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【求助】帮忙看下这个问题呢
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数学实在头疼，自己很长时间都没做出来，希望各位高手能帮我解决这个问题，真的会非常感激的，麻烦大家了。 如果金币不够还可以再加的。 [ Last edited by wenzhenzhong on 2009-3-3 at 12:13 ] |
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点点风(金币+2,VIP+0):感谢参与讨论，加分鼓励！ 3-6 16:39
点点风(金币+2,VIP+0):感谢参与讨论，加分鼓励！ 3-6 16:39
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下面几个回复是我做的一些结果，最终结果如下： 当h< 总长度（整个图形上面的一半）为B=n×h+n×(n+1)×(2n+1)×(h^3)/(12×a^2) 如果你是实际应用的话建议你不要考虑通式，而是数值解，我用MABLAB编了程序，并得到了几组解，供你分析 B为三角形个数为从1到n时另一边的长度 function B=solveb(a,h,n) B=[]; alpha=pi/2; for i=1:n [b a alpha]=tri(a,h,alpha); if i==1 B=b; else B=[B b+B(end)]; end end figure; hold on; grid on; plot(1:n,B); function [b c beta]=tri(a,h,alpha) alpha1=acos(h/a); alpha2=alpha-alpha1; beta=alpha2+pi/2; c1=a*sin(alpha1); b=h/cos(alpha2); c2=b*sin(alpha2); c=c1+c2; [ Last edited by fspdlh on 2009-3-6 at 19:36 ] |
2楼2009-03-06 14:52:15
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>> solveb(100,0.01,100) ans = 0.0100 0.0200 0.0300 0.0400 0.0500 0.0600 0.0700 0.0800 0.0900 0.1000 0.1100 0.1200 0.1300 0.1400 0.1500 0.1600 0.1700 0.1800 0.1900 0.2000 0.2100 0.2200 0.2300 0.2400 0.2500 0.2600 0.2700 0.2800 0.2900 0.3000 0.3100 0.3200 0.3300 0.3400 0.3500 0.3600 0.3700 0.3800 0.3900 0.4000 0.4100 0.4200 0.4300 0.4400 0.4500 0.4600 0.4700 0.4800 0.4900 0.5000 0.5100 0.5200 0.5300 0.5400 0.5500 0.5600 0.5700 0.5800 0.5900 0.6000 0.6100 0.6200 0.6300 0.6400 0.6500 0.6600 0.6700 0.6800 0.6900 0.7000 0.7100 0.7200 0.7300 0.7400 0.7500 0.7600 0.7700 0.7800 0.7900 0.8000 0.8100 0.8200 0.8300 0.8400 0.8500 0.8600 0.8700 0.8800 0.8900 0.9000 0.9100 0.9200 0.9300 0.9400 0.9500 0.9600 0.9700 0.9800 0.9900 1.0000 >> solveb(100,0.1,100) ans = 0.1000 0.2000 0.3000 0.4000 0.5000 0.6000 0.7000 0.8000 0.9000 1.0000 1.1000 1.2000 1.3000 1.4001 1.5001 1.6001 1.7001 1.8001 1.9001 2.0001 2.1002 2.2002 2.3002 2.4002 2.5003 2.6003 2.7003 2.8004 2.9004 3.0005 3.1005 3.2006 3.3006 3.4007 3.5007 3.6008 3.7009 3.8010 3.9010 4.0011 4.1012 4.2013 4.3014 4.4015 4.5016 4.6017 4.7018 4.8019 4.9020 5.0021 5.1023 5.2024 5.3026 5.4027 5.5028 5.6030 5.7032 5.8033 5.9035 6.0037 6.1039 6.2041 6.3043 6.4045 6.5047 6.6049 6.7051 6.8054 6.9056 7.0058 7.1061 7.2064 7.3066 7.4069 7.5072 7.6075 7.7078 7.8081 7.9084 8.0087 8.1090 8.2094 8.3097 8.4101 8.5104 8.6108 8.7112 8.8116 8.9120 9.0124 9.1128 9.2132 9.3136 9.4141 9.5145 9.6150 9.7155 9.8159 9.9164 10.0169 >> solveb(100,1,100) ans = 1.0001 2.0003 3.0007 4.0015 5.0028 6.0046 7.0070 8.0102 9.0143 10.0193 11.0253 12.0325 13.0410 14.0508 15.0621 16.0749 17.0894 18.1057 19.1238 20.1439 21.1661 22.1904 23.2170 24.2460 25.2774 26.3115 27.3482 28.3877 