ҹԨ¤Եʵѹҹ

 Mathematics in Lanna Yantra Research Project

 

ػҹԨҧҾԨ | ͡çҹԨ | зѺ | úԡԪҡ

 


 


 

ػҹԨ

 

֡ͧѹԧԵʵ ö餹繤öͧҳҧҹԵʵ 餹ʹ㨡֡һѵʵԧԵʵҡ觢 ѧöӼš֡ҹ㹡¹͹Եʵ鹡äԴФԴҧä ֧֡ԨѺѡ¹ ѡ֡ йѡԪҡ ҧҹԵʵлѵʵ ա

֡ѹԧԵʵ

ҡ仢 : Ҩԡ Ѥê, Шؾ Եڵ, .͵Ԫҵ ࡵоѹ

 

Ԩ֡ͧѹԧԵʵ .. 2554 çԨͧ ԵʵкŢѹҹҔ ѺʹѺʹعҡԷʵ Է§ 觷Ԩ»Сͺ .͵Ԫҵ ࡵоѹ ˹ͧԺѵԡԨ¤ԵʵԷʵҳ ҨШҤԪҤԵʵ Էʵ Է§ 㹰ҹ˹çԨ Ҩԡ Ѥê ǪҭҹлԷԹҹ Шؾ Եڵ 繾ԡط֡ͧѹҧǹҹ 駹ҹѧԨҤ͹ Է§


㹧ҹԨ¹ӡ֡ѹҹ ҡѺ ҹ ÿѺҹ ͡ôԨԵžѺҹ ࢵ鹷Ѳͧҹ 11 ѧѴ 觻Сͺ § Ӿٹ ӻҧ § ͧ͹ ҹ صôԵ ⢷ еҡ 㹾鹷ѧǨоѹŢҡҾ鹷蹢ͧ š֡鹾ѹŢٻẺ ǹ˭ѹŢẺѵʡ յ袹Ҵ 3x3, 4x4, 5x5, 6x6 件֧Ҵ 9x9 觨ѵʡ¶֧ҧŢٻѵ źǡŢǵ ǹ͹ Ƿ§ դҡѹ


ѺѹҸب (кح ػdz) Ѵҧ . .ҧ .§


Ѻ ѹ Ѵҵؤ . .ͧ .§

Ѻѹҹҷդʹ㨷ҧԵʵҡش˹ ѹ١ѹ֡˹ѧѹФҶҢͧͧ˹ ͧ Թ ª ѧҾ () ¹ ѹ١Ƿҧ͹ (ѹ١Թҧʹѹ) ͹Ţҷ辺ѹ¹Ţúԡ ŢѧҾ () 駹Ţ 20 Ҿ () ա䢨ҡŢ 10 辺ҡҾ () 觷ԨҹաäѴ͡ԴҴ (С¹Ţ 1 2 ẺŢҹ鹤¡ѹҡ)

 
() ѹ¹Ţ      () ѹŧŢúԡ

Ҿѹ鹹աŢ 16 7, 8, 9, 10, 11, 12, 13, 14, 14, 15, 16, 17, 18, 19, 20 21 ѧࡵյŢӡѹ˹觤 蹤 14 ѧѧࡵ 14 Ţ觡ҧҧ 7 21 ʹ ѧ鹨֧ѹ͡ѡɳ੾еǷ͹ Ҽźǡǵ ǹ͹ Ƿ§ ҨդҡѺ 56 觷ԨҵŢ 56 ͨӹǹҧ辺㹺Ǵԭоطس ԵԻ Ф ѧ ط ԪҨгѹ ؤ šԷ йص зж ѵ ҹѧ ط ФҵԔ ҷҹԨ駪ѹ ѹطس

֡ԸաŧŢѹطس


.͵Ԫҵ ѧ֡ѹطس ԧԵʵ ¾Ẻٻ (pattern) ҧԵʵʹҡ 30 ҷ źǡŢҡѺ 56 мźǡŢǵçҧҡѺ 56 繵 駹ѧդȨ ա ͧŢ¡ѧͧ ҡѺͧŢǵçҧ¡ѧͧ ¹ 72+172+202+122 = 882 162+82+112+212 = 882 觷ҤҳդöҧԵʵշ


.͵Ԫҵ ҧù ѵ ҡԷʧҹԹ ֡ҤҳŧŢѹⷹطس ҧ ͧʹҡѧ֡ҡ͹ ҡ㹡֡ͧ 㹷شöԸŧŢѹ֧ 2 Ẻ

֡ѹطس


㹻 .. 2558 .͵Ԫҵ ࡵоѹ ӧҹԨѺ ص ҧشҾ ׺ѧ ѡ֡ҽ֡ҹҤĴ͹ҡԷʧҹԹ ֡öӵŢ辺ѹطس 㹵ҧ 4x4 öҧѵʡẺ蹷ҧҡѹطس Ẻ


ҡ֡Ҿ ԸաŢѧẺŧ㹵ҧ 4x4 ҡ֧ 15! ͻҳ 1.3 ҹҹẺ ǹ˭繨ѵʡ Шҡ¹͵Ǩͺ繨ѵʡ 龺ẺԴѵʡŨ§ 1,064 Ẻҹ ;ٴ ѵǹͧ¹ŢẺǷԴѵʡŨ 1 1.2 ѹҹ 觶ҹҡ


駹ԨѧẺٻ 11 ͷ辺ѹطس ֡ººѺѵʡ 1,064 Ẻѧ 龺觷ʹҡ 蹤 ѵʡ蹷辺Ẻٻú 11 ѹطس § 15 Ẻҹ ҡ֡ҹ繪Ѵ ѹطس դⴴᵡҧҡѵʡǹ˭ҧѴਹ


Ҩ ѧջ繷ö֡ǡѺѹաҡҹ÷çҹԵʵç¹ ÷Ԩԧ֡дѺԷ աѧö·ʹͧѡ¹ ѡ֡ лЪҪ ѡʹ㨤Եʵҡ觢


 

ҧҾԨǢͧ

       

  • ͺԧԺѵԡͧ ȨͧԵʵѹҹҔ .͵Ԫҵ ࡵоѹ 㹧ҹˡԷʵ෤觪ҵ Шӻ 2558 ѹҷԵ 15 Ȩԡ¹ 2558 ҤêŹ ͧͧҹ Ѵ ͧþԾԸѳԷʵ觪ҵ (;Ǫ.) 

