円に内接する辺の長さが異なる自然数の多角形 -その10-

昨日の続き。

 

おさらい。

 

自然数の半径rの円に内接するn角形があり、

辺の長さがすべて異なる自然数で、

更には半径rや直径2rとも異なる、

 

このような条件のnにおける半径が最小となるものをみつけたい。

 

 

上記条件を満たす、円に内接する七角形以上になると、

組み合わせ爆発の影響でか、半径も大きくなってくるためか、

半径をインクリメントしながら探すプログラムでは、

なかなか答えを見つけるに至らない。

 

ということで、別アプローチとして、

180˚＋180＝360˚

120˚＋120˚＋120˚＝360˚

60˚＋120˚＋180˚＝360˚

60˚＋60˚＋120˚＋120˚＝360˚

60˚＋60˚＋60˚＋180˚＝360˚

60˚＋60˚＋60˚＋60˚＋120˚＝360˚

60˚＋60˚＋60˚＋60˚＋60˚＋60˚＝360˚

と、いくつかの扇型の和として考えることにした。

 

 

前回は、360˚におけるn＝11、12、13と、求めてみました。

 

今回は、n＝14について書いていくことになります。

 

n=11以降は、180˚＋180˚で、片方の180˚は60˚＋60˚＋60で、3＋3＋3、もう片方の180˚で合計nにするということになる。

 

