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Weaving Pattern: Dynamic Construction of Isosceles Triangles via Reflection and

Weaving Pattern: Dynamic Construction of Isosceles Triangles via Reflection and
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2016-01-09 09:30
TrianglePolygonSequenceTransformationGeometric Construction
① This example demonstrates a dynamic woven‑like array of isosceles triangles generated by successive reflections and symmetries. ② Core mathematical concepts include properties of isosceles triangles, reflection symmetry, vector translations, iterative sequences, and geometric transformations in the complex plane. ③ Construction highlights: Polygon creates the base triangle; Vector and Angle define reflection direction and angle; Sequence iterates the transformation to build the pattern; InputBox provides interactive parameter control; Textfield displays computed values. ④ Suitable for high‑school geometry and analytic geometry lessons, as well as university‑level geometric modeling and interactive exploration.

GeoGebra Commands & Parameters

  1. Polygon(A, B, C, D) → poly1, a_1, b, c, d_1
  2. Vector(A, B) → u
  3. Vector(A, D) → v
  4. Angle(B, A, D) → a
  5. Polygon(E, G, H, F) → poly2, e_1, g, h, f
  6. Textfield(d) → InputBox1
  7. Vector(E, F) → w
  8. Vector(E, G) → s
  9. Sequence(Sequence[Polygon[Translate[A, Vector[(((i + (0.5 * Mod[j, 2])) * (1 + d)) * (u + s)) + (((0.5 * j) * (1 + d)) * (w + v))]], Translate[B, Vector[(((i + (0.5 * Mod[j, 2])) * (1 + d)) * (u + s)) + (((0.5 * j) * (1 + d)) * (w + v))]], Translate[C, Vector[(((i + (0.5 * Mod[j, 2])) * (1 + d)) * (u + s)) + (((0.5 * j) * (1 + d)) * (w + v))]], Translate[D, Vector[(((i + (0.5 * Mod[j, 2])) * (1 + d)) * (u + s)) + (((0.5 * j) * (1 + d)) * (w + v))]]], i, (-N), N], j, (-N), N) → list1
  10. Sequence(Sequence[Polygon[Translate[E, Vector[(((i + (0.5 * Mod[j, 2])) * (1 + d)) * (u + s)) + (((0.5 * j) * (1 + d)) * (w + v))]], Translate[G, Vector[(((i + (0.5 * Mod[j, 2])) * (1 + d)) * (u + s)) + (((0.5 * j) * (1 + d)) * (w + v))]], Translate[H, Vector[(((i + (0.5 * Mod[j, 2])) * (1 + d)) * (u + s)) + (((0.5 * j) * (1 + d)) * (w + v))]], Translate[F, Vector[(((i + (0.5 * Mod[j, 2])) * (1 + d)) * (u + s)) + (((0.5 * j) * (1 + d)) * (w + v))]]], i, (-N), N], j, (-N) - 1, N - 1) → list2