尺規作圖找橢圓的中心
Author: 藍邦偉  老師

$ 尺規作圖找橢圓的中心 $

$ 1. \;移動A,B,C,D,E五個點，$
     $決定一橢圓 $

$ 2.\;作任意兩 平行弦，分別取$
　$\overline{PR},\overline{QS}的中點M_1,M_2$
    $連\overleftrightarrow{M_1M_2}$

$ 3.\;再作另兩平行弦，分別取$
　$\overline{FG},\overline{KH}的中點M_3,M_4$
    $連\overleftrightarrow{M_3M_4}$

$ 4.\;取\overleftrightarrow{M_1M_2}與\overleftrightarrow{M_3M_4}的交點O，$
     $即為所求 $

P

A

B

C

D

E

R

Q

S

M_1

M_2

F

G

K

H

M_3

M_4

O

u = Vector((x(Corner[1]), 0), (x(Corner[3]), 0))
v = Vector((0, y(Corner[1])), (0, y(Corner[3])))
O_1 = (0, 0)
Q_2: 0.7 * Corner[1] + 0.3 * Corner[2]
Q_3: (x(Q_2), y(Corner[4]))
poly1, q_1, q_2, q_4, q_3 = Polygon(Corner[1], Q_2, Q_3, Corner[4])
A = (1.1782644386839436, -0.3784004153531102)
B = (1.8275995519360455, 2.3717247701852027)
C = (3.145367870006488, 4.0523568280141715)
D = (6.831299542290479, 3.8995720954842654)
E_1 = (6.296552978435806, 0.40462133886265944)
c = Conic(A, B, C, D, E_1)
n = 0 (slider from 0 to 4, step 1)
P_1 = Point(c)
P_3 = Point(c)
P_2 = Point(c)
a = Segment(P_1, P_2)
b = Line(P_3, a)
d = Line(P_3, a)
P_4 = Intersect(c, d, 2)
e = Segment(P_3, P_4)
M_1 = Midpoint(P_1, P_2)
M_2 = Midpoint(P_3, P_4)
P_5 = Point(c)
P_7 = Point(c)
P_6 = Point(c)
f = Segment(P_5, P_6)
g = Line(P_7, f)
I, P_8 = Intersect(c, g)
h = Segment(P_7, P_8)
M_3 = Midpoint(P_7, P_8)
M_4 = Midpoint(P_5, P_6)
i = Line(M_1, M_2)
j = Line(M_4, M_3)
J = Point(j)
O = Intersect(j, i)