29.4301 30.4755 31.5240 32.5757 33.6308 34.6892 35.7512 36.8168 37.8862 38.9594 40.0366 41.1178 42.2032 43.2929 44.3870 45.4856 46.5888 47.6967 48.8095 49.9272 51.0499 52.1779 53.3111 54.4498 55.5939 56.7437 57.8992 59.0606 60.2279 61.4014 62.5811 63.7671 64.9596 66.1586 67.3643 68.5769 69.7964 71.0229 72.2567 73.4977 74.7462 76.0022 77.2659 78.5375 79.8170 81.1045 82.4003 83.7044 85.0169 86.3381 87.6679 89.0067 90.3544 91.7113 93.0774 94.4530 95.8381 97.2328 98.6375 100.0520 101.4767 102.9117 104.3570 105.8129 107.2795 108.7570 110.2454 111.7449 113.2558 114.7781 116.3120 117.8577 >> solveb(100,10,100) ans = 1.0e+006 * 0.0000 0.0000 0.0000 0.0000 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0002 0.0002 0.0002 0.0002 0.0003 0.0003 0.0003 0.0004 0.0004 0.0004 0.0005 0.0005 0.0006 0.0007 0.0007 0.0008 0.0009 0.0010 0.0011 0.0013 0.0014 0.0016 0.0017 0.0019 0.0021 0.0024 0.0026 0.0029 0.0033 0.0036 0.0040 0.0045 0.0050 0.0055 0.0061 0.0068 0.0076 0.0084 0.0094 0.0104 0.0115 0.0128 0.0143 0.0158 0.0176 0.0196 0.0217 0.0241 0.0268 0.0298 0.0331 0.0368 0.0409 0.0454 0.0505 0.0561 0.0623 0.0692 0.0769 0.0855 0.0950 0.1055 0.1173 0.1303 0.1448 0.1609 0.1787 0.1986 0.2207 0.2452 0.2724 0.3027 0.3363 0.3737 0.4152 0.4613 0.5126 0.5695 0.6328 0.7031 0.7813 0.8681 0.9645 1.0717 1.1908 1.3231 1.4701 1.6334 1.8149 >> [ Last edited by fspdlh on 2009-3-6 at 14:58 ] |
3楼2009-03-06 14:54:34
4楼2009-03-06 15:11:16
★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ...
jiangxy(金币+66,VIP+0):谢谢你，前段时间有事情回家了一趟，没即时赠送金币，不好意思 4-2 18:59
jiangxy(金币+66,VIP+0):谢谢你，前段时间有事情回家了一趟，没即时赠送金币，不好意思 4-2 18:59
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又搞了一下，分析数据变化趋势，得出，当h< 为验证结果，计算sqrt((bn-h)*2*(a^2)/(h^3)),修改程序如下： function B=solveb(a,h,n) B=[]; alpha=pi/2; for i=1:n [b a alpha]=tri(a,h,alpha); if i==1 B=b; else B=[B;b]; end end B=sqrt((B-h).*2.*(a.^2)./(h.^3)); function [b c beta]=tri(a,h,alpha) alpha1=acos(h/a); alpha2=alpha-alpha1; beta=alpha2+pi/2; c1=a*sin(alpha1); b=h/cos(alpha2); c2=b*sin(alpha2); c=c1+c2; 运行后如下： >> y=solveb(100,0.0005,100) y = 1.0000 2.0000 3.0000 4.0000 5.0000 6.0000 7.0000 8.0000 9.0000 10.0000 11.0000 12.0000 13.0000 14.0000 15.0000 16.0000 17.0000 18.0000 19.0000 20.0000 21.0000 22.0000 23.0000 24.0000 25.0000 26.0000 27.0000 28.0000 29.0000 30.0000 31.0000 32.0000 33.0000 34.0000 35.0000 36.0000 37.0000 38.0000 39.0000 40.0000 41.0000 42.0000 43.0000 44.0000 45.0000 46.0000 47.0000 48.0000 49.0000 50.0000 51.0000 52.0000 53.0000 54.0000 55.0000 56.0000 57.0000 58.0000 59.0000 60.0000 61.0000 62.0000 63.0000 64.0000 65.0000 66.0000 67.0000 68.0000 69.0000 70.0000 71.0000 72.0000 73.0000 74.0000 75.0000 76.0000 77.0000 78.0000 79.0000 80.0000 81.0000 82.0000 