TXM796
Letu,v∈.ThenwehaveCartesiancoordinatesof7rationalpoints
M
i
(
x
i
,
y
i
)asfollows:
In[]:=
x
1
=2
2
(-3
2
u
+
2
v
)
(6561
16
u
-8748
15
u
v-55404
14
u
2
v
-32076
13
u
3
v
+158436
12
u
4
v
-45036
11
u
5
v
+245772
10
u
6
v
-79404
9
u
7
v
+67030
8
u
8
v
-26468
7
u
9
v
+27308
6
u
10
v
-1668
5
u
11
v
+1956
4
u
12
v
-132
3
u
13
v
-76
2
u
14
v
-4 u
15
v
+
16
v
);​​
y
1
=8
2
u v
(
4
u
-
4
v
) (81
4
u
-
4
v
) (9
4
u
-22
2
u
2
v
+
4
v
) (9
4
u
+2
2
u
2
v
+
4
v
)
(486
10
u
-2538
8
u
2
v
-804
6
u
4
v
+268
4
u
6
v
+94
2
u
8
v
-2
10
v
);​​
x
2
=2
2
(9
5
u
-9
4
u
v+26
3
u
2
v
+6
2
u
3
v
+u
4
v
-
5
v
)
2
(-27
5
u
+9
4
u
v+18
3
u
2
v
+26
2
u
3
v
-3 u
4
v
+
5
v
)
;​​
y
2
=0;​​
x
3
=4 u (9
4
u
+2
2
u
2
v
-8 u
3
v
+
4
v
) (9
5
u
-9
4
u
v-22
3
u
2
v
-10
2
u
3
v
+u
4
v
-
5
v
)
2
(-27
5
u
+9
4
u
v+18
3
u
2
v
+26
2
u
3
v
-3 u
4
v
+
5
v
)
;​​
y
3
=8
2
u v
(
4
u
-
4
v
) (81
4
u
-
4
v
) (9
4
u
-22
2
u
2
v
+
4
v
) (9
4
u
+2
2
u
2
v
+
4
v
)
2
(-27
5
u
+9
4
u
v+18
3
u
2
v
+26
2
u
3
v
-3 u
4
v
+
5
v
)
;​​
x
4
=6 u
2
(9
5
u
-9
4
u
v+26
3
u
2
v
+6
2
u
3
v
+u
4
v
-
5
v
)
(243
9
u
-81
8
u
v-540
7
u
2
v
-180
6
u
3
v
+138
5
u
4
v
+138
4
u
5
v
+180
3
u
6
v
-20
2
u
7
v
+27 u
8
v
-
9
v
);​​
y
4
=12
2
u v
(
4
u
-
4
v
) (81
4
u
-
4
v
) (9
4
u
-22
2
u
2
v
+
4
v
) (9
4
u
+2
2
u
2
v
+
4
v
)
2
(9
5
u
-9
4
u
v+26
3
u
2
v
+6
2
u
3
v
+u
4
v
-
5
v
)
;​​
x
5
=4 u
2
(9
5
u
-9
4
u
v+26
3
u
2
v
+6
2
u
3
v
+u
4
v
-
5
v
)
(243
9
u
-81
8
u
v-540
7
u
2
v
-180
6
u
3
v
+138
5
u
4
v
+138
4
u
5
v
+180
3
u
6
v
-20
2
u
7
v
+27 u
8
v
-
9
v
);​​
y
5
=8
2
u v
(
4
u
-
4
v
) (81
4
u
-
4
v
) (9
4
u
-22
2
u
2
v
+
4
v
) (9
4
u
+2
2
u
2
v
+
4
v
)
2
(9
5
u
-9
4
u
v+26
3
u
2
v
+6
2
u
3
v
+u
4
v
-
5
v
)
;​​
x
6
=2 u (9
4
u
+2
2
u
2
v
-8 u
3
v
+
4
v
) (9
5
u
-9
4
u
v-22
3
u
2
v
-10
2
u
3
v
+u
4
v
-
5
v
)
2
(-27
5
u
+9
4
u
v+18
3
u
2
v
+26
2
u
3
v
-3 u
4
v
+
5
v
)
;​​
y
6
=4
2
u v
(
4
u
-
4
v
) (81
4
u
-
4
v
) (9
4
u
-22
2
u
2
v
+
4
v
) (9
4
u
+2
2
u
2
v
+
4
v
)
2
(-27
5
u
+9
4
u
v+18
3
u
2
v
+26
2
u
3
v
-3 u
4
v
+
5
v
)
;​​
x
7
=
2
(9
5
u
-9
4
u
v+26
3
u
2
v
+6
2
u
3
v
+u
4
v
-
5
v
)
2
(-27
5
u
+9
4
u
v+18
3
u
2
v
+26
2
u
3
v
-3 u
4
v
+
5
v
)
;​​
y
7
=0;​​points=Table[{
x
n
,
y
n
},{n,1,7}];
NOTE:uandvarechosensuchthat(
2
u
-
2
v
)(9
2
u
-
2
v
)(9
4
u
-22
2
u
2
v
+
4
v
)≥0
In[]:=
Manipulate[Module[{pp,condition,edges},​​condition=(
2
u
-
2
v
)(9
2
u
-
2
v
)(9
4
u
-22
2
u
2
v
+
4
v
);​​pp=Chop[points/.{u->a,v->b}];​​If[(condition/.{u->a,v->b})>=0,​​edges=Subsets[pp,{2}];​​Graphics[{Tooltip[Line[#],EuclideanDistance@@#]&/@edges,Tooltip[{Red,Point[#]},#]&/@pp}]]],​​{{a,1},-5,5,1/6,Appearance->"Labeled"},​​{{b,2},-5,5,1/6,Appearance->"Labeled"},SaveDefinitionsTrue]
Out[]=
​
a
11
6
b
2
Author: Minh Trinh Xuan