Steigung

rechte Intervallgrenze

Verschiebung um 1/n

P

Obersumme des Rotationskörpers darstellen

Rotationskörper darstellen

Schaubild um x-Achse rotieren lassen

Wähle nach einem Rechtsklick 
auf α den Befehl 'Animation ein'.

m = 0.3 (slider from 0 to 0.8, step 0.1)
f(x) = m * x
u = 6.8 (slider from 1 to 10, step 0.1)
U: (u, 0.0)
α = 1.5707963267948966 rad (slider from 0 to 6.283185307179586, step 0.17453292519943295)
P: (u + 0.5 * f(u) * cos(α), f(u) * sin(α))
A = (0, 0)
b_2(x) = y(P) / f(x(P)) * f(x)
a = CurveCartesian(u + 0.5 * f(u) * cos(α), f(u) * sin(α), α, 0°, 360.0°)
B = Point(a)
C = Point(a)
D = Point(a)
E = Point(a)
e = Conic(P, B, E, C, D)
n = 3 (slider from 1 to 10, step 1)
U_1: (x(U) / n, 0.0)
U_2: (x(U) / n * 2.0, 0.0)
U_3: (x(U) / n * 3.0, 0.0)
U_4: (x(U) / n * 4.0, 0.0)
U_5: (x(U) / n * 5.0, 0.0)
U_6: (x(U) / n * 6.0, 0.0)
U_7: (x(U) / n * 7.0, 0.0)
U_8: (x(U) / n * 8.0, 0.0)
U_9: (x(U) / n * 9.0, 0.0)
e_1 = Dilate(e, 1.0 / n, A)
e_2 = Dilate(e, 2.0 / n, A)
e_3 = Dilate(e, 3.0 / n, A)
e_4 = Dilate(e, 4.0 / n, A)
e_5 = Dilate(e, 5.0 / n, A)
e_6 = Dilate(e, 6.0 / n, A)
e_7 = Dilate(e, 7.0 / n, A)
e_8 = Dilate(e, 8.0 / n, A)
e_9 = Dilate(e, 9.0 / n, A)
v = Vector(U_1, A)
e'_2 = Translate(e_2, v)
e'_1 = Translate(e_1, v)
F = (5.88, -2.8000000000000003)
G = (6.3, -7)
w = Vector(F, G)
I = Translate(U_1, w)
A' = Translate(A, w)
z = Vector(I, A')
P_{10}: (u, f(u))
P_1: (u / n, f(u / n))
P_2: (2.0 * u / n, f(2.0 * u / n))
P_3: (3.0 * u / n, f(3.0 * u / n))
P_4: (4.0 * u / n, f(4.0 * u / n))
P_5: (5.0 * u / n, f(5.0 * u / n))
P_6: (6.0 * u / n, f(6.0 * u / n))
P_7: (7.0 * u / n, f(7.0 * u / n))
P_8: (8.0 * u / n, f(8.0 * u / n))
P_9: (9.0 * u / n, f(9.0 * u / n))
PL_{10} = Translate(P_{10}, z)
PL_9 = Translate(P_9, z)
PL_8 = Translate(P_8, z)
PL_7 = Translate(P_7, z)
PL_6 = Translate(P_6, z)
PL_5 = Translate(P_5, z)
PL_4 = Translate(P_4, z)
PL_3 = Translate(P_3, z)
PL_2 = Translate(P_2, z)
PL_1 = Translate(P_1, z)
so_1 = Segment(PL_1, P_1)
so_2 = Segment(PL_2, P_2)
so_3 = Segment(PL_3, P_3)
so_4 = Segment(PL_4, P_4)
so_5 = Segment(PL_5, P_5)
so_6 = Segment(PL_6, P_6)
so_7 = Segment(PL_7, P_7)
so_8 = Segment(PL_8, P_8)
so_9 = Segment(PL_9, P_9)
so_{10} = Segment(PL_{10}, P_{10})
e'_3 = Translate(e_3, v)
e'_4 = Translate(e_4, v)
e'_5 = Translate(e_5, v)
e'_6 = Translate(e_6, v)
e'_7 = Translate(e_7, v)
e'_8 = Translate(e_8, v)
e'_9 = Translate(e_9, v)
Q_{10}: (x(P_{10}), -1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * y(P_{10}))
Q_9: (x(P_9), -1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * y(P_9))
Q_8: (x(P_8), -1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * y(P_8))
Q_7: (x(P_7), -1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * y(P_7))
Q_6: (x(P_6), -1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * y(P_6))
Q_5: (x(P_5), -1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * y(P_5))
Q_4: (x(P_4), -1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * y(P_4))
Q_3: (x(P_3), -1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * y(P_3))
