Regular polygon with strings: All in one
Date: 13 January 2013

Use sliders, change form and observe

1

2

3

4

5

6

all

N

N

n

Regular polygon with strings: All in one 

\copyright \;Roman\;Chijner,\;Heidelberg\;2013

Six possibilities of strings:

Sewen\; possible\; variants:

Use sliders, change form and observe

(on\; click)

n34 = 30 (slider from 1 to n, step 1)
n = 30 (slider from 10 to 200, step 10)
N = 6 (slider from 2 to 500, step 1)
R2 = 2 (slider from 0 to 2, step 0.1)
p0b = Sequence((R2; π / N * (2 * i + 1)), i, 1, N)
p3 = Sequence(Element[p0b, 1] * (1 - i / n), i, 0, n)
R1 = 1.2 (slider from 0 to 2, step 0.1)
l1a = Sequence((R1; 2 * π / N * i), i, 1, N)
p0a = Append(l1a, Element[l1a, 1])
p4 = Sequence(Element[p0a, 1] * (1 - i / n), i, 0, n)
n23 = 30 (slider from 1 to n, step 1)
n12 = 30 (slider from 1 to n, step 1)
p2 = Sequence(Element[p0a, 2] + (Element[p0b, 1] - Element[p0a, 2]) * (1 - i / n), i, 0, n)
p1 = Sequence(Element[p0a, 1] + (Element[p0b, 1] - Element[p0a, 1]) * (1 - i / n), i, 0, n)
A = (0, 0)
c = Circle(A, R1)
d = Circle(A, R2)
l2a = Sequence(Segment[Element[l1a, i], Element[p0b, i]], i, 1, N)
s0_{12} = Sequence(Segment[Element[p1, i], Element[p2, n12 - i + 1]], i, 1, n12)
l2b = Sequence(Segment[Element[p0a, i + 1], Element[p0b, i]], i, 1, N)
s0_{34} = Sequence(Segment[Element[p4, i], Element[p3, n34 - i + 1]], i, 1, n34)
ss_{12} = Sequence(Rotate[s0_{12}, 2 * π / N * i], i, 1, N)
s0'_{34} = Mirror(s0_{34}, Line[A, Element[p0a, 1]])
s0_{23} = Sequence(Segment[Element[p2, i], Element[p3, n23 - i + 1]], i, 1, n23)
s0'_{23} = Mirror(s0_{23}, Line[A, Element[p0b, 1]])
n45 = 30 (slider from 1 to n, step 1)
p5 = Sequence(Element[p0a, 2] * (1 - i / n), i, 0, n)
s0_{45} = Sequence(Segment[Element[p4, i], Element[p5, n45 - i + 1]], i, 1, n45)
s0'_{45} = Mirror(s0_{45}, Line[A, Element[p0b, 1]])
ss0_{13}: {s0_{45}, s0'_{45}}
ss_{45} = Sequence(Rotate[ss0_{13}, 2 * π / N * i], i, 1, N)
ss0_{34}: {s0_{34}, s0'_{34}}
ss_{34} = Sequence(Rotate[ss0_{34}, 2 * π / N * i], i, 1, N)
ss0_{23}: {s0_{23}, s0'_{23}}
ss_{23} = Sequence(Rotate[ss0_{23}, 2 * π / N * i], i, 1, N)
n14 = 30 (slider from 1 to n, step 1)
s0_{14} = Sequence(Segment[Element[p4, i], Element[p1, i]], i, 1, n14)
s0'_{14} = Mirror(s0_{14}, Line[A, Element[p0b, 1]])
ss0_{14}: {s0_{14}, s0'_{14}}
ss_{14} = Sequence(Rotate[ss0_{14}, 2 * π / N * i], i, 1, N)
n15 = 30 (slider from 1 to n, step 1)
s0_{15} = Sequence(Segment[Element[p1, i], Element[p5, n15 - i + 1]], i, 1, n15)
s0'_{15} = Mirror(s0_{15}, Line[A, Element[p0b, 1]])
ss0_{15}: {s0_{15}, s0'_{15}}
ss_{15} = Sequence(Rotate[ss0_{15}, 2 * π / N * i], i, 1, N)