Koti v mnogokotniku

Vsi notranji koti v 

- kotniku merijo 

Vsota notranjih kotov v 

- kotniku je enaka

A22 = 0
a = 3
S = Intersect(yAxis, xAxis)
c = Circle(S, a)
A = Point(c)
n = 3 (slider from 3 to 20, step 1)
α: 360.0° / n
tocke = Sequence(Rotate[A, i * α, S], i, 0.0, n)
robovi = Sequence(Segment[Element[tocke, i], Element[tocke, i + 1.0]], i, 1.0, n)
A3 = 2
A2 = 1
A4: 2.0 * A3 - A2
A5: 2.0 * A4 - A3
A6: 2.0 * A5 - A4
A7: 2.0 * A6 - A5
A8: 2.0 * A7 - A6
A9: 2.0 * A8 - A7
A10: 2.0 * A9 - A8
A11: 2.0 * A10 - A9
A12: 2.0 * A11 - A10
A13: 2.0 * A12 - A11
A14: 2.0 * A13 - A12
A15: 2.0 * A14 - A13
A16: 2.0 * A15 - A14
A17: 2.0 * A16 - A15
A18: 2.0 * A17 - A16
A19: 2.0 * A18 - A17
A20: 2.0 * A19 - A18
A21: 2.0 * A20 - A19
B2 = If(A2 ≤ n, Element[tocke, A2], If[A2 ≟ n + 1.0, Element[tocke, 1.0]])
B3 = If(A3 ≤ n, Element[tocke, A3], If[A3 ≟ n + 1.0, Element[tocke, 1.0]])
B4 = If(A4 ≤ n, Element[tocke, A4], If[A4 ≟ n + 1.0, Element[tocke, 1.0]])
B5 = If(A5 ≤ n, Element[tocke, A5], If[A5 ≟ n + 1.0, Element[tocke, 1.0]])
B6 = If(A6 ≤ n, Element[tocke, A6], If[A6 ≟ n + 1.0, Element[tocke, 1.0]])
B7 = If(A7 ≤ n, Element[tocke, A7], If[A7 ≟ n + 1.0, Element[tocke, 1.0]])
B8 = If(A8 ≤ n, Element[tocke, A8], If[A8 ≟ n + 1.0, Element[tocke, 1.0]])
B9 = If(A9 ≤ n, Element[tocke, A9], If[A9 ≟ n + 1.0, Element[tocke, 1.0]])
B10 = If(A10 ≤ n, Element[tocke, A10], If[A10 ≟ n + 1.0, Element[tocke, 1.0]])
B11 = If(A11 ≤ n, Element[tocke, A11], If[A11 ≟ n + 1.0, Element[tocke, 1.0]])
B12 = If(A12 ≤ n, Element[tocke, A12], If[A12 ≟ n + 1.0, Element[tocke, 1.0]])
B13 = If(A13 ≤ n, Element[tocke, A13], If[A13 ≟ n + 1.0, Element[tocke, 1.0]])
B14 = If(A14 ≤ n, Element[tocke, A14], If[A14 ≟ n + 1.0, Element[tocke, 1.0]])
B15 = If(A15 ≤ n, Element[tocke, A15], If[A15 ≟ n + 1.0, Element[tocke, 1.0]])
B16 = If(A16 ≤ n, Element[tocke, A16], If[A16 ≟ n + 1.0, Element[tocke, 1.0]])
B17 = If(A17 ≤ n, Element[tocke, A17], If[A17 ≟ n + 1.0, Element[tocke, 1.0]])
B18 = If(A18 ≤ n, Element[tocke, A18], If[A18 ≟ n + 1.0, Element[tocke, 1.0]])
B19 = If(A19 ≤ n, Element[tocke, A19], If[A19 ≟ n + 1.0, Element[tocke, 1.0]])
B20 = If(A20 ≤ n, Element[tocke, A20], If[A20 ≟ n + 1.0, Element[tocke, 1.0]])
B21 = If(A21 ≤ n, Element[tocke, A21], If[A21 ≟ n + 1.0, Element[tocke, 1.0]])
B1 = Element(tocke, n)
C2 = Angle(B1, B2, B3)
C3 = Angle(B2, B3, B4)
C4 = Angle(B3, B4, B5)
C5 = Angle(B4, B5, B6)
C6 = Angle(B5, B6, B7)
C7 = Angle(B6, B7, B8)
C8 = Angle(B7, B8, B9)
C9 = Angle(B8, B9, B10)
C10 = Angle(B9, B10, B11)
C11 = Angle(B10, B11, B12)
C12 = Angle(B11, B12, B13)
C13 = Angle(B12, B13, B14)
C14 = Angle(B13, B14, B15)
C15 = Angle(B14, B15, B16)
C16 = Angle(B15, B16, B17)
C17 = Angle(B16, B17, B18)
C18 = Angle(B17, B18, B19)
C19 = Angle(B18, B19, B20)
C20 = Angle(B19, B20, B21)
B22: A
C21 = Angle(B20, B21, B22)
tekst2: n + ""
tekst4: C2 + "."
tekst6: n + ""
C22: C2 + C3 + C4 + C5 + C6 + C7 + C8 + C9 + C10 + C11 + C12 + C13 + C14 + C15 + C16 + C17 + C18 + C19 + C20 + C21
C1 = 0 rad (slider from 0 to 6.283185307179586, step 0.017453292519943295)
D2 = If(n ≟ 2.0, 0.0, 0.0)
L_1: {C2, C3, C4, C5, C6, C7, C8, C9, C10, C11, C12, C13, C14, C15, C16, C17, C18, C19, C20, C21, C22}
D4 = If(n ≟ 3.0, Sum[C2:C4 / °], 0.0)
D3 = If(n ≟ 2.0, Sum[C2:C3 / °], 0.0)
D10 = If(n ≟ 9.0, Sum[C2:C10 / °], 0.0)
D9 = If(n ≟ 8.0, Sum[C2:C9 / °], 0.0)
D8 = If(n ≟ 7.0, Sum[C2:C8 / °], 0.0)
D7 = If(n ≟ 6.0, Sum[C2:C7 / °], 0.0)
D6 = If(n ≟ 5.0, Sum[C2:C6 / °], 0.0)
D5 = If(n ≟ 4.0, Sum[C2:C5 / °], 0.0)
D11 = If(n ≟ 10.0, Sum[C2:C11 / °], 0.0)
D12 = If(n ≟ 11.0, Sum[C2:C12 / °], 0.0)
D13 = If(n ≟ 12.0, Sum[C2:C13 / °], 0.0)
D14 = If(n ≟ 13.0, Sum[C2:C14 / °], 0.0)
D15 = If(n ≟ 14.0, Sum[C2:C15 / °], 0.0)
D16 = If(n ≟ 15.0, Sum[C2:C16 / °], 0.0)
D17 = If(n ≟ 16.0, Sum[C2:C17 / °], 0.0)
D19 = If(n ≟ 18.0, Sum[C2:C19 / °], 0.0)
D21 = If(n ≟ 20.0, Sum[C2:C21 / °], 0.0)
D22 = 0
D20 = If(n ≟ 19.0, Sum[C2:C20 / °], 0.0)
D18 = If(n ≟ 17.0, Sum[C2:C18 / °], 0.0)
tekst8: "(" + n + " - 2) * 180° = " + (n - 2.0) + "* 180° =" + (Text[Object["D" + (n + 1.0)]]) + "°."