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HDZJY2009木虫 (正式写手)
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[求助]
使各个圆相交部分面积相等，求纵坐标
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如下图，有8个半径为5的圆沿Y轴罗列，已知圆1的圆心坐标为（5,5），求其他圆的坐标分别为多少时，能使圆1所截的各部分面积是相等的？即圆8与圆1的相交面积为圆面积的pi*5*5的1/8，圆7与圆1的相交面积为圆面积的2/8，这样圆8与圆7之间的面积也是圆面积的1/8,依次类推。 例子中是8个圆的，我要做的是35个圆的，能帮我得到做35个圆时，圆心纵坐标各自的值吗？  所夹的面积相等-3.jpg [ Last edited by HDZJY2009 on 2013-3-8 at 21:06 ] |
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HDZJY2009: 金币+150, ★★★★★最佳答案, 非常感谢，居然连图也给了，图是用matlab做的吗？顺便把程序给我吧 2013-03-09 14:29:23
感谢参与，应助指数 +1
HDZJY2009: 金币+150, ★★★★★最佳答案, 非常感谢，居然连图也给了，图是用matlab做的吗？顺便把程序给我吧 2013-03-09 14:29:23
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首先应该无解析解 8个的情形下的y坐标分别为 12.733898602563759280736579023416 11.347045926489442402527056525453 10.1458423138090761429485989637 9.039727510571245179500385832818 7.9904317306745460526790641141417 6.9764395001682878743743313503921 5.9833346959308628632804819059461 5 它们是方程 2*arccos((yi-5)/2/5)*5^2 - 2* (25-(yi-5)^2/4)^(0.5) *(yi-5)/2 = (N-i+1)/N *pi *25 的解。 35个圆时 [ 1, 14.165537622457287366799186533746] [ 2, 13.668528743815480457269196244901] [ 3, 13.24752297250298765894719002992] [ 4, 12.868408096361129663480370000015] [ 5, 12.517081838974052214423900375613] [ 6, 12.185988992310452299124047418117] [ 7, 11.870488250033117769672469830192] [ 8, 11.567470741845687876233937653017] [ 9, 11.274724893453649882935569774775] [ 10, 10.990605790555390961310020823067] [ 11, 10.713847109073235682684998706036] [ 12, 10.443446748832963085535806099172] [ 13, 10.178593549887409133624472471737] [ 14, 9.9186183087893783295609191829997] [ 15, 9.6629598761480137244981067044324] [ 16, 9.4111409941769388615577892746821] [ 17, 9.1627506390029620260206093438695] [ 18, 8.9174308331199258797934047970661] [ 19, 8.6748666064888354788137719420696] [ 20, 8.4347782235647880749325053042479] [ 21, 8.1969150719264140771542029718434] [ 22, 7.9610507896406753370124822864297] [ 23, 7.7269793296186974568033540724253] [ 24, 7.4945117417972033347053269643881] [ 25, 7.2634735113535584092502476772318] [ 26, 7.0337023317013247270031880072913] [ 27, 6.8050462200898331849674962699517] [ 28, 6.5773619047636664255967319736435] [ 29, 6.3505134281720696158979627214228] [ 30, 6.1243709222441346670493526815346] [ 31, 5.8988095203561772860239157165265] [ 32, 5.6737083770735489733221395621439] [ 33, 5.4489497715841969944735282616306] [ 34, 5.2244182743324640640883487380682] [ 35, 5] |
2楼2013-03-08 23:21:43
3楼2013-03-08 23:28:08