83.0000 84.0000 85.0000 86.0000 87.0000 88.0000 89.0000 90.0000 91.0000 92.0000 93.0000 94.0000 95.0000 96.0000 97.0000 98.0000 99.0000 100.0000 >> y=solveb(100,0.01,100) y = 1.0001 2.0001 3.0002 4.0002 5.0003 6.0003 7.0004 8.0004 9.0005 10.0005 11.0006 12.0006 13.0007 14.0007 15.0008 16.0008 17.0009 18.0009 19.0010 20.0010 21.0011 22.0011 23.0012 24.0012 25.0013 26.0013 27.0014 28.0014 29.0015 30.0015 31.0016 32.0016 33.0017 34.0017 35.0018 36.0018 37.0019 38.0019 39.0020 40.0020 41.0021 42.0021 43.0022 44.0022 45.0023 46.0023 47.0024 48.0025 49.0025 50.0026 51.0026 52.0027 53.0027 54.0028 55.0028 56.0029 57.0029 58.0030 59.0030 60.0031 61.0032 62.0032 63.0033 64.0033 65.0034 66.0034 67.0035 68.0035 69.0036 70.0037 71.0037 72.0038 73.0038 74.0039 75.0039 76.0040 77.0041 78.0041 79.0042 80.0042 81.0043 82.0043 83.0044 84.0045 85.0045 86.0046 87.0046 88.0047 89.0048 90.0048 91.0049 92.0049 93.0050 94.0051 95.0051 96.0052 97.0053 98.0053 99.0054 100.0054 >> y=solveb(100,0.1,100) y = 1.0050 2.0100 3.0150 4.0200 5.0250 6.0300 7.0351 8.0401 9.0451 10.0501 11.0551 12.0602 13.0652 14.0702 15.0753 16.0803 17.0854 18.0904 19.0955 20.1005 21.1056 22.1107 23.1157 24.1208 25.1259 26.1310 27.1361 28.1412 29.1464 30.1515 31.1566 32.1618 33.1669 34.1721 35.1773 36.1824 37.1876 38.1928 39.1980 40.2033 41.2085 42.2137 43.2190 44.2243 45.2295 46.2348 47.2401 48.2454 49.2508 50.2561 51.2614 52.2668 53.2722 54.2776 55.2830 56.2884 57.2938 58.2993 59.3047 60.3102 61.3157 62.3212 63.3268 64.3323 65.3379 66.3434 67.3490 68.3546 69.3603 70.3659 71.3716 72.3773 73.3830 74.3887 75.3944 76.4002 77.4060 78.4118 79.4176 80.4234 81.4293 82.4351 83.4410 84.4470 85.4529 86.4589 87.4649 88.4709 89.4769 90.4830 91.4890 92.4952 93.5013 94.5074 95.5136 96.5198 97.5260 98.5323 99.5385 100.5448 >> y=solveb(100,1,100) y = 1.5457 3.0915 4.6375 6.1837 7.7301 9.2768 10.8238 12.3711 13.9188 15.4670 17.0156 18.5647 20.1143 21.6646 23.2154 24.7669 26.3191 27.8721 29.4258 30.9803 32.5357 34.0920 35.6491 37.2073 38.7665 40.3267 41.8880 43.4504 45.0140 46.5788 48.1448 49.7121 51.2807 52.8507 54.4220 55.9949 57.5691 59.1449 60.7223 62.3012 63.8818 65.4640 67.0480 68.6337 70.2212 71.8105 73.4017 74.9948 76.5898 78.1868 79.7859 81.3870 82.9902 84.5956 86.2032 87.8130 89.4250 91.0394 92.6561 94.2752 95.8967 97.5207 99.1472 100.7762 102.4079 104.0421 105.6791 107.3187 108.9611 110.6063 112.2544 113.9053 115.5591 117.2159 118.8756 120.5385 122.2044 123.8734 125.5456 127.2210 128.8996 130.5816 132.2668 133.9555 135.6476 137.3431 139.0421 140.7447 142.4508 144.1606 145.8741 147.5912 149.3122 151.0369 152.7655 154.4979 156.2343 157.9747 159.7191 161.4675 >> [ Last edited by fspdlh on 2009-3-6 at 19:26 ] |
5楼2009-03-06 18:42:26