Q_2: (x(P_2), -1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * y(P_2))
Q_1: (x(P_1), -1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * y(P_1))
QL_{10} = Translate(Q_{10}, z)
QL_9 = Translate(Q_9, z)
QL_8 = Translate(Q_8, z)
QL_7 = Translate(Q_7, z)
QL_6 = Translate(Q_6, z)
QL_5 = Translate(Q_5, z)
QL_4 = Translate(Q_4, z)
QL_3 = Translate(Q_3, z)
QL_2 = Translate(Q_2, z)
QL_1 = Translate(Q_1, z)
su_1 = Segment(QL_1, Q_1)
su_2 = Segment(QL_2, Q_2)
su_3 = Segment(QL_3, Q_3)
su_4 = Segment(QL_4, Q_4)
su_5 = Segment(QL_5, Q_5)
su_6 = Segment(QL_6, Q_6)
su_7 = Segment(QL_7, Q_7)
su_8 = Segment(QL_8, Q_8)
su_9 = Segment(QL_9, Q_9)
su_{10} = Segment(QL_{10}, Q_{10})
w3 = false
w2 = false
w1 = true
f_2 = Line(A, P)
g_1 = Line(A, P)
s_1 = Segment(A, P)
R_{00}: (u + 0.5 * f(u) * cos(0.0 * °), f(u) * sin(0.0 * °))
R_{15}: (u + 0.5 * f(u) * cos(15.0 * °), f(u) * sin(15.0 * °))
R_{30}: (u + 0.5 * f(u) * cos(30.0 * °), f(u) * sin(30.0 * °))
R_{45}: (u + 0.5 * f(u) * cos(45.0 * °), f(u) * sin(45.0 * °))
R_{60}: (u + 0.5 * f(u) * cos(60.0 * °), f(u) * sin(60.0 * °))
R_{75}: (u + 0.5 * f(u) * cos(75.0 * °), f(u) * sin(75.0 * °))
R_{105}: (u + 0.5 * f(u) * cos(105.0 * °), f(u) * sin(105.0 * °))
R_{120}: (u + 0.5 * f(u) * cos(120.0 * °), f(u) * sin(120.0 * °))
R_{135}: (u + 0.5 * f(u) * cos(135.0 * °), f(u) * sin(135.0 * °))
R_{150}: (u + 0.5 * f(u) * cos(150.0 * °), f(u) * sin(150.0 * °))
R_{165}: (u + 0.5 * f(u) * cos(165.0 * °), f(u) * sin(165.0 * °))
R_{180}: (u + 0.5 * f(u) * cos(180.0 * °), f(u) * sin(180.0 * °))
R_{195}: (u + 0.5 * f(u) * cos(195.0 * °), f(u) * sin(195.0 * °))
R_{210}: (u + 0.5 * f(u) * cos(210.0 * °), f(u) * sin(210.0 * °))
R_{225}: (u + 0.5 * f(u) * cos(225.0 * °), f(u) * sin(225.0 * °))
R_{240}: (u + 0.5 * f(u) * cos(240.0 * °), f(u) * sin(240.0 * °))
R_{255}: (u + 0.5 * f(u) * cos(255.0 * °), f(u) * sin(255.0 * °))
R_{270}: (u + 0.5 * f(u) * cos(270.0 * °), f(u) * sin(270.0 * °))
R_{285}: (u + 0.5 * f(u) * cos(285.0 * °), f(u) * sin(285.0 * °))
R_{300}: (u + 0.5 * f(u) * cos(300.0 * °), f(u) * sin(300.0 * °))
R_{315}: (u + 0.5 * f(u) * cos(315.0 * °), f(u) * sin(315.0 * °))
R_{330}: (u + 0.5 * f(u) * cos(330.0 * °), f(u) * sin(330.0 * °))
R_{345}: (u + 0.5 * f(u) * cos(345.0 * °), f(u) * sin(345.0 * °))
r_{00} = Segment(A, R_{00})
r_{15} = Segment(A, R_{15})
r_{30} = Segment(A, R_{30})
r_{45} = Segment(A, R_{45})
r_{60} = Segment(A, R_{60})
r_{75} = Segment(A, R_{75})
r_{90} = Segment(A, P_{10})
r_{105} = Segment(A, R_{105})
r_{120} = Segment(A, R_{120})
r_{135} = Segment(A, R_{135})
r_{150} = Segment(A, R_{150})
r_{165} = Segment(A, R_{165})
r_{180} = Segment(A, R_{180})
r_{195} = Segment(A, R_{195})
r_{210} = Segment(A, R_{210})
r_{225} = Segment(A, R_{225})
r_{240} = Segment(A, R_{240})
r_{255} = Segment(A, R_{255})
r_{270} = Segment(A, R_{270})
r_{285} = Segment(A, R_{285})
r_{300} = Segment(A, R_{300})
r_{315} = Segment(A, R_{315})
r_{330} = Segment(A, R_{330})
r_{345} = Segment(A, R_{345})