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%% emuch2 我写的程序比较土，可以用eval把它写简洁点 %% http://muchong.com/bbs/viewthread.php?tid=5591194&fpage=1 syms y kk = 1 ; % 1 for N=8, 0 for N=35 if(kk==1) Y(1)=solve('acos((y-5)/2/5)*5^2-(25-((y-5)^2/4))^0.5*(y-5)/2-1/8*3.14159267*25/2'); Y(2)=solve('acos((y-5)/2/5)*5^2-(25-((y-5)^2/4))^0.5*(y-5)/2-2/8*3.14159267*25/2'); Y(3)=solve('acos((y-5)/2/5)*5^2-(25-((y-5)^2/4))^0.5*(y-5)/2-3/8*3.14159267*25/2'); Y(4)=solve('acos((y-5)/2/5)*5^2-(25-((y-5)^2/4))^0.5*(y-5)/2-4/8*3.14159267*25/2'); Y(5)=solve('acos((y-5)/2/5)*5^2-(25-((y-5)^2/4))^0.5*(y-5)/2-5/8*3.14159267*25/2'); Y(6)=solve('acos((y-5)/2/5)*5^2-(25-((y-5)^2/4))^0.5*(y-5)/2-6/8*3.14159267*25/2'); Y(7)=solve('acos((y-5)/2/5)*5^2-(25-((y-5)^2/4))^0.5*(y-5)/2-7/8*3.14159267*25/2'); Y(8)=5; Cx(1:360)= 5*cos((1:360)/360*2*pi); Cy(1:360)= 5*sin((1:360)/360*2*pi); for k=1:8 plot(Cx+5,Cy+Y(k)); hold on end axis equal end if(kk==0) Y(1)=solve('acos((y-5)/2/5)*5^2-(25-((y-5)^2/4))^0.5*(y-5)/2-1/35*3.14159267*25/2'); Y(2)=solve('acos((y-5)/2/5)*5^2-(25-((y-5)^2/4))^0.5*(y-5)/2-2/35*3.14159267*25/2'); Y(3)=solve('acos((y-5)/2/5)*5^2-(25-((y-5)^2/4))^0.5*(y-5)/2-3/35*3.14159267*25/2'); Y(4)=solve('acos((y-5)/2/5)*5^2-(25-((y-5)^2/4))^0.5*(y-5)/2-4/35*3.14159267*25/2'); Y(5)=solve('acos((y-5)/2/5)*5^2-(25-((y-5)^2/4))^0.5*(y-5)/2-5/35*3.14159267*25/2'); Y(6)=solve('acos((y-5)/2/5)*5^2-(25-((y-5)^2/4))^0.5*(y-5)/2-6/35*3.14159267*25/2'); Y(7)=solve('acos((y-5)/2/5)*5^2-(25-((y-5)^2/4))^0.5*(y-5)/2-7/35*3.14159267*25/2'); Y(1+7)=solve('acos((y-5)/2/5)*5^2-(25-((y-5)^2/4))^0.5*(y-5)/2-7/35*3.14159267*25/2-1/35*3.14159267*25/2'); Y(2+7)=solve('acos((y-5)/2/5)*5^2-(25-((y-5)^2/4))^0.5*(y-5)/2-7/35*3.14159267*25/2-2/35*3.14159267*25/2'); Y(3+7)=solve('acos((y-5)/2/5)*5^2-(25-((y-5)^2/4))^0.5*(y-5)/2-7/35*3.14159267*25/2-3/35*3.14159267*25/2'); Y(4+7)=solve('acos((y-5)/2/5)*5^2-(25-((y-5)^2/4))^0.5*(y-5)/2-7/35*3.14159267*25/2-4/35*3.14159267*25/2'); Y(5+7)=solve('acos((y-5)/2/5)*5^2-(25-((y-5)^2/4))^0.5*(y-5)/2-7/35*3.14159267*25/2-5/35*3.14159267*25/2'); Y(6+7)=solve('acos((y-5)/2/5)*5^2-(25-((y-5)^2/4))^0.5*(y-5)/2-7/35*3.14159267*25/2-6/35*3.14159267*25/2'); Y(7+7)=solve('acos((y-5)/2/5)*5^2-(25-((y-5)^2/4))^0.5*(y-5)/2-7/35*3.14159267*25/2-7/35*3.14159267*25/2'); Y(1+14)=solve('acos((y-5)/2/5)*5^2-(25-((y-5)^2/4))^0.5*(y-5)/2-14/35*3.14159267*25/2-1/35*3.14159267*25/2'); Y(2+14)=solve('acos((y-5)/2/5)*5^2-(25-((y-5)^2/4))^0.5*(y-5)/2-14/35*3.14159267*25/2-2/35*3.14159267*25/2'); Y(3+14)=solve('acos((y-5)/2/5)*5^2-(25-((y-5)^2/4))^0.5*(y-5)/2-14/35*3.14159267*25/2-3/35*3.14159267*25/2'); Y(4+14)=solve('acos((y-5)/2/5)*5^2-(25-((y-5)^2/4))^0.5*(y-5)/2-14/35*3.14159267*25/2-4/35*3.14159267*25/2'); Y(5+14)=solve('acos((y-5)/2/5)*5^2-(25-((y-5)^2/4))^0.5*(y-5)/2-14/35*3.14159267*25/2-5/35*3.14159267*25/2'); Y(6+14)=solve('acos((y-5)/2/5)*5^2-(25-((y-5)^2/4))^0.5*(y-5)/2-14/35*3.14159267*25/2-6/35*3.14159267*25/2'); Y(7+14)=solve('acos((y-5)/2/5)*5^2-(25-((y-5)^2/4))^0.5*(y-5)/2-14/35*3.14159