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Nested Polygons Example

Nested Polygons Example
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2016-04-04 23:21
PolygonVectorIntegralGeometric Construction
This example demonstrates the construction and properties of complex geometric figures formed by nesting multiple polygons. It involves core mathematical concepts such as polygon construction, geometric transformations, vector operations, and definite integrals. The construction utilizes GeoGebra commands like Circle, Intersect, Segment, Sequence, Polygon, Point, Angle, Vector, Distance, and Ray. It is suitable for high school and above students to explore geometric construction techniques and polygonal properties.

GeoGebra Commands & Parameters

  1. Circle(A, 4) → c
  2. Intersect(c, xAxis, 2) → B
  3. Segment(B, C) → a_2
  4. Sequence(((4 * cos(a)), (4 * sin(a))), a, 0, (2 * π), (2 * π / n)) → list1
  5. Polygon(B, C, n) → poly1, a, k, l, m, p, q, r, s, t, b_1, c_1, b, d_1, D, E, F, G, H, I, J, K, L, d, M, N, O, P, Q, R, T, U, V, e, f, g, h, i, j
  6. Point(a_2) → S
  7. Segment(A, S) → a_1
  8. Angle(B, A, S) → α
  9. Vector(A, S) → u
  10. Sequence(Vector[Rotate[u, ((2 * π) * k / n)]], k, 1, n) → u'
  11. Distance(B, S) → BS
  12. Distance(B, C) → BC
  13. Sequence(Segment[Rotate[A, ((2 * π) * k / n)], Rotate[S, ((2 * π) * k / n)]], k, 1, n, 1) → list2
  14. Sequence(Vector[A, Element[list1, k]], k, 1, n, 1) → list3
  15. Distance(C, D) → CD
  16. Ray(A, Vector[Element[u', 1]]) → e_1
  17. Intersect(e_1, b) → W
  18. Polygon(S, W, n) → poly2, f_1, p_1, q_1, r_1, s_1, t_1, b_2, c_2, d_2, e_2, f_2, g_1, g_2, Z, A_1, B_1, C_1, D_1, E_1, F_1, G_1, H_1, h_1, I_1, J_1, K_1, L_1, M_1, N_1, O_1, P_1, Q_1, i_1, j_1, k_1, l_1, m_1, n_1