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Move Points!

Move Points!
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2016-09-19 17:43
FunctionCoordinate GeometryGeometric Construction
This example demonstrates how to explore spatial relationships by moving points. Key mathematical concepts include geometric transformations and functions. Using GeoGebra commands such as PointIn, Polygon, and FitPoly, students can intuitively understand the concepts of geometric transformations and functions. Suitable for middle school and above students for geometric construction and exploration.

GeoGebra Commands & Parameters

  1. PointIn(i) → A
  2. PointIn(b) → I
  3. PointIn(a) → E
  4. Polygon((x(E), y(E)), (x(A), y(A)), (x(I), y(I)), (x(E), y(I))) → Polígon1, p, q, r, f_1
  5. PointIn(a) → B
  6. PointIn(a) → C
  7. PointIn(a) → D
  8. PointIn(b) → F
  9. PointIn(b) → G
  10. PointIn(b) → H
  11. FitPoly({(y(A), z(A)), (y(F), z(F)), (y(G), z(G)), (y(H), z(H)), (y(I), z(I))}, 4) → f
  12. FitPoly({(x(A), z(A)), (x(B), z(B)), (x(C), z(C)), (x(D), z(D)), (x(E), z(E))}, 4) → g
  13. CurveCartesian(x(A), t, f(t), t, y(A), y(I)) → c
  14. CurveCartesian(t, y(A), g(t), t, x(E), x(A)) → d
  15. Surface(u, v, g(u) + f(v), u, x(E), x(A), v, y(A), y(I)) → e
  16. OrthogonalLine(E, xOyPlane) → j
  17. OrthogonalLine(I, xOyPlane) → k
  18. Intersect(j, xOyPlane) → J
  19. Intersect(k, xOyPlane) → K
  20. Surface(t + x(M) - x(L), s + y(M) - y(L), g(t) + f(s), t, x(E), x(A), s, y(A), y(I)) → l
  21. Surface((2 * x(A)) - u, v, g(u) + f(v), u, x(E), x(A), v, y(A), y(I)) → e_x
  22. Surface(u, (2 * y(A)) - v, g(u) + f(v), u, x(E), x(A), v, y(A), y(I)) → e_y
  23. Sequence(Sequence[Surface[u + ((2 * k) * s), v + ((2 * l) * t), g(u) + f(v), u, x(E), x(A), v, y(A), y(I)], k, -2, 2], l, -2, 2) → l1
  24. Sequence(Sequence[Surface[(2 * x(A)) - u + ((2 * k) * s), v + ((2 * l) * t), g(u) + f(v), u, x(E), x(A), v, y(A), y(I)], k, -2, 2], l, -2, 2) → l2
  25. Sequence(Sequence[Surface[u + ((2 * l) * s), (2 * y(A)) - v + ((2 * k) * t), g(u) + f(v), u, x(E), x(A), v, y(A), y(I)], k, -2, 2], l, -2, 2) → l3
  26. Surface((2 * x(A)) - u, (2 * y(A)) - v, g(u) + f(v), u, x(E), x(A), v, y(A), y(I)) → e_{xy}
  27. Sequence(Sequence[Surface[(2 * x(A)) - u + ((2 * l) * s), (2 * y(A)) - v + ((2 * k) * t), g(u) + f(v), u, x(E), x(A), v, y(A), y(I)], k, -2, 2], l, -2, 2) → l4
  28. PointIn(Polígon1) → PP
  29. Sequence(Sequence[((2 * x(A)) - x(PP) + ((2 * k) * s), y(PP) + ((2 * l) * t), g(x(PP)) + f(y(PP))), k, -2, 2], l, -2, 2) → lp2
  30. Sequence(Sequence[(x(PP) + ((2 * l) * s), (2 * y(A)) - y(PP) + ((2 * k) * t), g(x(PP)) + f(y(PP))), k, -2, 2], l, -2, 2) → lp3
  31. Sequence(Sequence[((2 * x(A)) - x(PP) + ((2 * l) * s), (2 * y(A)) - y(PP) + ((2 * k) * t), g(x(PP)) + f(y(PP))), k, -2, 2], l, -2, 2) → lp4
  32. Sequence(Sequence[(x(PP) + ((2 * k) * s), y(PP) + ((2 * l) * t), g(x(PP)) + f(y(PP))), k, -2, 2], l, -2, 2) → lp1

AI Drawing Prompt Reference

Draw a polygon using points A, B, C, D, E, F, G, H, and I, then fit polynomial functions f and g through these points. Next, draw curves c and d starting from points E and I respectively. Finally, draw surface e using points E and I, and create a series of surfaces l1 to l4 around these points.
The prompt above was compiled from the original drawing commands and is for reference only.