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GeoGebra 3D Geometry and Vector Construction Example

GeoGebra 3D Geometry and Vector Construction Example
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2018-09-01 09:39
VectorSolid GeometryGeometric Construction
This example demonstrates constructing geometric figures such as triangles, vectors, and surfaces in three-dimensional space. Key mathematical concepts include vector operations, solid geometry, and geometric construction. The construction involves using commands like Point, Segment, Line, Intersect, Vector, and Polygon, along with objects such as A, B, C, D, E, F. It is suitable for high school students or math enthusiasts to learn geometric construction and spatial visualization.

GeoGebra Commands & Parameters

  1. Point(xAxis) → A
  2. Point(yAxis) → B
  3. Segment(A, B) → f
  4. Line(B, f) → g
  5. Line(B, f) → h
  6. Intersect(xAxis, yAxis) → C
  7. Line(C, f) → i
  8. Point(i) → D
  9. Segment(E, F) → j
  10. Line(E, j) → k
  11. Vector(C, F) → u
  12. Point(k) → H
  13. Polygon(G, H, I, J) → q1, g_1, h_1, i_1, j_1
  14. Point(k) → K
  15. Polygon(K, L, I, H) → q2, k_1, l_2, i_2, h_2
  16. Polygon(L, M, J, I) → q3, l_1, m, j_2, i_3
  17. Point(yAxis) → N
  18. Vector(C, N) → v
  19. Point(i) → O
  20. Vector(C, O) → w
  21. Sequence(Translate[Element[L_1, 1], Vector[(i * v)]], i, 1, t - 1) → L_5
  22. Sequence(Translate[Element[L_2, 1], Vector[(i * v)]], i, 1, t - 1) → L_6
  23. Sequence(Translate[Element[L_4, 1], Vector[(i * u)]], i, 1, p - 1) → L_9
  24. Sequence(Translate[Element[L_3, 1], Vector[(i * w)]], i, 1, l - 1) → L_10
  25. Sequence(Translate[L_3, Vector[(v * i)]], i, 1, t - 1) → L_11
  26. Sequence(Translate[L_10, Vector[(v * i)]], i, 1, t - 1) → L_12
  27. Sequence(Translate[L_4, Vector[(v * i)]], i, 1, t - 1) → L_13

AI Drawing Prompt Reference

Draw a 3D geometric figure including triangles, vectors, and surfaces. Start by creating points A and B on the x-axis and y-axis, then form a segment f connecting A and B. Next, create two lines g and h through B and f, and create a line i through the intersection of x-axis and y-axis C, then create point D through line i. Then, create points E and F, form a segment j connecting E and F, and create a line k through E and j. Next, create vector u from C to F, then create point H through line k. Then, create three quadrilaterals q1, q2, and q3, and finally create vector v from C to N and vector w from C to O, and use v and w for translation operations to generate a series of new segments.
The prompt above was compiled from the original drawing commands and is for reference only.