ON THE CHINESE CHECKER SPHERE. Mine TURAN, Nihal DONDURMACI ÇİN DAMA KÜRESİ ÜZERİNE

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1 DÜ Fen Bilimlei Enstitüsü Degisi Sı 9 Ağustos 9 On The Chinese Cheke Sphee M. Tun N. Donumı ON THE CHINESE CHECKER SHERE Mine TURAN Nihl DONDURMACI Deptment of Mthemtis Fult of Ats n Sienes Dumlupin Univesit Küth Geliş Tihi: Kul Tihi:..9 ABSTRACT The ojet of the pesent ppe is to stu efine the sphee in ptiul meti on n etemine the piees of the sphee whih is fome these plnes. It is use the istne etween n two points t thee imensionl Chinese Cheke spe. AMS Sujet Clssifition: 5K5 5K99 Kewos: Chinese Cheke plne Chinese Cheke spe Chinese Cheke istne. ÇİN DAMA KÜRESİ ÜZERİNE ÖZET Bu çlışm öel metikli uın küei tnımlk küei oluştun pçl elilenmektei. Bunu pken öel metik olk üç outlu Çin Dm Uın iki nokt sınki uklığı veen Çin Dm metiği kullnılmktı. Anht Kelimele: Çin Dm ülemi Çin Dm uı Çin Dm uklığı.. INTRODUCTION In Chinese Chekes gme the stle of movement is fom southwest to nothest fom est to west n noth n south. Kuse E. F. [5] keeping this ule in min ske the uestions of how to evelop meti whih woul e simil to the movements me pling Chinese Chekes. Chen G. [] hs intoue the meti C L S whee L m n min S Y in the nltil plne. The Chinese Cheke plne 7. The ove meti n e genelie n the Chinese Cheke spe of imension thee n e intoue using this meti in thee imensionl nlitil spe fo n two points X n geomet hs een stuie n impove up to now see 4 6 whee C L S m L n

2 DÜ Fen Bilimlei Enstitüsü Degisi On The Chinese Cheke Sphee Sı 9 Ağustos 9 M. Tun N. Donumı min S inste of the well known Eulien meti E whee n. 4 In this wok the Chinese Cheke sphee t the Chinese Cheke spe hs een intoue n genel sphee eution hs een fomulte. Thought this stu we wite CC inste of Chinese Cheke fot he ske of shot.. CHINESE CHECKER METRIC FOR THREE DIMENSIONAL SACE In [4] In thee imensinol CC spe points lines n plnes e the sme with in Eulien se. It n e shown tht if : C S L C. whee C is meti spe.. CHINESE CHECKER SHERE In this wok we now efine CC-sphee poeeing oing to use nologous Eulien pesiption. : X M X C C tht is : X M X M X C S L min m. n M. Theoem.: The set C given Eution. is CC-sphee. oof: Consie. one n see tht the eutions with solute vlue epessions must e solve in ll the possile ses of. We give the pof fo one se fo the othe ses the pof simill. A B C D E F G H I J K L M

3 DÜ Fen Bilimlei Enstitüsü Degisi On The Chinese Cheke Sphee Sı 9 Ağustos 9 M. Tun N. Donumı Let. We otine fo the suses whee. hs solution If then in the omin we tke emin of the line in the omin we tke emin of the line in the omin we tke emin of the line If then in the omin

4 DÜ Fen Bilimlei Enstitüsü Degisi On The Chinese Cheke Sphee Sı 9 Ağustos 9 M. Tun N. Donumı 4 we tke emin of the line in the omin we tke emin of the line in the omin we tke emin of the line If then in the omin we tke emin of the line in the omin we tke emin of the line

5 DÜ Fen Bilimlei Enstitüsü Degisi Sı 9 Ağustos 9 On The Chinese Cheke Sphee M. Tun N. Donumı in the omin we tke emin of the line 4 If then -+-+-= ==-+-= ==++-= ==+-+= then -<- in the omin =-++-= = = we tke emin of the line ++ in the omin =-+-+= = için = için we tke emin of the line -<- in the omin =+-+-= = = we tke emin of the line 5If then -+-+-= ==--+= ==-+-= 5

6 DÜ Fen Bilimlei Enstitüsü Degisi Sı 9 Ağustos 9 On The Chinese Cheke Sphee M. Tun N. Donumı ==+-+= -<- in the omin =--+-= = = we tke emin of the line +<+ in the omin = -+-+= = = we tke emin of the line +<+ in the omin =+-+-= = = we tke emin of the line 6 If then -+-+-= ==---= ==-+-= ==+--= +<+ in the omin = --+-= = = we tke emin of the line +<+ in the omin 6

7 DÜ Fen Bilimlei Enstitüsü Degisi Sı 9 Ağustos 9 On The Chinese Cheke Sphee M. Tun N. Donumı = -+--= = için = için. we tke emin of the line iken ->- in the omin =+-+-= = = we tke emin of the line 7 If then -+-+-= ==--+= ==-+-= == +-+= ++ in the omin = --+-= = = we tke emin of the line -- in the omin = -+-+= = için we tke emin of the line = için +>+ in the omin =+-+-= = 7

8 DÜ Fen Bilimlei Enstitüsü Degisi Sı 9 Ağustos 9 On The Chinese Cheke Sphee M. Tun N. Donumı = we tke emin of the line 8If then -+-+-= ==---= ==-+-= ==+--= ->- in the omin = --+-= = = we tke emin of the line ->- in the omin = -+--= = = we tke emin of the line ->- in the omin =+-+-= = = we tke emin of the line Emple. CC-sphee with ius = n entee t M = C X : M X M X L S m min In thjs emple the CC-sphee n e onstute using the theoem.. Gph of CC- sphee n e esil wn if it is epesente n eution of the fom given in theoem.. Gph of some of the CC-sphee e given figue. 8

9 DÜ Fen Bilimlei Enstitüsü Degisi Sı 9 Ağustos 9 On The Chinese Cheke Sphee M. Tun N. Donumı Figue. CC sphee with ius of = n entee t M = sle moel Figue. Chnge spet of the CC-sphee. sl moel Figue. CC sphee with ius of = n entee t M =. the shpe of CC- sphee one in eight 9

10 DÜ Fen Bilimlei Enstitüsü Degisi Sı 9 Ağustos 9 On The Chinese Cheke Sphee M. Tun N. Donumı REFERENCES [] Donumı N. On The Chinese Cheke Spe MsC Thesis Dumlupın Univesit Deptment of Mthemtis 8. [] Akç Z. K R. On The Distne Fomul in Thee Dimensionl Ti Spe Honi Jounl Vol. 7 No [] Chen G. Lines n Ciles in Ti Geomet MsC Thesis Centl Missout Stte Univesit Deptment of Mthemtis n Compute Ciene 99. [4] Gelişgen Ö. K R. n Ön M. Distne Fomul in the Chinese Cheke Spe Int. J. ue Appl. Mth [5] Kuse E.F. Ti Geomet Aison-Wesle Menlo k Clifoni 975. [6] Tun M. On the Chinese Cheke Conis h.d. Thesis Osmngi Univesit Deptment of Mthemtis 4. [7] Um A.Ç. Chinese Cheke Cile n Its popeties MsC. Thesis Osmngi Univesit Deptment of Mthemtis. [8] http: www. jgmes.om/hinesehekest 4

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