin ger (the sum of dis tal and midd le pha lan ge al lengths of in dex fin ger [f2], the sum of dis tal and midd le phalan ge al lengths of midd le fin ger [f3], the sum of distal and midd le pha lan ge al lengths of ring fin ger [f4], the sum of dis tal and midd le pha lan ge al lengths of litt le fin ger [f5]), ex cept the thumb, we - re me a su red. Si mi larly, the dif fe ren ces bet we en the lengths of me ta car pals (mc2, mc3, mc4, mc5) and the sum of pro xi mal pha lan ge al and midd le phalan ge al lengths (sum of pro xi mal pha lan ge al and midd le pha lan ge al lengths of in dex fin ger [f2a], sum of pro xi mal pha lan ge al and midd le pha lan ge - al lengths of midd le fin ger [f3a], sum of pro xi mal pha lan ge al and midd le pha lan ge al lengths of ring fin ger [f4a], sum of pro xi mal pha lan ge al and midd le pha lan ge al lengths of litt le fin ger [f5a]) we re cal cu la ted (Fig. 1). Owing to the ab sen ce of midd - le pha lanx in the thumb, the dif fe ren ce bet we en the first me ta car pal (mc1) and the sum of dis tal (dp1) and pro xi mal pha lan ge al lengths of first finger we re cal cu la ted to in ves ti ga te the con for mity to Fi bo nac ci se qu en ce. STA TIS TI CAL ANALY SIS Bland & Alt man Met hod The Bland & Alt man plot is a sta tis ti cal met hod to com pa re two me a su re ments tech ni qu es. In this grap hi cal met hod, the dif fe ren ces (or al ter na ti vely the ra ti os) bet we en the two tech ni qu es are plot ted aga inst the ave ra ges of the two tech ni qu es. Ho ri - zon tal li nes are drawn at the me an dif fe ren ce, and at the li mits of ag re e ment, which are de fi ned as the me an dif fe ren ce plus and mi nus 1.96 ti mes the stan dard de vi a ti on of the dif fe ren ces. The Bland- Alt man met hod was used in eva lu a ti on of the ni ne pa ra me ters; one of the thumb (f1-m1), two pa ra - me ters of each of the ot her fin gers (f2-pp2, f2a-m2, Anatomi FIGURE 1: PA radiogram of a hand. Bone lengths identified by the name of the field used for statistical analysis. pp- proximal phalanx; dp-distal phalanx; mp-middle phalanx; mc-metacarpal; Thumb-1;Index finger- 2;Middle finger- 3; Ring finger -4; Little finger -5. TABLE 1: Descriptive statistics of difference values. %95 Confidence Interval Differences Mean SD Lower Limit Upper Limit f1-m f2-pp f2a-m f3-pp f3a-m f4-pp f4a-m f5-pp f5a-m f3-pp3, f3a-m3, f4-pp4, f5-pp5, and f5a-m5). In the Bland-Alt man met hod, to be ab le to talk abo ut harmony, the 95% con fi den ce in ter val (d ± 1.96 SD) sho uld inc lu de ze ro and the dis tri bu ti on of the va l- u es sho uld be wit hin con fi den ce li mits as much as pos sib le. 11 RESULTS The va lu es ob ta i ned by the sub trac ti on of pro xi mal pha lan ge al and me ta car pal lengths from the sum of 692 Turkiye Klinikleri J Med Sci 2010;30(2)

4 Anatomy Yılmaz et al FIGURE 2: Distribution graph of f1-m1 average against difference value FIGURE 3: Distribution graph of f2-pp2 average against difference value FIGURE 4: Distribution graph of f2a-m2 average against difference value FIGURE 5: Distribution graph of f3-pp3 average against difference value two pre vi o us bo ne lengths are shown in Tab le 1. Dis tri bu ti on grap hics of each pa ra me ter ac cor ding to Bland-Alt man analy sis can be fo und in Figs In the exa mi na ti on of f1-m1, f2-pp2, f2a-m2, f3-pp3, f4-pp4, f5-pp5, and f5a-m5 dis tri bu ti on grap hics, it can ea sily be se en that all grap hics inc - lu ded ze ro and are in har mony with the Fi bo nac ci se qu en ce. When the Tab le 1 is sub jec ted to scru tiny, it can be se en that f2-pp2 is the most har mo ni o us para me ter with -0.3 ± 2.3 dif fe ren ce va lu e (95% confi den ce in ter val: -4.6 to 4.1) fol lo wed by f3-pp3 and f4-pp4 co up les, res pec ti vely. Dis cor dant pa ra me - ters we re f4a-m4 with 8.9 ± 2.8 dif fe ren ce va lu e FIGURE 6: Distribution graph of f3a-m3 average against difference value Turkiye Klinikleri J Med Sci 2010;30(2) 693

