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3D Algebra Tiles Illustrator (Dynamic & Modifiable)

3D Algebra Tiles Illustrator (Dynamic & Modifiable)
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2017-02-25 03:42
PolygonVectorSolid GeometryGeometric Construction
In collections Geom. & Alg.: Quadratics Geom. & Alg.: Exponential Functions & Logarithms
This example demonstrates a dynamic 3D algebra tiles model that combines cubes, polygonal faces, vectors, and translations to visualize polynomials, quadratic expressions, and factorization in three-dimensional space. Core mathematical concepts include algebra, difference and slope, line segments, vectors, quadratic equations, and links to statistics and linear optimization. The construction uses GeoGebra commands Cube, Point, Polygon, Vector, and Translate, along with face, edge, and poly objects to assemble modifiable 3D algebra tiles. It is suitable for middle and high school mathematics instruction, classroom demonstrations, and student-centered exploration of algebraic-geometric modeling.

GeoGebra Commands & Parameters

  1. Cube((0, 0), (1, 0), (1, 1)) → e, A, face5, faceBCDE, edge2, edge1, edge4, edge6, edge3, edgeAE, edgeBE, edgeBC, B, edge5, edgeCD, edge7, edgeDE, C, D, E, face1, face3, face2, face4
  2. Point(xAxis) → F
  3. Polygon(F, G, 4) → poly1, f, g, h, i, H, I
  4. Polygon((4, 0), (5, 0), (5, 0.2), (4, 0.2)) → poly2, j, k, l, m
  5. Polygon((6, 0), (6.2, 0), (6.2, 0.2), (6, 0.2)) → p, p_2, p_3, p_4, p_5
  6. Vector((0, 0), (0, 1)) → u
  7. Translate(e, Vector[(2 * u)]) → e'
  8. Translate(e, Vector[(4 * u)]) → e'_1
  9. Translate(e, Vector[(6 * u)]) → e'_2
  10. Translate(e, Vector[(8 * u)]) → e'_3
  11. Translate(poly1, Vector[(2 * u)]) → poly1'
  12. Translate(poly1, Vector[(4 * u)]) → poly1'_1
  13. Translate(poly1, Vector[(6 * u)]) → poly1'_2
  14. Translate(poly1, Vector[(8 * u)]) → poly1'_3
  15. Translate(poly2, Vector[(2 * u)]) → poly2'
  16. Translate(poly2, Vector[(4 * u)]) → poly2'_1
  17. Translate(poly2, Vector[(6 * u)]) → poly2'_2
  18. Translate(poly2, Vector[(8 * u)]) → poly2'_3
  19. Translate(p, Vector[(2 * u)]) → p'
  20. Translate(p, Vector[(4 * u)]) → p'_1
  21. Translate(p, Vector[(6 * u)]) → p'_2
  22. Translate(p, Vector[(8 * u)]) → p'_3

AI Drawing Prompt Reference

Create a dynamic 3D algebra tiles model featuring cubes, polygonal faces, vectors, and translations to visualize polynomials, quadratic expressions, and factorization in 3D space. The model should display a cube with multiple copies arranged vertically along an axis, generated by translating the cube using vectors, and include several small polygonal faces that also move along the height to form the appearance of algebra tiles, suitable for educational demonstrations and student exploration.
The prompt above was compiled from the original drawing commands and is for reference only.