Polynome 4. Grades mit Wendepunkten und Fünfecken
Author: Prof. Dr. Dörte Haftendorn

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WendepunkteGerade

Flächen

Polynome 4. Grades mit zwei Wendepunkten

Ha Feb 09

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goldener Schnitt

Wendeflächen

Fünfeck 1

Fünfeck 2

Fünfecke 3 und 4

Wendetangenten

t = 0.04333333333333335
w = 3
a = 0.5
g(x) = t x * (x^(3) - 2 w x^(2) + w^(3))
f(x) = g(x) + a x
h(x) = a x
c: x = w
φ = 0.6180339887498949
Φ: 1 / φ
A, B, C, D = Root(g)
b: w^(3) + a / t
d: x = x(C)
e: x = x(D)
E, F, G, H = Intersect(f, h)
i = Integral(h, f, x(A), x(B))
j = Integral(h, f, x(G), x(H))
k = Integral(f, h, x(B), x(G))
n = true
o = false
p = false
q: x = -w
r: x = 2 w
s(x) = t b x
f_1(x) = f'(w) * (x - w) + f(w)
V, P, O, Q = Intersect(f_1, f)
Q = Intersect(g, f, 1)
R = Intersect(g, f, 1)
S = Intersect(g, f, 1)
T, U = Intersect(s, f)
v = Integral(f_1, f, -w, w)
u = Integral(s, f, 0, 2 w)
Z = Intersect(f_1, s)
z = false
a_1: x = x(A)
b_1 = false
W = Intersect(f_1, c)
c_1: v / i
d_1 = false
V_x = Intersect(q, xAxis)
U_x = Intersect(r, xAxis)
poly1, ew, g_1, h_1, i_1, j_1, A_1, B_1, C_1 = Polygon(B, W, 5)
poly2, kg_1, l_1, m_1, n_1, p_1, D_1, E_1, F_1 = Polygon(A_1, C_1, 5)
poly3, qq_1, r_1, s_1, t_1, a_2, G_1, H_1, I_1 = Polygon(A_1, W, 5)
poly4, bb_2, c_2, d_2, e_2, f_2, J_1, K_1, L_1 = Polygon(B, C_1, 5)
g_2 = Segment(J_1, D_1)
h_2 = Segment(I_1, F_1)
l = false
m = false
o_1 = false
u_1 = false
I = Intersect(h, r)
J = Intersect(h, q)
i_2 = Segment(C_1, E_1)
j_2 = Segment(A_1, E_1)
ee_1 = Segment(B, K_1)
kk_1 = Segment(W, H_1)