n＝14

r a b c d e f g h i j k l m n A˚ B˚ C˚ D˚ E˚ F˚ G˚ H˚ I˚ J˚ K˚ L˚ M˚ N˚ sum
12103 169 443 931 2093 2702 3458 4543 4606 5681 5947 6419 7733 8827 19019 0.8000549785 2.0972855845 4.4084550079 9.9206808110 12.8180213741 16.4264214035 21.6349313899 21.9386472066 27.1471571930 28.4443877990 30.7555572225 37.2612978149 42.7735236180 103.5735785965 360.0000000000
12103 169 443 931 2093 2302 2702 3458 4606 5681 6419 7733 8113 8827 19019 0.8000549785 2.0972855845 4.4084550079 9.9206808110 10.9141956004 12.8180213741 16.4264214035 21.9386472066 27.1471571930 30.7555572225 37.2612978149 39.1651235886 42.7735236180 103.5735785965 360.0000000000
12103 169 443 931 2093 2302 2702 3458 4606 5681 5947 6419 8827 9842 19019 0.8000549785 2.0972855845 4.4084550079 9.9206808110 10.9141956004 12.8180213741 16.4264214035 21.9386472066 27.1471571930 28.4443877990 30.7555572225 42.7735236180 47.9820336045 103.5735785965 360.0000000000
12103 169 443 931 2093 2302 2702 3458 4606 5681 5947 6419 7733 10894 19019 0.8000549785 2.0972855845 4.4084550079 9.9206808110 10.9141956004 12.8180213741 16.4264214035 21.9386472066 27.1471571930 28.4443877990 30.7555572225 37.2612978149 53.4942594076 103.5735785965 360.0000000000
12103 169 931 2093 2302 2702 3458 4606 5681 5947 6419 7007 7733 8113 16562 0.8000549785 4.4084550079 9.9206808110 10.9141956004 12.8180213741 16.4264214035 21.9386472066 27.1471571930 28.4443877990 30.7555572225 33.6528977855 37.2612978149 39.1651235886 86.3471022145 360.0000000000
12103 169 443 931 2093 2702 3458 4606 5681 5947 6419 7007 7733 9842 16562 0.8000549785 2.0972855845 4.4084550079 9.9206808110 12.8180213741 16.4264214035 21.9386472066 27.1471571930 28.4443877990 30.7555572225 33.6528977855 37.2612978149 47.9820336045 86.3471022145 360.0000000000
12103 169 443 931 2093 2302 3458 4543 4606 5681 5947 7007 8827 10894 16562 0.8000549785 2.0972855845 4.4084550079 9.9206808110 10.9141956004 16.4264214035 21.6349313899 21.9386472066 27.1471571930 28.4443877990 33.6528977855 42.7735236180 53.4942594076 86.3471022145 360.0000000000
12103 443 931 2093 2302 2702 3458 4543 4606 5681 5947 6419 7007 10894 16562 2.0972855845 4.4084550079 9.9206808110 10.9141956004 12.8180213741 16.4264214035 21.6349313899 21.9386472066 27.1471571930 28.4443877990 30.7555572225 33.6528977855 53.4942594076 86.3471022145 360.0000000000
12103 169 443 931 2093 2702 3458 4543 4606 5947 6419 7007 7733 10894 16562 0.8000549785 2.0972855845 4.4084550079 9.9206808110 12.8180213741 16.4264214035 21.6349313899 21.9386472066 28.4443877990 30.7555572225 33.6528977855 37.2612978149 53.4942594076 86.3471022145 360.0000000000
12103 169 443 931 2093 2302 2702 3458 4606 6419 7007 7733 8113 10894 16562 0.8000549785 2.0972855845 4.4084550079 9.9206808110 10.9141956004 12.8180213741 16.4264214035 21.9386472066 30.7555572225 33.6528977855 37.2612978149 39.1651235886 53.4942594076 86.3471022145 360.0000000000
12103 169 443 931 2093 2302 2702 3458 4606 5681 7007 7733 8827 10894 16562 0.8000549785 2.0972855845 4.4084550079 9.9206808110 10.9141956004 12.8180213741 16.4264214035 21.9386472066 27.1471571930 33.6528977855 37.2612978149 42.7735236180 53.4942594076 86.3471022145 360.0000000000
12103 169 931 2093 2302 2702 3458 4543 4606 5681 5947 6419 7007 11138 16562 0.8000549785 4.4084550079 9.9206808110 10.9141956004 12.8180213741 16.4264214035 21.6349313899 21.9386472066 27.1471571930 28.4443877990 30.7555572225 33.6528977855 54.7914900135 86.3471022145 360.0000000000
