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Making Equilateral Triangles on Isometric Grid

Making Equilateral Triangles on Isometric Grid
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2019-12-01 14:51
TrianglePolygonGeometric Construction
This example demonstrates how to construct equilateral triangles on an isometric grid. Key math concepts include properties of equilateral triangles and applications of isometric grids. The construction utilizes GeoGebra commands like IndexOf, Sequence, Join, Flatten, RandomElement, Segment, If, along with objects such as ListTriType, TriType, ListTri1b, ListTri1a, etc., for triangle generation and manipulation. Suitable for middle school and above students for learning and exploring geometric constructions.

GeoGebra Commands & Parameters

  1. IndexOf(SelectedElement[ListTriType], ListTriType) → TriType
  2. Sequence(Sequence[((sqrt(3) * s) + sqrt(3) / 2, t + 1 / 2), s, 2, 9], t, 2, 9) → ListTri1b
  3. Sequence(Sequence[((sqrt(3) * s), t), s, 2, 9], t, 2, 9) → ListTri1a
  4. Join({ListTri1a, ListTri1b}) → ListTri1
  5. Sequence(Sequence[((sqrt(3) * s), t), s, 4, 8], t, 5, 8) → ListTri2a
  6. Sequence(Sequence[((sqrt(3) * s) + sqrt(3) / 2, t + 1 / 2), s, 4, 7], t, 5, 8) → ListTri2b
  7. Join({ListTri2a, ListTri2b}) → ListTri2
  8. Flatten(If[TriType ≟ 1, ListTri1, ListTri2]) → ListTri
  9. RandomElement(ListTri) → Redb0
  10. RandomElement(ListTri) → Reda
  11. Segment(Blue1a, Blue1b) → SegBlue1
  12. Segment(Blue2a, Blue2b) → SegBlue2
  13. If(Reda ≟ Redb0, Redb0 + (0, 1), Redb0) → Redb
  14. Sequence(Sequence[((sqrt(3) * s) + sqrt(3) / 2, t + 1 / 2), s, -1, 13], t, -4, 13) → ListDots2
  15. Sequence(Sequence[((sqrt(3) * s), t), s, -1, 13], t, -4, 13) → ListDots1
  16. Segment(Reda, Redb) → SegRed