5 Yılmaz ve ark. Anatomi FIGURE 7: Distribution graph of f4-pp4 average against difference value FIGURE 8: Distribution graph of f4a-m4 average against difference value FIGURE 9: Distribution graph of f5-pp5 average against difference value FIGURE 10: Distribution graph of f5a-m5 average against difference value (95% con fi den ce in ter val: ), and f3a-m3 with 6.3 ± 3.3 dif fe ren ce va lu e (95% con fi den ce inter val: ). When pro xi mal pha lan ge al lengths were ta ken in to con si de ra ti on, it was se en that the va lu e of in - dex fin ger was be low ze ro in most of the pa ti ents. Midd le, ring and litt le fin ger va lu es of the sub jects we re abo ve ze ro in ge ne ral. The dif fe ren ce va lu es we re de ter mi ned as equ al to ze ro in in dex fin gers of fo ur pa ti ents and in ring fin ger and litt le fin ger of two pa ti ents. In the eva lu a ti on of me ta car pals, it was se en that the dif fe ren ce of se cond me ta car pal was ge ne - rally be low ze ro, whe re as the va lu es of the ot her fin gers were abo ve ze ro. In first and fifth me ta car - pals of one sub ject, the dif fe ren ce va lu e was equ al to ze ro, sho wing per fect har mony. DISCUSSION Ac cor ding to the re sults of this study, it is pos sib - le to say that dis tal, midd le, and pro xi mal pha lan - ge al lengths of all the sub jects are in har mony with Fi bo nac ci se qu en ce. Ho we ver, the har mony bet - we en midd le and pro xi mal pha lan ge al lengths was ob ser ved only in the se cond and the fifth me ta car - pals, when the me ta car pals lengths were substracted from the sum of midd le and pro xi mal pha lan ge al lengths. 694 Turkiye Klinikleri J Med Sci 2010;30(2)

6 Anatomy This num ber se qu en ce that is tho ught to be the fo un da ti on of hu man aest he tics has at trac ted sci en tists in te rest sin ce an ci ent ti mes and is re cog - ni zed in many ani ma te and ina ni ma te ob jects. Af ter be co ming awa re of the spi ral of flo rets in the da isy and by the le a ves aro und its stem, which fol low pre ci sely the Fi bo nac ci se ri es in mat - he ma tics, Tu ring and his stu dents wro te se ve ral papers ad dres sed to the prob lem of le af ar ran ge ment (phyllo ta xis), which con ti nu es to exer ci se many bio lo gists to day. Tu ring s pa per has ins pi red a cur rent ge ne ra ti on of mat he ma ti cal mo de ling of spa ti al patterns in li ving or ga nism. 12 In his study On Growth and For m, Thompson po in ted out how the Fi bo nac ci se qu en ce under li es many na tu ral forms such as the spi ra ling Na u ti lus shell, the ar ran ge ment of sca le rows on Nor way spru ce co nes, cel lu lar struc tu re, ar ran ge - ments of le a ves and ani mal horns. Ac tu ally, Thomp son has de mons tra ted that the re is a law ful un derl ying mat he ma ti cal struc tu re to forms ba sed on the gol den sec ti on and Fi bo nac ci se qu en ce. 13,14 Ad di ti o nally, Car son, Arn he im, and Nay lor sta ted that spi rals of gro wing flo wers we re re la ted to the Fi bo nac ci se qu en ce. 10,15,16 Fen som, in his ar tic le, tal - ked abo ut the pos si bi lity that hu man evo lu ti on stops when it re ac hes the gol den num ber. 17 Ya ma - gis hi et al., in his study, put for ward the com pa ti - bi lity bet we en the hu man ge ne nuc le o ti de ar ran ge ment and the Fi bo nac ci se qu en ce. 18 Mo re o - ver, McWhin ni e stu di ed the gol den me an of hu - man growth, bi o logy, and arc hi tec tu re. 14 The first bo ok in his tory de fi ning hu man pro por ti ons is Poly cle i tus Ca non. Ac cor ding to To bin, Poly cle i - tus men ti o ned se ve ral ra ti os in his bo ok. 19 The app li ca ti on of the gol den ra ti o to den tal aest he tics was first do cu men ted by Le win in 1978 who al so exp la i ned its his tory and mat he ma tics. He al so exp la i ned re gar ding the as so ci a ti on of the propor ti on with an aest he ti cally ple a sing den ti ti on and smi le. 20 Est he ti cal den tists ha ve used many such formu las whi le re cons truc ting the te eth to ob ta in a ni ce smi le. Lom bar di cla i med the exis ten ce of gol den me an bet we en the hu man te eth as well. 21 