 

 


 

͡çҹԨ


       
͡çҹԨ·Ѻءҹʹ㨨֡Ңͧѹ֡ѧҷաùʹͼҹŪ ö任Ѻ㹡¹͹ԵʵдѺж֡Ҷ֧дѺԷ ÷çҹԵʵ ÷ӡ֡Ԩԧ֡дѺԷ㹴ҹԵʵѹҡ (Recreational mahtematics) ԵʵҵԾѹ (Ethnomatheamtisc) лѵʵ (History) ͡ҡҧҹѧӤ蹡Ѻصա ҨҤͧöѺ硷ǡźŢдѺж֡仨֧ѡԨ੾зҧдѺԷ


       
ҡӧҹԨ´ҹҧ֡ҵ͡س¹ҧԧ֧ҹԨ¢ҧ ҡ÷ӧҹǢͧǡѺѹԹҡҡö駼š֡Ԩ·Һ ͨй餹价Һջѭ÷ зӧҹӫ͹ѹ


       
駹աùʹͼŧҹԨ ա÷͡º

 

  • ҹԨͧ "ѵʡšѺѹҹ" 㹡ý֡ԨҤĴ͹ çþѲҡѧҹԷʵ зǧԷʵ ҧó ѵ ѡ֡һշ 3 ԷʧҹԹ ա֡ 3/2555 .͵Ԫҵ ࡵоѹ 繷֡ҡ÷Ԩ - 㹧ҹԨ¹֡Ԩ¡ŧŢѹⷹطس ռ֡ҡ͹ شöԸŧŢ 2 Ẻ (Ŵ PDF 1 MB)
 
  • ҹԨͧ "ѵʡšѺѹҹ" 㹡ý֡ԨҤĴ͹ çþѲҡѧҹԷʵ зǧԷʵ ص ҧشҾ ׺ѧ ѡ֡ҽ֡ҹҤĴ͹ҡԷʧҹԹ  .͵Ԫҵ ࡵоѹ 繷֡ҡ÷Ԩ - 㹧ҹԨ¹֡ öӵŢ辺ѹطس 㹵ҧ 4x4 öҧѵʡẺ蹷ҧҡѹطس Ẻ ¡ յҧʴѵʡŷ鹾 1,064 Ẻ ( )

 


 

зѺ

 

ҡͺԧԺѵԡͧ ȨͧԵʵѹҹҔ  㹧ҹˡԷʵ෤觪ҵ Шӻ 2558 ѹ 15 Ȩԡ¹ 2558 ҤêŹ ͧͧҹ

 

ͺǤԴͧҨФ 繤ӤѭͧԵʵеͺ⨷ ¹Եʵ Ô 餳Եʵդس й֡ҡ ҧʹء㹡¹¤ зѺ㹡ͺ駹ҡ¤Д

ؾ Ѵ
 

"Һ Magic Square ء˹š ֧ҹҷ Magic Square §ҡ Magic Square ҹҷ§ҡ ˹㹹鹤 ѹⷹطس ѹ੾ФѡԷ դ§ԧԵʵ 觷׹ѹ Եʵء˹ء 繸ҵԷءء ҡѹöѧ˹ѡ㹤ӤѭͧԵʵҡ觢 ѹջªҡ Ѻ

ѭ Թм

 

ҤԪҡ㹤駹 Ѻҧҡ 㹴ҹԷʵ Եʵ ѵʵ зҧҹŻ ѺǡѺԻѭҢͧҳ ҧҹʵ Եʵ Ż 㹡ҧä觡ҧҧ Ե¡þ觾Ҹҵѷʹ㹡ôԹԵ 觷ӤҷҤѡ лзѺ㹤ҹҡ

˭ԧ Գ Թ ѡ¹Ѹ֡һշ 2

 

ѺͧԨ ͧ繤ȨҧԵʵ 㹻ѵʵ ͧ ѡ˵ؼŷҧԵʵ Ѻ ѡͷҧоطʹҹöͧǡѹ ѹ觷ʹҡѺ ͺسҨҡѺ

˭ԧ ѵԡó ǧ ѡ¹Ѹ֡һշ 2

 

зѺҡ پҺ͡͹ 秧Դҷͧ֡ҡҵ͹á Ҩ͵Ԫҵ ͸Ժ ǡѺҧʹء Ҩ͵Ԫҵ 蹡ʹءա ҡաèѴԨẺç¹ѹᾧ

Էص ʧപ

 

Ҥ¤駹ջª͹ѡ¹ҡѺ 褹 ѴС÷ӡᾧФͧͧ§ ԸաѴѺ鹢ͧ¡͹Тͧҧѹ ôٹҧ ش¤ѺиҵǡѺӻҧ Ҥ¤駹繡Ҥ¹ͧͧǻ ҡѸѺѹ駻Ȕ

硪 Ҥ ѡ¹Ѹ֡һշ 1

 

͢ͺس .͵Ԫҵ ࡵоѹ Ѵ㹤駹 ͺسԨ Դ ػ ѡ׺ʹѹҹФʹ仔

þ ʹ

 


 

úԡԪҡ

 

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