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2D Vector Grid

2D Vector Grid
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2019-01-31 20:29
VectorTrigonometryCoordinate Geometry
This example demonstrates the construction of a 2D vector grid. Key mathematical concepts include vectors and equilateral triangles. Using GeoGebra commands such as Intersect, Vector, Translate, and Polygon, a series of equilateral triangle grids can be constructed. Suitable for high school mathematics education and learning about vectors and triangles.

GeoGebra Commands & Parameters

  1. Intersect(xAxis, yAxis) → A
  2. Vector(A, B) → u
  3. Vector(A, C) → v
  4. Translate(C, u) → C'
  5. Vector(C, C') → w
  6. Translate(B, v) → B'
  7. Vector(B, B') → a
  8. Polygon(A, C, C', B) → q1, a_1, c, c', b
  9. Sequence(Sequence[Segment[A + (j * v) + (k * u), A + (k * u) + ((j + 1) * v)], k, -20, 20], j, -20, 20) → L_2
  10. Sequence(Sequence[Segment[A + (j * v) + (k * u), A + ((k + 1) * u) + (j * v)], k, -20, 20], j, -20, 20) → L_1

AI Drawing Prompt Reference

Draw a 2D vector grid starting from the origin, with two non-collinear vectors forming a parallelogram. Use this parallelogram as a basic unit, repeatedly translating it along both vector directions to cover the entire plane. The grid consists of two families of parallel line segments: one family parallel to the first vector, the other parallel to the second vector, intersecting to form countless congruent parallelograms. Each parallelogram is bounded by two adjacent vectors, creating a uniform oblique grid pattern that illustrates vector addition and translation.
The prompt above was compiled from the original drawing commands and is for reference only.