267*25/2-7/35*3.14159267*25/2'); Y(1+21)=solve('acos((y-5)/2/5)*5^2-(25-((y-5)^2/4))^0.5*(y-5)/2-21/35*3.14159267*25/2-1/35*3.14159267*25/2'); Y(2+21)=solve('acos((y-5)/2/5)*5^2-(25-((y-5)^2/4))^0.5*(y-5)/2-21/35*3.14159267*25/2-2/35*3.14159267*25/2'); Y(3+21)=solve('acos((y-5)/2/5)*5^2-(25-((y-5)^2/4))^0.5*(y-5)/2-21/35*3.14159267*25/2-3/35*3.14159267*25/2'); Y(4+21)=solve('acos((y-5)/2/5)*5^2-(25-((y-5)^2/4))^0.5*(y-5)/2-21/35*3.14159267*25/2-4/35*3.14159267*25/2'); Y(5+21)=solve('acos((y-5)/2/5)*5^2-(25-((y-5)^2/4))^0.5*(y-5)/2-21/35*3.14159267*25/2-5/35*3.14159267*25/2'); Y(6+21)=solve('acos((y-5)/2/5)*5^2-(25-((y-5)^2/4))^0.5*(y-5)/2-21/35*3.14159267*25/2-6/35*3.14159267*25/2'); Y(7+21)=solve('acos((y-5)/2/5)*5^2-(25-((y-5)^2/4))^0.5*(y-5)/2-21/35*3.14159267*25/2-7/35*3.14159267*25/2'); Y(1+28)=solve('acos((y-5)/2/5)*5^2-(25-((y-5)^2/4))^0.5*(y-5)/2-28/35*3.14159267*25/2-1/35*3.14159267*25/2'); Y(2+28)=solve('acos((y-5)/2/5)*5^2-(25-((y-5)^2/4))^0.5*(y-5)/2-28/35*3.14159267*25/2-2/35*3.14159267*25/2'); Y(3+28)=solve('acos((y-5)/2/5)*5^2-(25-((y-5)^2/4))^0.5*(y-5)/2-28/35*3.14159267*25/2-3/35*3.14159267*25/2'); Y(4+28)=solve('acos((y-5)/2/5)*5^2-(25-((y-5)^2/4))^0.5*(y-5)/2-28/35*3.14159267*25/2-4/35*3.14159267*25/2'); Y(5+28)=solve('acos((y-5)/2/5)*5^2-(25-((y-5)^2/4))^0.5*(y-5)/2-28/35*3.14159267*25/2-5/35*3.14159267*25/2'); Y(6+28)=solve('acos((y-5)/2/5)*5^2-(25-((y-5)^2/4))^0.5*(y-5)/2-28/35*3.14159267*25/2-6/35*3.14159267*25/2'); Y(35)=5; Cx(1:360)= 5*cos((1:360)/360*2*pi); Cy(1:360)= 5*sin((1:360)/360*2*pi); for k=1:35 plot(Cx+5,Cy+Y(k)); hold on end axis equal end |
4楼2013-03-09 19:10:52
wgdxidname
木虫 (著名写手)
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5楼2013-03-10 13:53:57
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[ 1, 13.176027151195730887376037511169] [ 2, 12.069645466497588461407977633746] [ 3, 11.118769462055524345291348660186] [ 4, 10.250316519654125503870780330281] [ 5, 9.4338861837026170888342452698181] [ 6, 8.6529420407157626908937775258771] [ 7, 7.8970435547786043823469930500081] [ 8, 7.1588843487875437210536890928014] [ 9, 6.4329153888473456695247094804758] [ 10, 5.7146069654980091268508018372835] [ 11, 5] 还是改成容易执行的给你吧， %% emuch2 clear all syms y NN = 11; %%% number of circles NNstr = int2str(NN); for k=1: NN-1 kstr = int2str(k); expstr = strcat('Y(',kstr,')=solve(acos((y-5)/2/5)*5^2-(25-((y-5)^2/4))^0.5*(y-5)/2-',kstr,'/',NNstr,'*3.14159267*25/2);'); eval(expstr); end clear expstr Y(NN)=5; [[1:NN]',Y'] Cx(1:360)= 5*cos((1:360)/360*2*pi); Cy(1:360)= 5*sin((1:360)/360*2*pi); for k=1:NN plot(Cx+5,Cy+Y(k)); hold on end axis equal |
6楼2013-03-11 12:00:59
HDZJY2009
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7楼2013-03-11 15:06:33
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