$B$

$B'$

$A$

$C$

$A'$

$C'$

$ Lagarange插值多項式 $

C_1 = (3.6327272727272737, 4.252727272727271)
B_1 = (4.68, 1.08)
A_1 = (5.378181818181819, 2.816363636363636)
B = DynamicCoordinates(B_1, floor(x(B_1)), floor(y(B_1)))
B': (x(B), 0)
A = DynamicCoordinates(A_1, floor(x(A_1)), floor(y(A_1)))
C = DynamicCoordinates(C_1, floor(x(C_1)), floor(y(C_1)))
A': (x(A), 0)
C': (x(C), 0)
f_1 = Polynomial({A, B', C'})
f_2 = Polynomial({A', B, C'})
f_3 = Polynomial({A', B', C})
f(x) = f_1(x) + f_2(x) + f_3(x)
Q_2: 0.35 * Corner[2] + 0.65 * Corner[1]
Q_3: (x(Q_2), y(Corner[3]))
poly, q_1, q_2, q_3, q_4 = Polygon(Corner[1], Q_2, Q_3, Corner[4])
text3: "$ 考慮A'(" + (LaTeX[x(A)]) + ",0),B'(" + (LaTeX[x(B)]) + ",0),C'(" + (LaTeX[x(C)]) + ",0)三點 $"
a: x(A)
b: x(B)
c: x(C)
text4: "$ f_(x)=f_1(x)+f_2(x)+f_3(x) $
$\;\;\;\;\;\;\;=" + (LaTeX[Polynomial[{A, B, C}]]) + "$"
text2: "$ 已知A" + (LaTeX[A]) + ",B" + (LaTeX[B]) + ",C" + (LaTeX[C]) + "三點，$
$試求通過A,B,C\;的多項式.$"
step = 0 (slider from 0 to 5, step 1)
text5: "$ 通過A,B',C'\;三點的多項式$
$f_1(x)=α(x" + (LaTeX[If[b > 0, "-" * b, If[b < 0, "+" + (-b), ""]]]) + " )(x" + (LaTeX[If[c > 0, "-" * c, If[c < 0, "+" + (-c), ""]]]) + " )將" + (LaTeX[A]) + "代入$
$⇒f_1(x)= " + (LaTeX[f_1]) + " $"
text6: "$ 通過A',B,C'\;三點的多項式$
$f_2(x)=β(x" + (LaTeX[If[a > 0, "-" * a, If[a < 0, "+" + (-a), ""]]]) + " )(x " + (LaTeX[If[c > 0, "-" * c, If[c < 0, "+" + (-c), ""]]]) + ")將" + (LaTeX[B]) + "代入$
$⇒f_2(x)= " + (LaTeX[f_2]) + " $"
text7: "$ 通過A',B',C\;三點的多項式$
$f_3(x)=γ(x" + (LaTeX[If[a > 0, "-" * a, If[a < 0, "+" + (-a), ""]]]) + " )(x" + (LaTeX[If[b > 0, "-" * b, If[b < 0, "+" + (-b), ""]]]) + " )將 " + (LaTeX[C]) + "代入$
$⇒f_3(x)= " + (LaTeX[f_3]) + " $"
list_1 = Coefficients(f_1)
list_2 = Coefficients(f_2)
list_3 = Coefficients(f_3)
list_4 = Coefficients(f)