MathPlotAI Logo MathPlotAI

Wavy Polygons

Wavy Polygons
Loading the math board and drawing, please wait…
2017-05-22 18:44
PolygonFunctionIntegral
This example demonstrates wavy polygons. It involves concepts of polygons, integrals, and functions. Using GeoGebra commands such as Sequence and Element, wavy polygons can be constructed. Suitable for high school math education or student exploration of geometry and functions.

GeoGebra Commands & Parameters

  1. Sequence(Sequence[(i, j) + (Mod[i + j + 1, 2] * (g(a + i), v(a + j))) + (Mod[i + j, 2] * (v(a + j), g(a + i))), i, 0, n], j, 0, n) → Ld
  2. Sequence(Sequence[(i, j) - (Mod[i + j + 1, 2] * (g(a + i), v(a + j))) - (Mod[i + j, 2] * (v(a + j), g(a + i))), i, 0, n], j, 0, n) → Lg
  3. Element(Element[Lg, 2], 2) → Lg22
  4. Element(Element[Ld, 1], 1) → Ld11
  5. Element(Element[Lg, 3], 3) → Lg33
  6. Element(Element[Ld, 2], 1) → Ld21
  7. Element(Element[Ld, 2], 2) → Ld22
  8. Element(Element[Lg, 2], 1) → Lg21
  9. Element(Element[Lg, 1], 2) → Lg12
  10. Sequence(Sequence[Segment[Element[Element[Ld, i], j], Element[Element[Lg, i - 1], j + 1]], i, 2, n + 2, 2], j, 2, n + 2, 2) → T4
  11. Sequence(Sequence[Segment[Element[Element[Lg, i + 1], j], Element[Element[Ld, i], j + 1]], i, 1, n + 2, 2], j, 1, n + 2, 2) → T5
  12. Sequence(Sequence[Segment[Element[Element[Lg, i + 1], j], Element[Element[Ld, i], j - 1]], i, 1, n + 2, 2], j, 1, n + 2, 2) → T6
  13. Sequence(Sequence[Segment[Element[Element[Lg, i + 1], j], Element[Element[Ld, i], j - 1]], i, 2, n + 2, 2], j, 2, n + 2, 2) → T7
  14. Sequence(Sequence[Segment[Element[Element[Ld, i + 0], j + 2], Element[Element[Lg, i + 1], j + 1]], i, 2, n + 2, 2], j, 1, n + 2, 2) → T8
  15. Sequence(Sequence[Segment[Element[Element[Lg, i], j], Element[Element[Ld, i + 1], j - 1]], i, 2, n + 2, 2], j, 2, n + 2, 2) → T1
  16. Element(Ld, 1) → Ld1
  17. Element(Lg, 1) → Lg2
  18. Sequence(Sequence[Segment[(i, j) - (Mod[i + j + 1, 2] * (g(a + i), v(a + j))) - (Mod[i + j, 2] * (v(a + j), g(a + i))), (i, j) + (Mod[i + j + 1, 2] * (g(a + i), v(a + j))) + (Mod[i + j, 2] * (v(a + j), g(a + i)))], i, 0, n], j, 0, n) → LT
  19. Sequence(Sequence[Circle[Element[Element[Lg, i], j], Element[Element[Ld, i - 1], j - 1]], i, 2, n + 2, 2], j, 2, n + 2, 2) → T2
  20. Sequence(Sequence[Polygon[Element[Element[Ld, i], j], Element[Element[Lg, i + 1], j + 1], sid], i, 2, n + 2, 2], j, 2, n + 3, 2) → T3