Author: Daniel Mentrard

Cylindrical coordinates:

M( r ;θ ; z)

Cartesian coordinates:

M (x ; y ; z)

 \vec{ i } 

 \vec{ j } 

 \vec{ k } 

O is movable

θ = 1.8849555921538759 rad (slider from 0 to 6.283185307179586, step 0.017453292519943295)
r = 0.65 (slider from 0 to 5, step 1.0E-4)
g: 1 / ((π * r^(2)))
O = (6.432013773728125, 1.0024126781939606)
Zoom = 2.8 (slider from 0.1 to 5, step 0.1)
View3d = (-1.3695401453118792, 4.026295277057614)
ya: y(View3d)
costheta: cos(ya)
sintheta: sin(ya)
xa: x(View3d)
cosphi: cos(xa)
xy: (((-Zoom) * cosphi) * sintheta)
sinphi: sin(xa)
B_1 = (6.4198177517084565, 0.9902166561742932)
Z: (x(B_1) + (Zoom * cosphi), y(B_1) + ((Zoom * sinphi) * sintheta))
w = Vector(B_1, Z)
Y: (x(B_1), y(B_1) + (Zoom * costheta))
v = Vector(B_1, Y)
X: (x(B_1) + (Zoom * sinphi), y(B_1) + xy)
u = Vector(B_1, X)
M': O + ((r * cos(θ)) * u) + ((r * sin(θ)) * v)
a_1 = OrthogonalLine(View3d, yAxis)
b = OrthogonalLine(View3d, xAxis)
c: cos(ya)
n = 10 (slider from 1 to 10, step 1)
nn = 0.42 (slider from 0 to 1, step 0.01)
z = 0.012732395447351627 (slider from 0 to g, step 0.1)
liste1b = Sequence(O + ((0.3 * sin(k)) * v) + ((0.3 * cos(k)) * u), k, 0, θ + 0.05, 0.1)
liste2b = Sequence(Segment[Element[liste1b, i], Element[liste1b, i + 1]], i, 1, Length[liste1b] + 1)
liste3b = Sequence(Polygon[O, Element[liste1b, i], Element[liste1b, i + 1]], i, 1, Length[liste1b] + 1)
O' = Translate(O, Vector[(r * u)])
d = Segment(O, O')
e = Segment(O, M')
C: O + (g * w)
f = CurveCartesian(x(C - (r * (((0 * sin(i°)) * w) + (sin(i°) * u) - (cos(i°) * v)))), y(C - (r * (((0 * sin(i°)) * w) + (sin(i°) * u) - (cos(i°) * v)))), i, 0, 360)
M: M' + (g * w)
h = Vector(O, M)
i = Segment(M, M')
liste1 = Sequence(O - (r * (((0 * sin(i°)) * w) + (sin(i°) * u) - (cos(i°) * v))), i, 0, 360, n)
liste2 = Sequence(C - (r * (((0 * sin(i°)) * w) + (sin(i°) * u) - (cos(i°) * v))), i, 0, 360, n)
liste3 = Sequence(Polygon[Element[liste1, i], Element[liste1, i + 1], Element[liste2, i + 1], Element[liste2, i]], i, 1, Length[liste1])
texte3: " M  ( " + r + " ; " + θ + " ; " + z + " )"
texte6: "x = r cos θ = " + ((r * cos(θ)))
texte7: " y = r sinθ = " + ((r * sin(θ)))
texte8: " z = " + z
texte9: " M  ( " + ((r * cos(θ))) + " ; " + ((r * sin(θ))) + " ; " + z + " )"
xx: (r * cos(θ))
yy: (r * sin(θ))
texte10: " \vec{ OM } = " + ((r * cos(θ))) + "  \vec{ i } " + (If[yy  <  0, "", "+"]) + ((r * sin(θ))) + "  \vec{ j }  " + (If[z  <  0, "", "+"]) + z + " \vec{ k }"
B = Midpoint(B_1, X)
D = Midpoint(B_1, Y)
E = Midpoint(Z, B_1)
j = Segment(C, M)
k = Segment(C, O)
PP = Element(liste1b, Length[liste1b] / 2)
texte15: "" + θ
A = (-1, 6)
F = (3, 6)
G = (3, 4)
H = (-1, 4)
poly1, a_2, f_1, g_1, h_1 = Polygon(A, F, G, H)
I = (9, 6)
J = (13.371550302918902, 6.002781706257615)
K = (13.383746324938569, 3.2830687958717735)
L = (8.993178397858289, 3.246480729812771)
poly2, i_1, j_1, k_1, l = Polygon(I, J, K, L)
a = -2 (slider from -5 to 5, step 1)
tilavuus: ((π * r^(2)) * g)
teksti1: "V=\pi r^2h=\pi·" + (LaTeX[r]) + "^2·" + (LaTeX[g]) + "=" + (LaTeX[tilavuus]) + "  \;   (dm^3)"
pellintarve: ((2 * π) * r^(2)) + (((2 * π) * r) * g)
teksti2: "Tarvittava pellin määrä  =  " + (LaTeX[pellintarve]) + "  (dm²)"