果树问题讨论:这两个问题等价么？

wreck · 发表于 2019-11-15 18:31:33

请问能给下openf4的下载链接吗

mathe · 发表于 2019-11-16 13:43:46

到github搜索即可 https://github.com/nauotit/openf4

mathe · 发表于 2019-11-30 07:42:17

好像找到一个24棵树33行的复数解
print(ABGIAFHLBCHJCDIKDEJLEFGKAMOSBNPTCOQUDPRVEMQWFNRXAKRTBLMUCGNVDHOWEIPXFJQSGRSUHMTVINUWJOVXKPSWLQTXGJMPHKNQILORACWXAEUVBDSXBFVWCESTDFTU);
solve([+1-3*X_Y+3*X_Y*X_Y,+2/7+1*Q_Y-12/7*X_Y,+1*J_X-2*X_Y,-8/7+1*Q_X+6/7*X_Y,-2/3+1*S_X,-1/2+1*R_Y-1/2*X_Y,-1+1*V_X+1*X_Y,+1*T_Y-3/2*X_Y,+1*D_X-1*X_Y,-3/2+1*N_X+3/2*X_Y,-1/2+1*P_X-1/2*X_Y,+1*U_Y-2*X_Y,+3+1*G_Y-3*X_Y,+1/2+1*K_Y-3/2*X_Y,-1+1*I_Y+3*X_Y,-1/2+1*T_X,-2/3+1*O_Y,+1+1*E_Y-3*X_Y,-2/3+1*O_X,+1*M_Y-2*X_Y,+1*P_Y-3/2*X_Y,-2/3+1*M_X,-1+1*W_X,-1+1*X_X,-1+1*U_X+1*X_Y,-1+1*E_X+1*X_Y,+1*D_Y-1*X_Y,+1*S_Y-1*X_Y,-1+1*W_Y,-1+1*V_Y,+1*N_Y-3/2*X_Y,+1*L_Y-2*X_Y,-1/2+1*R_X,-1/2+1*K_X],[X_Y,Q_Y,J_X,Q_X,S_X,R_Y,V_X,T_Y,D_X,N_X,P_X,U_Y,G_Y,K_Y,I_Y,T_X,O_Y,E_Y,O_X,M_Y,P_Y,M_X,W_X,X_X,U_X,E_X,D_Y,S_Y,W_Y,V_Y,N_Y,L_Y,R_X,K_X]);
print("A=(0,1,0) B=(1,0,0) C_x=1 C_y=0 F_x=0 F_y=1 G=(1,G_y,0) H_x=0 H_y=0 I=(1,I_y,0) J_y=0 L_x=0 ");

https://emathgroup.github.io/blog/orchard-planting-problem#others

mathe · 发表于 2020-1-5 14:34:59

mathe 发表于 2008-8-13 16:36
现在采用上面的思路，证明了13个点最多9条线
使用方法如下:
首先使用计算机穷举关于问题2在n=13时线的数 ...

13棵树如果仅把B投影到无穷远可以得到一个对称图案

但是不存在不包含无穷远点的对称图

mathe · 发表于 2020-1-5 17:13:04

mathe 发表于 2008-8-18 09:59
上面的例子显然不行，有重复点（A和B坐标相同），使用另外一个例子可以得到结果:
-3/4+1*L_X
-1/4+1*M_X
...

这个14棵树的解无法对称，
给个去除无穷远点的图:

mathe · 发表于 2020-1-5 19:14:09

14棵树10行的结果很多，但是整数解中对称的只找出一组
s14.1.png

A(1/2, 7/6) B(0, 0), C(1,0) D(1, 1) E(5/8, 9/8) F(1/4, 5/4) G(3/8, 9/8) H(0, 1) I(3/4, 5/4) J(3/4, 3/4) K[1:1:0] L(1/4, 3/4) M[1:-1:0] N(1/2, 3/2)

mathe · 发表于 2020-1-5 19:40:40

上面的图消除无穷远点:
s14.2.png

mathe · 发表于 2020-1-5 19:47:50

还可以是

添加一个Geogebra图，修改参数h可以得到不同的对称图

s14.3.rar (37.28 KB, 下载次数: 4)

mathe · 发表于 2020-1-5 20:02:32

另外14棵10行实数解程序判断可能存在对称图的还有:
      Parameter [-1+2*t^2+1*t^3=0]
      A[+1 ,+2+3*t+1*t^2 , 0]
      B[+1/2-1*t-1/2*t^2 ,+1/2+1*t+1/2*t^2 , +1]
      C[0 ,+1 , 0]
      D[+1 ,0 , 0]
      E[+1 ,+2*t+1*t^2 , 0]
      F[0 ,0 , +1]
      G[+1 ,+2+3*t+1*t^2 , +1]
      H[+1*t^2 ,+1+1*t , +1]
      I[0 ,+1 , +1]
      J[+1 ,0 , +1]
      K[-1*t ,+1+1*t , +1]
      L[0 ,+1+1*t , +1]
      M[+1 ,+1+2*t+1*t^2 , +1]
      N[-2*t-1*t^2 ,0 , +1]
ACDEAFGHBIJKBLMNCFILCGJMDFJNDHKLEGKNEHIM