12103 169 443 931 2093 2302 2702 3458 4606 5681 6419 7007 9842 11138 16562 0.8000549785 2.0972855845 4.4084550079 9.9206808110 10.9141956004 12.8180213741 16.4264214035 21.9386472066 27.1471571930 30.7555572225 33.6528977855 47.9820336045 54.7914900135 86.3471022145 360.0000000000
12103 169 443 931 2093 3458 4543 4606 5681 5947 6419 7007 7733 8113 16562 0.8000549785 2.0972855845 4.4084550079 9.9206808110 16.4264214035 21.6349313899 21.9386472066 27.1471571930 28.4443877990 30.7555572225 33.6528977855 37.2612978149 39.1651235886 86.3471022145 360.0000000000
12103 169 443 931 2093 2702 4543 4606 5681 5947 6419 7007 7733 8827 16562 0.8000549785 2.0972855845 4.4084550079 9.9206808110 12.8180213741 21.6349313899 21.9386472066 27.1471571930 28.4443877990 30.7555572225 33.6528977855 37.2612978149 42.7735236180 86.3471022145 360.0000000000
12103 443 931 2093 2302 2702 3458 4543 4606 5681 6419 7007 8113 8827 16562 2.0972855845 4.4084550079 9.9206808110 10.9141956004 12.8180213741 16.4264214035 21.6349313899 21.9386472066 27.1471571930 30.7555572225 33.6528977855 39.1651235886 42.7735236180 86.3471022145 360.0000000000
12103 169 443 931 2093 2302 2702 4606 5681 6419 7007 7733 8113 8827 16562 0.8000549785 2.0972855845 4.4084550079 9.9206808110 10.9141956004 12.8180213741 21.9386472066 27.1471571930 30.7555572225 33.6528977855 37.2612978149 39.1651235886 42.7735236180 86.3471022145 360.0000000000
12103 169 443 931 2093 2302 3458 4543 4606 5681 6419 7007 8113 11138 16562 0.8000549785 2.0972855845 4.4084550079 9.9206808110 10.9141956004 16.4264214035 21.6349313899 21.9386472066 27.1471571930 30.7555572225 33.6528977855 39.1651235886 54.7914900135 86.3471022145 360.0000000000
12103 169 443 931 2093 2702 3458 4543 4606 5681 6419 7007 7733 11138 16562 0.8000549785 2.0972855845 4.4084550079 9.9206808110 12.8180213741 16.4264214035 21.6349313899 21.9386472066 27.1471571930 30.7555572225 33.6528977855 37.2612978149 54.7914900135 86.3471022145 360.0000000000
12103 169 931 2093 2302 2702 3458 4543 4606 5947 6419 7007 8113 8827 16562 0.8000549785 4.4084550079 9.9206808110 10.9141956004 12.8180213741 16.4264214035 21.6349313899 21.9386472066 28.4443877990 30.7555572225 33.6528977855 39.1651235886 42.7735236180 86.3471022145 360.0000000000
12103 169 443 931 2093 2702 3458 4543 4606 5947 6419 7007 8827 9842 16562 0.8000549785 2.0972855845 4.4084550079 9.9206808110 12.8180213741 16.4264214035 21.6349313899 21.9386472066 28.4443877990 30.7555572225 33.6528977855 42.7735236180 47.9820336045 86.3471022145 360.0000000000
12103 169 443 931 2093 2302 3458 4606 5681 5947 6419 7007 8113 9842 16562 0.8000549785 2.0972855845 4.4084550079 9.9206808110 10.9141956004 16.4264214035 21.9386472066 27.1471571930 28.4443877990 30.7555572225 33.6528977855 39.1651235886 47.9820336045 86.3471022145 360.0000000000
12103 169 443 931 2093 2302 2702 4606 5681 5947 6419 7007 8827 9842 16562 0.8000549785 2.0972855845 4.4084550079 9.9206808110 10.9141956004 12.8180213741 21.9386472066 27.1471571930 28.4443877990 30.7555572225 33.6528977855 42.7735236180 47.9820336045 86.3471022145 360.0000000000
12103 169 443 931 2093 2302 3458 4543 4606 5947 6419 7007 8113 10894 16562 0.8000549785 2.0972855845 4.4084550079 9.9206808110 10.9141956004 16.4264214035 21.6349313899 21.9386472066 28.4443877990 30.7555572225 33.6528977855 39.1651235886 53.4942594076 86.3471022145 360.0000000000
12103 169 443 931 2093 2302 2702 4606 5681 5947 6419 7007 7733 10894 16562 0.8000549785 2.0972855845 4.4084550079 9.9206808110 10.9141956004 12.8180213741 21.9386472066 27.1471571930 28.4443877990 30.7555572225 33.6528977855 37.2612978149 53.4942594076 86.3471022145 360.0000000000