Yılmaz et al Pres ton stu di ed the re la ti ons hip of the gol den ra ti o in ma xil lary den ti ti on and fo und a gol den ra - ti o bet we en the per ce i ved width of the ma xil lary cen tral and la te ral in ci sors. 22 Mack dis cus sed the im por tan ce of tre a ting the den ti ti on ac cor ding to the fa ce ba sed on the gol den ra ti o. He sta ted that the lo wer one thirds of the fa ce sig ni fi cantly inf lu en ces the fa ci al ap pe a ran ce and war ned re gar ding po ten ti al comp li ca ti ons occur ring in fa ci al aest he tics when only mo un ted casts we re used for di ag no sis. 23 Ro bert Ric ketts, an ort ho don tist, dis cus sed the gol den ra ti o in ide al fa ce pro por ti ons by using his self-de sig ned to ol the gol den di vi dend. 24 Li ke wi - se, Step han Mar qu art, who has per for med many im por tant stu di es on the ra ti os of hu man aest he tic and symmetry, de sig ned a se ri es of be a uty masks ba sed on the gol den ra ti o. 3 Jef fer son il lus tra ted many gol den ra ti o di ag - rams and com pu ter ge ne ra ted pho tog raphs pro vi - ding an ide al pic tu re of the comp le te he ad and sup por ted his work with cep ha lo met ric tra cings. 25 Litt ler ob ser ved an arith me ti cal re la ti on among the bo nes that sha pe the hand and sa id that fin ger mo ve ments form equ i an gu lar spi rals. 8 Ad di - ti o nally, Po well re la ted the rum ba dan ce and mu - sic to the Fi bo nac ci se qu en ce. 9 Twen ti eth-cen tury mu sic has be en di rectly re la ted to the Fi bo nac ci sequ en ce by Kra mer, Ma nu el and San ti a go, and Wal - ker sta ted that the gol den me an co uld be used in cal cu la ting elec tri cal cir cu it re sis tan ce Ne vert - he less, the re are many stu di es that con tra dict the re se arch abo ut the gol den ra ti o and Fi bo nac ci se qu - en ce. 29 Du ring a re vi ew of the li te ra tu re, we ca me ac - ross many stu di es on the lengths of hand bo nes, rati os among the fin gers and the fac tors af fec ting the se ra ti os. We we re ab le to find two ar tic les in which the Fi bo nac ci se qu en ce and the gol den ra ti - o of the length of fin gers we re dis cus sed. In one of the se two stu di es Park et al. wor ked on 100 handgrap hics and in the ot her study Ha mil ton and Duns mu ir wor ked on 197 grap hics. 30,31 Alt ho ugh both of the se stu di es had used the sa me pa ra me ters, the po ints used in the me a su re ments dif fer. Ha mil ton Turkiye Klinikleri J Med Sci 2010;30(2) 695

7 Yılmaz ve ark. and Duns mu ir me a su red the dis tan ce bet we en the ro ta ti on cen ters of the hand bo nes. On the ot her hand, Park et al. me a su red the dis tan ce bet we en the mid-po ints of jo int ca vi ti es. In the pre sent study, we fo und the ac tu al bo ne length by me a su - ring the dis tan ce bet we en the ba se and dis tal tip po ints of me ta car pals and pha lan ges. Ex cept for the thumb, whe re pro xi mal pha lan - ge al length was sub trac ted from the sum of dis tal and midd le pha lan ge al lengths, we de ter mi ned that the 0 va lu e was in the 95% con fi den ce in ter val in each fin ger. Li ke wi se, when the me ta car pal length was sub trac ted from the sum of pro xi mal and midd le pha lan ge al lengths of f2a-m2 and f5af5, we ob ser ved that the 0 va lu e was in 95% confi den ce in ter val for each fin ger. The thumb, which has no midd le pha lanx re ve a led 0 va lu e in 95% con fi den ce in ter val when its me ta car pal length was sub trac ted from the sum of pro xi mal and dis tal pha lan ge al lengths. Un li ke the pre sent study, Park et al. co uld not find any cor re la ti on to the Fi bo nac ci se qu en ce in any of the fin gers. In the ir study, Ha mil ton and Anatomi Duns mu ir did not lo ok for the Fi bo nac ci se qu en ce, but lo o ked for the gol den ra ti o, which was tho ught to be the re sult of the Fi bo nac ci se qu en ce. They co - uld not pro ve the exis ten ce of the gol den ra ti o. CONCLUSION It can be suggested that all of the bo nes that form the fin gers were in har mony with the Fi bo nac ci