Author: B. Spier

Höhensatz des Euklid: h² = p q

h²

h

q

q

p q

n = 2.02 (slider from 0 to 3, step 0.01)
A = (-2.72, -0.92)
B = (7.28, -0.92)
i = Line(A, B)
k = Semicircle(A, B)
C = Point(k)
a = Segment(B, C)
c = Segment(A, B)
d = Line(C, c)
z = OrthogonalLine(C, c)
H = Intersect(z, c)
e = Circle(C, H)
D = Intersect(e, d, 2.0)
j = OrthogonalLine(D, i)
E = Intersect(i, j)
Vieleck2, h, h_2, e_2, d_2 = Polygon(C, H, E, D)
q = Segment(A, H)
s: a + q + h
u = If(n ≤ 3.0 * q / s, n * s / 3.0 / q, If[n ≤ 3.0 * (q + a) / s, s / 3.0 / a * (n - 3.0 * q / s) + 1.0, s / 3.0 / h * (n - 3.0 * (q + a) / s) + 2.0])
p = Segment(H, B)
M = Intersect(j, Line[B, C])
F: (If[u ≤ 1.0, x(C), If[u ≤ 2.0, x(C) + (u - 1.0) * (x(B) - x(C)), x(B)]], If[u ≤ 1.0, y(C), If[u ≤ 2.0, y(C) + (u - 1.0) * (y(B) - y(C)), y(B)]])
J: (x(H), y(H))
G: (If[u ≤ 1.0, x(D) - u * (x(D) - x(M)), If[u ≤ 2.0, x(F) + x(M) - x(C), x(B) + x(M) - x(C) - (u - 2.0) * (x(D) - x(C))]], If[u ≤ 1.0, y(D) - u * (y(D) - y(M)), If[u ≤ 2.0, y(F) + y(M) - y(C), y(B) + y(M) - y(C) - (u - 2.0) * (y(D) - y(C))]])
b = Segment(C, A)
f = OrthogonalLine(D, p)
I: (If[u ≤ 1.0, x(G) - x(D) + x(E), If[u ≤ 2.0, x(M) - x(D) + x(E), x(G) - x(B) + x(J)]], If[u ≤ 1.0, y(G) - y(D) + y(E), If[u ≤ 2.0, y(M) - y(D) + y(E), y(G) - y(B) + y(J)]])
Vieleck1, f_1, j_1, i_1, g_1 = Polygon(F, J, I, G)
r = Circle(J, A)
K = Intersect(r, z, 1.0)
s_1 = CircleArc(J, A, K)
t = Segment(J, K)
a_1 = Line(K, i)
b_1 = Line(B, z)
L = Intersect(a_1, b_1)
c_1 = Segment(K, L)
d_1 = Segment(L, B)
e_1 = Segment(D, M)
Vieleck3, h_1, k_1, l, b_2 = Polygon(H, K, L, B)
γ = Angle(A, C, B)