12103 169 443 931 2093 2702 3458 4543 4606 5681 5947 6419 7733 10894 17537 0.8000549785 2.0972855845 4.4084550079 9.9206808110 12.8180213741 16.4264214035 21.6349313899 21.9386472066 27.1471571930 28.4443877990 30.7555572225 37.2612978149 53.4942594076 92.8528428070 360.0000000000
12103 169 443 931 2093 2302 2702 3458 4606 5681 6419 7733 8113 10894 17537 0.8000549785 2.0972855845 4.4084550079 9.9206808110 10.9141956004 12.8180213741 16.4264214035 21.9386472066 27.1471571930 30.7555572225 37.2612978149 39.1651235886 53.4942594076 92.8528428070 360.0000000000
12103 169 931 2093 2302 2702 3458 4543 4606 5681 5947 6419 8113 8827 17537 0.8000549785 4.4084550079 9.9206808110 10.9141956004 12.8180213741 16.4264214035 21.6349313899 21.9386472066 27.1471571930 28.4443877990 30.7555572225 39.1651235886 42.7735236180 92.8528428070 360.0000000000
12103 169 443 931 2093 2702 3458 4543 4606 5681 5947 6419 8827 9842 17537 0.8000549785 2.0972855845 4.4084550079 9.9206808110 12.8180213741 16.4264214035 21.6349313899 21.9386472066 27.1471571930 28.4443877990 30.7555572225 42.7735236180 47.9820336045 92.8528428070 360.0000000000
12103 169 443 931 2093 2302 3458 4543 4606 5681 5947 6419 8113 10894 17537 0.8000549785 2.0972855845 4.4084550079 9.9206808110 10.9141956004 16.4264214035 21.6349313899 21.9386472066 27.1471571930 28.4443877990 30.7555572225 39.1651235886 53.4942594076 92.8528428070 360.0000000000
12103 169 443 931 2093 2702 3458 4606 5681 5947 6419 7733 8113 9842 15694 0.8000549785 2.0972855845 4.4084550079 9.9206808110 12.8180213741 16.4264214035 21.9386472066 27.1471571930 28.4443877990 30.7555572225 37.2612978149 39.1651235886 47.9820336045 80.8348764114 360.0000000000
12103 169 443 931 2093 2302 3458 4543 4606 5681 5947 8113 8827 10894 15694 0.8000549785 2.0972855845 4.4084550079 9.9206808110 10.9141956004 16.4264214035 21.6349313899 21.9386472066 27.1471571930 28.4443877990 39.1651235886 42.7735236180 53.4942594076 80.8348764114 360.0000000000
12103 443 931 2093 2302 2702 3458 4543 4606 5681 5947 6419 8113 10894 15694 2.0972855845 4.4084550079 9.9206808110 10.9141956004 12.8180213741 16.4264214035 21.6349313899 21.9386472066 27.1471571930 28.4443877990 30.7555572225 39.1651235886 53.4942594076 80.8348764114 360.0000000000
12103 169 443 931 2093 2702 3458 4543 4606 5947 6419 7733 8113 10894 15694 0.8000549785 2.0972855845 4.4084550079 9.9206808110 12.8180213741 16.4264214035 21.6349313899 21.9386472066 28.4443877990 30.7555572225 37.2612978149 39.1651235886 53.4942594076 80.8348764114 360.0000000000
12103 169 443 931 2093 2302 2702 3458 4606 5681 7733 8113 8827 10894 15694 0.8000549785 2.0972855845 4.4084550079 9.9206808110 10.9141956004 12.8180213741 16.4264214035 21.9386472066 27.1471571930 37.2612978149 39.1651235886 42.7735236180 53.4942594076 80.8348764114 360.0000000000
12103 169 931 2093 2302 2702 3458 4543 4606 5681 5947 6419 8113 11138 15694 0.8000549785 4.4084550079 9.9206808110 10.9141956004 12.8180213741 16.4264214035 21.6349313899 21.9386472066 27.1471571930 28.4443877990 30.7555572225 39.1651235886 54.7914900135 80.8348764114 360.0000000000
12103 169 443 931 2093 2302 2702 3458 4606 5681 6419 8113 9842 11138 15694 0.8000549785 2.0972855845 4.4084550079 9.9206808110 10.9141956004 12.8180213741 16.4264214035 21.9386472066 27.1471571930 30.7555572225 39.1651235886 47.9820336045 54.7914900135 80.8348764114 360.0000000000
12103 169 443 931 2093 3458 4543 4606 5681 5947 6419 7007 8113 8827 15694 0.8000549785 2.0972855845 4.4084550079 9.9206808110 16.4264214035 21.6349313899 21.9386472066 27.1471571930 28.4443877990 30.7555572225 33.6528977855 39.1651235886 42.7735236180 80.8348764114 360.0000000000
