■和算と算額(その48)

w=(z+a)/(az+1)=(z-3/4)=(-3z/4+1))=(4z-3)/(4-3z)

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[1]

1/2+isqr(3)/6=(4z-3)/(4-3z)

2+i4sqr(3)/6-3z/2-i3zsqr(3)/6=4z-3

11z/2+i3zsqr(3)/6=5+i4sqr(3)/6

(33+i3sqr(3))z=30+i4sqr(3)

1116z=(30+i4sqr(3))(33-i3sqr(3))=1026+i42sqr(3)

(1026/1116,42sqr(3)/1116)

[2]

1/6+isqr(3)/6=(4z-3)/(4-3z)

2/3+i4sqr(3)/6-z/2-i3zsqr(3)/6=4z-3

9z/2+i3zsqr(3)/6=11/3+i4sqr(3)/6

(27+i3sqr(3))z=22+i4sqr(3)

756z=(22+i4sqr(3))(27-i3sqr(3))=630+i42sqr(3)

(630/756. ,42sqr(3)/756)

[3]

i2/3=(4z-3)/(4-3z)

i8/3-i2z=4z-3

(4+i2)z=3+i8/3

(12+i6)z=9+i8

180x=(9+i8)(12-i6)=156+42i

(156/180. ,42/180)

[4]

-1/6+isqr(3)/6=(4z-3)/(4-3z)

-2/3+i4sqr(3)/6+z/2-i3zsqr(3)/6=4z-3

7z/2+i3zsqr(3)/6=7/3+i4sqr(3)/6

(21+i3sqr(3))z=14+i4sqr(3)

468z=(14+i4sqr(3))(21-i3sqr(3))=330+i42sqr(3)

(330/468. ,42sqr(3)/458)

[5]

-1/2+isqr(3)/6=(4z-3)/(4-3z)

-2+i4sqr(3)/6+3z/2-i3zsqr(3)/6=4z-3

5z/2+i3zsqr(3)/6=1+i4sqr(3)/6

(15+i3sqr(3))z=6+i4sqr(3)

252z=(6+i4sqr(3))(15-i3sqr(3))=126+i42sqr(3)

(126/468. ,42sqr(3)/126)

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[a] (42/45,0)

[b] (32/45,0)

[c] (-10/45,0)

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[1][a]と[2][b]の交点

[1][a]との距離

[2][b]との距離

[4][b]と[5][c]の交点

[4][b]との距離

[5][c]との距離

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