      Parameter [-1-1*t+1*t^2=0]{Real}
      A[+1 ,-1 , 0]
      B[0 ,0 , +1]
      C[+1+1*t ,+1 , +1]
      D[-1*t ,+1-1*t , +1]
      E[0 ,+1 , +1]
      F[+1 ,0 , +1]
      G[+1+1*t ,-1*t , +1]
      H[+1 ,-2+1*t , 0]
      I[0 ,+1-1*t , +1]
      J[-1*t ,0 , +1]
      K[-1*t ,+1 , +1]
      L[+1+1*t ,+1-1*t , +1]
      M[0 ,+1 , 0]
      N[+1 ,0 , 0]
AEFGAHMNBEIMBFJNCEKNCGLMDILNDJKMFHKLGHIJ

      Parameter [-1+1*t+1*t^2=0]
      A[+1 ,-1-1*t , 0]
      B[+1 ,-1*t , 0]
      C[0 ,0 , +1]
      D[+1 ,+1-1*t , +1]
      E[+1-1*t ,+1 , +1]
      F[0 ,+1 , +1]
      G[+1 ,-1*t , +1]
      H[+1 ,0 , +1]
      I[-1*t ,+1 , +1]
      J[0 ,+1-1*t , +1]
      K[+1-1*t ,0 , +1]
      L[0 ,+1 , 0]
      M[+1 ,0 , 0]
      N[+1-1*t ,+1-1*t , +1]
ABLMAFGNBHINCFJLCHKMDGHLDJMNEFIMEKLNGIJK

      Parameter [+1+2*t+2*t^2+1*t^3=0]
      A[+1 ,+1*t+1*t^2 , 0]
      B[+1 ,-1-2*t-1*t^2 , 0]
      C[0 ,+1 , +1]
      D[-2*t-1*t^2 ,-1-1*t , +1]
      E[+1 ,0 , +1]
      F[-1*t ,-1-2*t-1*t^2 , +1]
      G[0 ,-1-2*t-1*t^2 , +1]
      H[+1 ,-1-1*t , +1]
      I[0 ,0 , +1]
      J[-1*t ,-1-1*t , +1]
      K[0 ,+1 , 0]
      L[+1 ,0 , 0]
      M[-1*t ,0 , +1]
      N[+1 ,-1-2*t-1*t^2 , +1]
ABKLAGHMBIJNCDMNCGIKDHJLEHKNEILMFGLNFJKM

mathe · 发表于 2020-1-5 20:53:28

15棵12行整数解可能对称图形:
      A[0 ,+1 , 0]
      B[+1 ,-1 , +1]
      C[+2 ,-1 , +1]
      D[+1 ,0 , 0]
      E[+2 ,-3 , +1]
      F[+1 ,0 , +1]
      G[+1 ,-1 , 0]
      H[+1 ,-2 , 0]
      I[0 ,+1 , +1]
      J[+3 ,-3 , +1]
      K[0 ,0 , +1]
      L[0 ,+3 , +1]
      M[+1 ,-3 , +1]
      N[+2 ,0 , +1]
      O[+4/3 ,-1 , +1]
ADGHCFGIBEHIBGJKCHJLAIKLABFMDEJMACENDFKNBCDOEFLO
(ABC) (DEF) (GHI) (JKL) (MNO)

      A[0 ,0 , +1]
      B[+1 ,0 , 0]
      C[+1 ,+1 , 0]
      D[0 ,+1 , +1]
      E[0 ,+1 , 0]
      F[+1 ,0 , +1]
      G[+1 ,-1 , 0]
      H[-1 ,-1 , +1]
      I[0 ,-1 , +1]
      J[-1 ,+1 , +1]
      K[-1 ,0 , +1]
      L[+1 ,-1 , +1]
      M[+1/2 ,+1/2 , +1]
      N[+2 ,+1 , +1]
      O[+1 ,+2 , +1]
BCEGADEIABFKEHJKBHILAGJLDFGMACHMCFINBDJNCDKOEFLO
(ABE) (CDF) (GIK) (HJL) (MNO)