12103 169 443 931 2093 2702 3458 4606 5681 6419 7007 7733 8113 8827 15694 0.8000549785 2.0972855845 4.4084550079 9.9206808110 12.8180213741 16.4264214035 21.9386472066 27.1471571930 30.7555572225 33.6528977855 37.2612978149 39.1651235886 42.7735236180 80.8348764114 360.0000000000
12103 169 443 931 2093 2702 4543 4606 5681 5947 6419 7733 8113 8827 15694 0.8000549785 2.0972855845 4.4084550079 9.9206808110 12.8180213741 21.6349313899 21.9386472066 27.1471571930 28.4443877990 30.7555572225 37.2612978149 39.1651235886 42.7735236180 80.8348764114 360.0000000000
12103 169 443 931 2093 2702 3458 4543 4606 5681 6419 7733 8113 11138 15694 0.8000549785 2.0972855845 4.4084550079 9.9206808110 12.8180213741 16.4264214035 21.6349313899 21.9386472066 27.1471571930 30.7555572225 37.2612978149 39.1651235886 54.7914900135 80.8348764114 360.0000000000
12103 169 931 2093 2302 2702 3458 4606 5681 5947 6419 7007 8113 8827 15694 0.8000549785 4.4084550079 9.9206808110 10.9141956004 12.8180213741 16.4264214035 21.9386472066 27.1471571930 28.4443877990 30.7555572225 33.6528977855 39.1651235886 42.7735236180 80.8348764114 360.0000000000
12103 169 443 931 2093 2702 3458 4543 4606 5947 6419 8113 8827 9842 15694 0.8000549785 2.0972855845 4.4084550079 9.9206808110 12.8180213741 16.4264214035 21.6349313899 21.9386472066 28.4443877990 30.7555572225 39.1651235886 42.7735236180 47.9820336045 80.8348764114 360.0000000000
12103 169 443 931 2093 2302 2702 4606 5681 5947 6419 8113 8827 9842 15694 0.8000549785 2.0972855845 4.4084550079 9.9206808110 10.9141956004 12.8180213741 21.9386472066 27.1471571930 28.4443877990 30.7555572225 39.1651235886 42.7735236180 47.9820336045 80.8348764114 360.0000000000
12103 169 443 931 2093 2302 3458 4606 5681 5947 6419 7007 8113 10894 15694 0.8000549785 2.0972855845 4.4084550079 9.9206808110 10.9141956004 16.4264214035 21.9386472066 27.1471571930 28.4443877990 30.7555572225 33.6528977855 39.1651235886 53.4942594076 80.8348764114 360.0000000000
12103 169 443 931 2093 2302 2702 4606 5681 5947 6419 7733 8113 10894 15694 0.8000549785 2.0972855845 4.4084550079 9.9206808110 10.9141956004 12.8180213741 21.9386472066 27.1471571930 28.4443877990 30.7555572225 37.2612978149 39.1651235886 53.4942594076 80.8348764114 360.0000000000
12103 169 931 2093 2302 2702 3458 4606 5681 5947 6419 7733 8113 9842 14231 0.8000549785 4.4084550079 9.9206808110 10.9141956004 12.8180213741 16.4264214035 21.9386472066 27.1471571930 28.4443877990 30.7555572225 37.2612978149 39.1651235886 47.9820336045 72.0179663955 360.0000000000
12103 169 443 931 2093 2302 3458 4543 4606 5681 5947 8827 9842 10894 14231 0.8000549785 2.0972855845 4.4084550079 9.9206808110 10.9141956004 16.4264214035 21.6349313899 21.9386472066 27.1471571930 28.4443877990 42.7735236180 47.9820336045 53.4942594076 72.0179663955 360.0000000000
12103 443 931 2093 2302 2702 3458 4543 4606 5681 5947 6419 9842 10894 14231 2.0972855845 4.4084550079 9.9206808110 10.9141956004 12.8180213741 16.4264214035 21.6349313899 21.9386472066 27.1471571930 28.4443877990 30.7555572225 47.9820336045 53.4942594076 72.0179663955 360.0000000000
12103 169 443 931 2093 2702 3458 4543 4606 5947 6419 7733 9842 10894 14231 0.8000549785 2.0972855845 4.4084550079 9.9206808110 12.8180213741 16.4264214035 21.6349313899 21.9386472066 28.4443877990 30.7555572225 37.2612978149 47.9820336045 53.4942594076 72.0179663955 360.0000000000

※文字数制限を超えるデータのため、すべてを掲載していません。

 

残すはn＝18となります。
 

 

ではでは