Star Polygon Construction

Star Polygon Construction
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2015-04-10 17:26
This example demonstrates how to construct regular star polygons, denoted by {p/q}, by connecting specific vertices of a regular polygon. Key mathematical concepts include regular polygons, vertex connection, fractional notation (p/q), and geometric construction. The construction utilizes GeoGebra commands such as Polygon, Append, Sequence, and PolyLine, where parameters q and p control the shape and density of the star polygon. The Sequence command generates a vertex sequence based on these parameters. This example is suitable for high school mathematics education, helping students understand the relationship between regular polygons and star polygons, as well as the application of parametric equations in geometric constructions.

GeoGebra Commands & Parameters

  1. Polygon(A, B, p) → regolare, b, k, l, p_1, q_1, r, s, t, a_1, b_1, C, c, D, E, F, G, H, I, J, K, L, M, d, N, O, P, Q, R, e, f, g, h, i, j
  2. Append(Sequence[Vertex[regolare, k], k, 1, p], A) → vertici
  3. Sequence(Element[vertici, Element[indici, k]], k, 1, p + 1) → vertici2
  4. PolyLine(vertici2) → stellato