el = CurveCartesian(0.5 * f(u) * cos(t) + u, f(u) * sin(t), t, 1.5708, 4.71239)
e' = Translate(e, v)
el'_{10} = Translate(el, z)
PL1 = 0
ko = Line(PL_1, PL_{10})
ku = Line(QL_1, QL_{10})
A_{links} = Intersect(ko, ku)
el_5 = CurveCartesian(0.5 * f(u * 5.0 / n) * cos(t) + u * 5.0 / n, f(u * 5.0 / n) * sin(t), t, 1.5708, 4.71239)
el_6 = CurveCartesian(0.5 * f(u * 6.0 / n) * cos(t) + u * 6.0 / n, f(u * 6.0 / n) * sin(t), t, 1.5708, 4.71239)
el_7 = CurveCartesian(0.5 * f(u * 7.0 / n) * cos(t) + u * 7.0 / n, f(u * 7.0 / n) * sin(t), t, 1.5708, 4.71239)
el_8 = CurveCartesian(0.5 * f(u * 8.0 / n) * cos(t) + u * 8.0 / n, f(u * 8.0 / n) * sin(t), t, 1.5708, 4.71239)
el_9 = CurveCartesian(0.5 * f(u * 9.0 / n) * cos(t) + u * 9.0 / n, f(u * 9.0 / n) * sin(t), t, 1.5708, 4.71239)
el_4 = CurveCartesian(0.5 * f(u * 4.0 / n) * cos(t) + u * 4.0 / n, f(u * 4.0 / n) * sin(t), t, 1.5708, 4.71239)
el_3 = CurveCartesian(0.5 * f(u * 3.0 / n) * cos(t) + u * 3.0 / n, f(u * 3.0 / n) * sin(t), t, 1.5708, 4.71239)
el_2 = CurveCartesian(0.5 * f(u * 2.0 / n) * cos(t) + u * 2.0 / n, f(u * 2.0 / n) * sin(t), t, 1.5708, 4.71239)
el_1 = CurveCartesian(0.5 * f(u * 1.0 / n) * cos(t) + u * 1.0 / n, f(u * 1.0 / n) * sin(t), t, 1.5708, 4.71239)
el'_1 = Translate(el_1, z)
el'_2 = Translate(el_2, z)
el'_3 = Translate(el_3, z)
el'_4 = Translate(el_4, z)
el'_5 = Translate(el_5, z)
el'_6 = Translate(el_6, z)
el'_7 = Translate(el_7, z)
el'_8 = Translate(el_8, z)
el'_9 = Translate(el_9, z)
MO_8, S_8 = Intersect(e'_9, so_8)
J, S_9 = Intersect(e', so_9)
S_7, MO_7 = Intersect(e'_8, so_7)
S_6, MO_6 = Intersect(e'_7, so_6)
S_5, MO_5 = Intersect(e'_6, so_5)
S_4, MO_4 = Intersect(e'_5, so_4)
S_3, MO_3 = Intersect(e'_4, so_3)
S_1, MO_1 = Intersect(e'_2, so_1)
S_2, MO_2 = Intersect(e'_3, so_2)
sl1 = Segment(PL_1, S_1)
sl2 = Segment(PL_2, S_2)
sl9 = Segment(S_9, PL_9)
sl8 = Segment(S_8, PL_8)
sl7 = Segment(S_7, PL_7)
sl6 = Segment(S_6, PL_6)
PL3 = 0
sl3 = Segment(PL_3, S_3)
sl4 = Segment(PL_4, S_4)
sl5 = Segment(PL_5, S_5)
sl_1 = Segment(PL_1, MO_1)
sl_2 = Segment(PL_2, MO_2)
sl_3 = Segment(PL_3, MO_3)
sl_4 = Segment(PL_4, MO_4)
sl_5 = Segment(PL_5, MO_5)
sl_6 = Segment(PL_6, MO_6)
sl_7 = Segment(PL_7, MO_7)
sl_8 = Segment(PL_8, MO_8)
sl_9 = Segment(PL_9, J)
V2, Z2 = Intersect(e'_3, su_2)
V3, Z3 = Intersect(e'_4, su_3)
V4, Z4 = Intersect(e'_5, su_4)
V6, Z6 = Intersect(e'_7, su_6)
V7, Z7 = Intersect(e'_8, su_7)
V9, Z9 = Intersect(e', su_9)
ul2 = Segment(QL_2, V2)
ul3 = Segment(QL_3, V3)
ul4 = Segment(QL_4, V4)
ul6 = Segment(QL_6, V6)
ul7 = Segment(QL_7, V7)
ul9 = Segment(QL_9, V9)
Z1, V1 = Intersect(e'_2, su_1)
K = Intersect(e'_9, su_8, 1.0)
Z5, V5 = Intersect(e'_6, su_5)
ru_2 = Segment(QL_2, Z2)
ru_3 = Segment(QL_3, Z3)
ru_4 = Segment(QL_4, Z4)
ru_5 = Segment(QL_5, Z5)
ru_6 = Segment(QL_6, Z6)
ru_7 = Segment(QL_7, Z7)
ru_8 = Segment(QL_8, K)
ru_9 = Segment(QL_9, Z9)
ul5 = Segment(QL_5, V5)
Z8, Q = Intersect(e'_9, su_8)
V8 = Intersect(e'_9, su_8, 2.0)
ul1 = Segment(QL_1, V1)
ru_1 = Segment(QL_1, Z1)
ul8 = Segment(QL_8, V8)