Schriftformat  10p

Schriftformat   12p

Schriftformat  14p 

Schriftformat   16p

Schriftformat   18p

1

1

1

x

y

z

Koordinatensystem

Raumlage

Netz eines Pyramidenstumpfs

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Netz 1

Körper

Grundkantenlängen

Umklappung

Pyramidenstumpf

Oberfläche

o_1 = -0.2 (slider from -1 to 1, step 0.1)
h = 6 (slider from 0 to 10, step 0.1)
b_G = 6 (slider from 0 to 10, step 0.1)
a_G = 6 (slider from 0 to 10, step 0.1)
a_D = 6 (slider from 0 to a_G, step 0.1)
xa: (a_G - a_D) / 2
wa = If(xa ≠ 0, ((atan(h / xa) * 180) * ° / π), 90*°)
hb: sqrt(xa^(2) + h^(2))
b_D: (a_D * b_G / a_G)
β = 5.672320068981571 rad (slider from 0 to 360*°, step 1*°)
Kz: (0, cos(β))
α = 0.8726646259971648 rad (slider from 0 to 360*°, step 1*°)
Ky: (cos(α), (sin(α) * sin(β)))
Kx: (sin(α), ((-cos(α)) * sin(β)))
O = Intersect(yAxis, xAxis)
evz = Vector(O, Kz)
evy = Vector(O, Ky)
evx = Vector(O, Kx)
k = 5 (slider from 0 to 50, step 0.1)
A_1: O + (k * evx)
B_1: O + (k * evy)
C_1: O + (k * evz)
u = Vector(O, A_1)
v = Vector(O, B_1)
w = Vector(O, C_1)
D_1: O - ((0.5 * k) * evx)
E_1: O - ((0.5 * k) * evy)
F_1: O - ((0.5 * k) * evz)
b_1 = Segment(O, D_1)
c_1 = Segment(O, E_1)
d = Segment(O, F_1)
o = false
A: O + (b_G / 2 * evx) - (a_G / 2 * evy)
B: O + (b_G / 2 * evx) + (a_G / 2 * evy)
C: O - (b_G / 2 * evx) + (a_G / 2 * evy)
D: O - (b_G / 2 * evx) - (a_G / 2 * evy)
Vieleck1, g, h_1, i, j = Polygon(A, B, C, D)
E: O + (b_D / 2 * evx) - (a_D / 2 * evy) + (h * evz)
F: O + (b_D / 2 * evx) + (a_D / 2 * evy) + (h * evz)
G: O - (b_D / 2 * evx) + (a_D / 2 * evy) + (h * evz)
H: O - (b_D / 2 * evx) - (a_D / 2 * evy) + (h * evz)
xb: (b_G - b_D) / 2
ha: sqrt(xb^(2) + h^(2))
u_1 = false
wb = If(xb ≠ 0, ((atan(h / xb) * 180) * ° / π), 90*°)
H_2: O - ((a_G / 2 + hb) * evy) + (b_D / 2 * evx)
I_2: O - ((a_G / 2 + hb) * evy) - (b_D / 2 * evx)
J_2: O + ((b_G / 2 + ha) * evx) + (a_D / 2 * evy)
K_2: O + ((b_G / 2 + ha) * evx) - (a_D / 2 * evy)
L_2: J_2 + (b_D * evx)
M_2: K_2 + (b_D * evx)
A_3 = (0, 0)
B_3: A_3 + Vector[A]
C_3: A_3 + Vector[B]
D_3: A_3 + Vector[C]
E_3: A_3 + Vector[D]
F_3: A_3 + Vector[E]
G_3: A_3 + Vector[F]
H_3: A_3 + Vector[G]
I_3: A_3 + Vector[H]
Vieleck8, f_3, g_3, h_2, i_3 = Polygon(F_3, G_3, H_3, I_3)
Vieleck9, b_3, c_3, d_3, e_3 = Polygon(B_3, C_3, D_3, E_3)
f_2 = Segment(G_3, C_3)
g_2 = Segment(F_3, B_3)
j_2 = Segment(I_3, E_3)
n_2 = Segment(H_3, D_3)
z = false
I: (((-b_G)) / 2, 0)
J: (b_G / 2, 0)
K: (((-b_D)) / 2, h)
L: (b_D / 2, h)
K' = Rotate(K, ((-(1 + o_1)) * wb), L)
M = If(o_1 ≤ 0, O + (x(K') * evx) + (y(K') * evz))
K'_1 = Rotate(K, (-wb), L)
N = Rotate(K'_1, ((-o_1) * (180° - wb)), J)
P = If(o_1 > 0, O + (x(N) * evx) + (y(N) * evz))
L' = Rotate(L, ((-o_1) * (180° - wb)), J)
Q = If(o_1 ≥ 0, O + (x(L') * evx) + (y(L') * evz))
R: M + (a_D / 2 * evy)
R' = Mirror(R, M)
Vieleck3, r, r', e_1, f_1 = Polygon(R, R', E, F)
S: P + (a_D / 2 * evy)
S' = Mirror(S, P)
T: Q + (a_D / 2 * evy)
T' = Mirror(T, Q)
Vieleck6, s', s, t, t' = Polygon(S', S, T, T')
Vieleck7, t_1, b_2, a_1, t'_1 = Polygon(T, B, A, T')
Vieleck4 = If(o_1  <  0, Polygon[A, B, F, E])
K'_2 = Rotate(K, (o_1 * (180° - wb)), I)
U = If(o_1 ≥ 0, O + (x(K'_2) * evx) + (y(K'_2) * evz))
V_1: U + (a_D / 2 * evy)
V' = Mirror(V_1, U)
Vieleck5, c_2, v_1, v', d_1 = Polygon(C, V_1, V', D)
Vieleck10 = If(o_1  <  0, Polygon[C, D, H, G])
W: (((-a_G)) / 2, 0)
Z: (a_G / 2, 0)
G_1: (((-a_D)) / 2, h)
H_1: (a_D / 2, h)
I_1 = Rotate(G_1, (o_1 * (180° - wa)), W)
J_1 = Mirror(I_1, yAxis)
L_1 = If(o_1 ≥ 0, O + (x(I_1) * evy) + (y(I_1) * evz))
M_1 = If(o_1 ≥ 0, O + (x(J_1) * evy) + (y(J_1) * evz))
N_1: L_1 + (b_D / 2 * evx)
O_1 = Mirror(N_1, L_1)
Vieleck11, a_2, d_2, o_2, n_1 = Polygon(A, D, O_1, N_1)
Vieleck12 = If(o_1  <  0, Polygon[A, E, H, D])
P_1: M_1 + (b_D / 2 * evx)
Q_1 = Mirror(P_1, M_1)
Vieleck13, c_4, b_4, p_1, q_1 = Polygon(C, B, P_1, Q_1)
Vieleck14 = If(o_1  <  0, Polygon[B, C, G, F])
Text6: "Deckkante  a_D = " + a_D + ""
Text13: "a_G = " + a_G + ""
Text14: "b_G = " + b_G + ""
Text9: "Körperhöhe h = " + h + ""
A_G: (a_G * b_G)
A_D: (a_D * b_D)
Asa: ((a_G + a_D) / 2 * ha)
Asb: ((b_G + b_D) / 2 * hb)
A_O: A_D + A_G + (2 * Asa) + (2 * Asb)
V: (h / 3 * (A_G + sqrt((A_G * A_D)) + A_D))
a = false
Text17: " A_O = " + A_O + ""