sequ en ce mat he ma ti cally. Si mi larly, the exis ten ce of this mat he ma ti cal se qu en ce can be se en in f1-m1, f2a-m2, and f5a-m5. Ho we ver, be ca u se of not ha v- ing any 0 va lu e in the 95% con fi den ce in ter val, f3a-m3 and f4-m4, do not con form to the Fi bo nac - ci se qu en ce. The re are many stu di es in which so me numbers and ra ti os in na tu re are used by ar tists thro ug - ho ut his tory. In this study, we cla im that it is pos sib le to re la te the bo nes for ming the hu man hand with the Fi bo nac ci se qu en ce. As a conc lu si on, the Fi bo nac ci se qu en ce can be used as an al ter na - ti ve op ti on in re cons truc ti on of the hu man hand af ter a se ri o us tra u ma or in case of con ge ni tal abnormalities. 1. Gürcan S, Adıyaman S. [Anatomy and kinesiology of the hand]. Turkiye Klinikleri J PM&R- Special Topics 2008;1(1): Jakubietz RG, Jakubietz MG, Kloss D, Gruenert JG. Defining the basic aesthetics of the hand. Aesthetic Plast Surg 2005;29(6): Marquardt SR. Dr. Stephen R. Marquardt on the Golden Decagon and human facial beauty. Interview by Dr. Gottlieb. J Clin Orthod 2002;36(6): Seghers MJ, Longacre JJ, DeStefano GA. The golden proportion of beauty. Plast Reconstr Surg 1964;34(4): Peterson RG. Critical calculations: measure and symmetry in literature. PMLA 1976;91(3): Plug C. The golden section hypothesis. Am J Psychol 1980;93(3): Bell ET. The golden and platinum proportions. National Mathematic Magazine 1944; 19(1): REFERENCES 8. Littler JW. On the adaptability of man's hand (with reference to the equiangular curve). Hand 1973;5(3): Powell NW. Fibonacci and the gold mean: rabbits, rumbas, and rondeaux. J Music Theor 1979;23(2): Arnheim R. A review of proportion. J Aesthet Art Critic 1955;14(1): Bland JM, Altman DG. Statistical methods for assessing agreement between two methods of clinical measurement. Lancet 1986; 1(8476): Wan Ho M. Reanimating nature: the integration of science with human experience. Leonardo 1991;24(5): Neperud RW, Serlin RC. The fibonacci sequence: proportional and semantic bases of children s aesthetic preferences. Stud Art Educ 1984;25(2): McWhinnie HJ. A biological basis for the golden section in art and design. Leonardo 1989; 22(1): Carson J. Fibonacci numbers and pineapple phyllotaxy. The Two-Year College Mathematics Journal 1978;9(3): Naylor M. Golden, 2, and π Flowers: A Spiral Story. Mathematics Magazine 2002;75(3): Fensom DS. The golden section and human evolution. Leonardo 1981;14(3): Yamagishi ME, Shimabukuro AI. Nucleotide frequencies in human genome and fibonacci numbers. Bull Math Biol 2008;70(3): Tobin R. The Canon of polykleitos. AJA 1975;79(4): Levin EI. Dental esthetics and the golden proportion. J Prosthet Dent 1978;40(3): Lombardi RE. The Principles of Visual Perception and Their Clinical Application to Denture esthetics. J Prosthet Dent 1973;29(4): Preston JD. The Golden Proportion Revisited. J Esthet Dent 1993;5(6): Turkiye Klinikleri J Med Sci 2010;30(2)

8 Anatomy 23. Mack MR. Vertical Dimension: A Dynamic Concept Based on Facial Form and Oropharyngeal Function. J Prosthed Dent 1991; 66(4): Ricketts RM. Esthetics, environment, and the law of lip relation. Am J Orthod 1968;54(4): Jefferson Y. Skeletal types: key to unraveling the mystery of facial beauty and its biologic significance. J Gen Orthod 1996;7(2): Kramer J. The fibonacci series in twentiethcentury music. Journal of Music Theory 1973; 17(1): Manuel G, Santiago A. An Unexpected Appearance of the Golden Ratio. The College Mathematics Journal 1988; 19(2): Walker RC. An electrical network and the golden section. The Mathematical Gazette 1975; 59(409): Markowsky G. Misconceptions about the Yılmaz et al golden ratio. The College Mathematics Journal 1992;23(1): Park AE, Fernandez JJ, Schmedders K, Cohen MS. The Fibonacci sequence: relationship to the human hand. J Hand Surg Am 2003;28(1): Hamilton R, Dunsmuir RA. Radiographic assessment of the bones of the lengths of the fingers of the human hand. J Hand Surg Br 2002;27(6): Turkiye Klinikleri J Med Sci 2010;30(2) 697