α = %v

r = %v

Flächeninhalt Kreissektor - Zusammenhänge erkunden

Werte übernehmen

Tabelle löschen

Radius fixieren

Winkel fixieren

Flächeninhalt

Flächeninhalt

α in °

Radius r

M = Intersect(xAxis, yAxis)
α = 1.2217304763960306 rad (slider from 0 to 359.99999°, step 0.017453292519943295)
r = 10 (slider from 0 to 50, step 0.5)
c = Circle(M, r)
A = Point(c)
A' = Rotate(A, α, M)
β = Angle(A, M, A')
d = CircleSector(M, A, A')
f = Segment(M, A)
a = Area(c)
Punktc = PointIn(c)
b = Area(d)
Punktd = PointIn(d)
s = Ray(M, Rotate[A, α / 2])
S = Intersect(Circle[M, r + 2], s)
k = Ray(M, Rotate[A, α / 2 + 180°])
K = Intersect(Circle[M, r + 2], k)
L: {}
L_{a}: {"α in °"}
L_{F}: {"Flächeninhalt"}
L_{r}: {"Radius r"}
e = false
g = false
Text3: "Mittelpunktswinkel α = " + α + ""
Text4: "Radius r = " + r + ""
Text5 = TableText(L_{r}, L_{F}, "_010 |01 c")
Text2 = TableText(L_{a}, L_{F}, "_010 |01 c")
Tab_r: "Mittelpunktswinkel: " + (LaTeX[α]) + "\\ {" + (LaTeX[Text5]) + ""
Tab_a: "Radius: " + (LaTeX[r]) + "\\ " + (LaTeX[Text2]) + ""
L_{r1} = Remove(L_{r}, First[L_{r}])
L_{F1} = Remove(L_{F}, First[L_{F}])
L_{a1} = Remove(L_{a}, First[L_{a}])
L_{rplot}: (L_{r1}, L_{F1})
A_{mr} = Area(CircleSector[(0, 0), (50, 0), Rotate[(40, 0), α]])
s_{yr} = If(A_{mr} ≤ 75, 5, If[A_{mr} ≤ 150, 10, If[A_{mr} ≤ 300, 20, If[A_{mr} ≤ 750, 50, If[A_{mr} ≤ 1500, 100, If[A_{mr} ≤ 3000, 200, If[A_{mr} ≤ 8000, 500]]]]]])
y_{mr}: (ceil(A_{mr} / s_{yr}) * s_{yr}) + s_{yr}
L_{aplot}: ((L_{a1} * 180 / π), L_{F1})
A_{ma} = Area(CircleSector[(0, 0), (0, r), Rotate[(0, r), 360°]])
s_{ya} = If(A_{ma} ≤ 75, 5, If[A_{ma} ≤ 150, 10, If[A_{ma} ≤ 300, 20, If[A_{ma} ≤ 750, 50, If[A_{ma} ≤ 1500, 100, If[A_{ma} ≤ 3000, 200, If[A_{ma} ≤ 8000, 500]]]]]])
y_{ma}: (ceil(A_{ma} / s_{ya}) * s_{ya}) + s_{ya}
P_{yr}: (0, y_{mr})
L_{yr}: (0, Sequence[s_{yr}, y_{mr} - s_{yr}, s_{yr}])
yachse_r = Segment((0, 0), P_{yr})
P_{ya}: (0, y_{ma})
yachse_{a} = Segment((0, 0), P_{ya})
L_{ya}: (0, Sequence[s_{ya}, y_{ma} - s_{ya}, s_{ya}])
P_{xa}: (405, 0)
P_{xr}: (55, 0)
xachse_{a} = Segment((0, 0), P_{xa})
xachse_{r} = Segment((0, 0), P_{xr})
L_{xr}: (Sequence[5, 50, 5], 0)
L_{xa}: (Sequence[45, 360, 45], 0)
B = If(g ≟ 0 ∧ e ≟ 1, (405, 0), If[g ≟ 1 ∧ e ≟ 0, (55, 0)])
L_{tyr} = Sequence(Text[Element[Sequence[s_{yr}, y_{mr} - s_{yr}, s_{yr}], i], Element[L_{yr}, i] + (0.5, (-(s_{yr} / 10)))], i, 1, Length[L_{yr}])
L_{txr} = Sequence(Text[Element[Sequence[5, 50, 5], i], Element[L_{xr}, i] + (-1, s_{yr} / 10)], i, 1, Length[L_{xr}])
L_{tya} = Sequence(Text[Element[Sequence[s_{ya}, y_{ma} - s_{ya}, s_{ya}], i], Element[L_{ya}, i] + (4.5, (-(s_{ya} / 10)))], i, 1, Length[L_{ya}])
L_{txa} = Sequence(Text[Element[Sequence[45, 360, 45], i], Element[L_{xa}, i] + (-9, s_{ya} / 10)], i, 1, Length[L_{xa}])
gy_a = Sequence(Ray[(0, i), (i, i)], i, s_{ya}, y_{ma} + s_{ya}, s_{ya})
gx_r = Sequence(Ray[(i, 0), (i, i)], i, 5, 60, 5)
gy_r = Sequence(Ray[(0, i), (i, i)], i, s_{yr}, y_{mr} + s_{yr}, s_{yr})
gx_a = Sequence(Ray[(i, 0), (i, i)], i, 45, 450, 45)
Textc: "A_{Kreis}= " + a + ""
Textd: "A_{Sektor}= " + b + ""