      A[0 ,+1 , +1]
      B[+1 ,0 , 0]
      C[0 ,+1 , 0]
      D[-1 ,+1 , +1]
      E[+1 ,+1 , 0]
      F[+1 ,0 , +1]
      G[0 ,0 , +1]
      H[+1 ,-1 , 0]
      I[0 ,+2 , +1]
      J[+1 ,+2 , +1]
      K[-1 ,0 , +1]
      L[-1/2 ,+3/2 , +1]
      M[+1 ,+1 , +1]
      N[-2 ,+2 , +1]
      O[-1 ,+5/3 , +1]
BCEHACGIBFGKAEJKAFHLDEILABDMCFJMDGHNBIJNCDKOLMNO
(AB) (C) (D)  (EG) (FJ) (HI) (K) (LN) (M) (O)  ： C,D,K,M,O必须在对称轴或无穷远直线上。（比如CDKO为对称轴,O为无穷远点）

      A[0 ,+1 , +1]
      B[+1 ,0 , 0]
      C[+1/2 ,+1 , +1]
      D[+1 ,-1 , 0]
      E[0 ,+1 , 0]
      F[+1 ,-2 , 0]
      G[+1 ,0 , +1]
      H[0 ,+2 , +1]
      I[+1/2 ,0 , +1]
      J[0 ,0 , +1]
      K[-1/2 ,+2 , +1]
      L[-1 ,+2 , +1]
      M[-1 ,+1 , +1]
      N[+1/2 ,-1/2 , +1]
      O[-1 ,+5/2 , +1]
BDEFCFGHAEHJBGIJAFIKADGLBHKLABCMCEINDJMNCDKOELMO
(A) (B) (C) (DE) (F) (GH) (IK) (JL) (M) (NO)  (ACM 和BF分别为对称轴和无穷远直线）

      A[+1 ,0 , +1]
      B[+1 ,0 , 0]
      C[0 ,+1 , +1]
      D[0 ,-1 , +1]
      E[+1 ,-1 , 0]
      F[0 ,+1 , 0]
      G[+1 ,+1 , 0]
      H[0 ,0 , +1]
      I[+1 ,-1 , +1]
      J[-1 ,0 , +1]
      K[+2 ,-1 , +1]
      L[+2 ,+1 , +1]
      M[+1 ,+2 , +1]
      N[-1 ,+1 , +1]
      O[+2 ,-3 , +1]
BEFGCDFHABHJACEKBDIKADGLAFIMCGJMEHINBCLNDEJOFKLO
（ABD）（CEF）（GHK）（IJL）（MNO)

      A[0 ,+1 , +1]
      B[+1 ,0 , 0]
      C[0 ,+1/2 , +1]
      D[-1 ,+1 , +1]
      E[+1 ,-1 , 0]
      F[0 ,+1 , 0]
      G[+1 ,0 , +1]
      H[+1 ,-1/2 , 0]
      I[-1 ,+3/2 , +1]
      J[0 ,0 , +1]
      K[+1 ,+1/2 , +1]
      L[-1 ,0 , +1]
      M[-1/2 ,+1 , +1]
      N[+1/2 ,+1/2 , +1]
      O[+1 ,-1 , +1]
BEFHCDGHACFJAHIKDFILBGJLABDMCEIMAEGNBCKNDEJOFGKO
(A) (BE) (C) (DG)  (F) (H) (IK)  (J) (LO) (MN)

      A[0 ,0 , +1]
      B[-1 ,+2 , +1]
      C[+1 ,0 , 0]
      D[+1 ,-2 , 0]
      E[0 ,+1 , 0]
      F[+1 ,-1 , 0]
      G[0 ,+1 , +1]
      H[-1 ,+1 , +1]
      I[+1 ,0 , +1]
      J[0 ,+2 , +1]
      K[-1 ,0 , +1]
      L[-2 ,+2 , +1]
      M[-1/2 ,+1 , +1]
      N[-1/2 ,+3 , +1]
      O[-1/2 ,-1 , +1]
CDEFBFGIAEGJBEHKACIKAFHLBCJLABDMCGHMDIJNDKLOEMNO
(AB) (C) (D) (E)  (F) (GH) (IL) (JK) (M) (NO)

      A[0 ,0 , +1]
      B[+1 ,0 , +1]
      C[+1 ,-1 , +1]
      D[0 ,+1 , +1]
      E[+1 ,0 , 0]
      F[0 ,+1 , 0]
      G[+1 ,+1 , 0]
      H[+1 ,-1 , 0]
      I[0 ,-1 , +1]
      J[+1 ,+1 , +1]
      K[+1/2 ,-1/2 , +1]
      L[+1/2 ,0 , +1]
      M[+1/3 ,+1/3 , +1]
      N[+2 ,-1 , +1]
      O[+1/2 ,+1 , +1]
EFGHADFIBCFJACHKBGIKABELAGJMCDLMBDHNCEINDEJOFKLO
(AF) (B) (CE) (D) (GK) (H) (I) (JL) (MO)  (N)

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[求助] 果树问题讨论:这两个问题等价么？