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Trigonometric Polygons

Trigonometric Polygons
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2016-07-02 06:47
PolygonVectorTrigonometryGeometric Construction
This example demonstrates how using polygons instead of circles affects the cosine function, exploring core concepts like polygons, vectors, intersections, equilateral triangles, perimeter, and combinatorics. It leverages GeoGebra commands such as Sequence, Intersect, Segment, and Translate, utilizing objects like n, K, P, t, i_t, A, a, f, b, c, d, y_A, u, g, g_1, B, h, O. Ideal for high school and advanced learners to understand dynamic geometric relationships between trigonometric functions and polygons.

GeoGebra Commands & Parameters

  1. Sequence((cos(((2 * π) * (i + 0.5) / n)), sin(((2 * π) * (i + 0.5) / n))), i, 0, n - 1) → K
  2. Sequence(Segment[K(i), K(Mod[i, n] + 1)], i, 1, n) → P
  3. Intersect(Ray[(0, 0), (cos(((2 * π) * t)), sin(((2 * π) * t)))], Line[K(Mod[i_t - 1, n] + 1), K(Mod[i_t, n] + 1)]) → A
  4. Segment((0, 0), A) → f
  5. Translate(g, (1, 0)) → g_1
  6. Segment(A, B) → h