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Dynamic Drawing of Prism Nets

Dynamic Drawing of Prism Nets
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2017-03-26 09:27
PolygonTrigonometrySolid GeometryTransformationSlider Animation
This example demonstrates how to dynamically draw the nets (unfolded surfaces) of prisms, such as triangular prisms, using GeoGebra, transforming 3D solids into 2D polygon arrangements. The core mathematical concepts involve solid geometry (prism structure, surface nets) and plane geometry (polygons, segments, equilateral triangles). Construction highlights: commands like Sequence, Element, Polygon, and Segment are used to build prism vertices and faces; rotation matrices (R_x, R_y, R_z) and trigonometric functions (sin, cos) control 3D rotations; sliders (α, β) enable dynamic viewpoint changes; lists (listepoints) and point objects (A, E, C_1, D, etc.) define the unfolded planar shapes. Suitable for high school or early college students to understand the correspondence between 3D solids and their 2D nets, and as a visual teaching aid in mathematics.

GeoGebra Commands & Parameters

  1. Sequence((Mat * Element[cube, k]), k, 1, 8) → cube'
  2. Element(Element[AE, 3], 1) → droite
  3. Sequence(I + (Element[cube', k, 1, 1], Element[cube', k, 2, 1]), k, 1, 8) → listepoints
  4. Element(listepoints, 2) → A
  5. Element(listepoints, 1) → E
  6. Element(listepoints, 4) → C_1
  7. Element(listepoints, 3) → D
  8. Polygon(A, E, C_1, D) → poly1, a_1, b, c_1, d
  9. Element(listepoints, 6) → B
  10. Element(listepoints, 7) → F
  11. Element(listepoints, 8) → G
  12. Element(listepoints, 5) → H
  13. Polygon(B, F, G, H) → poly2, e, f, g, h
  14. Element(listepoints, 3) → C
  15. Polygon(F, C, A, B) → poly3, f_1, i, a_2, b_1
  16. Element(AB, 3, 1) → avant
  17. Polygon(C_1, G, H, E) → poly4, c_2, g_1, h_1, e_1
  18. Element(AC, 3, 1) → dessus
  19. Polygon(F, C, C_1, G) → poly5, f_2, c_3, c_4, g_2
  20. Polygon(A, B, H, E) → poly6, a_3, b_2, h_2, e_2
  21. Segment(E, A) → c
  22. Segment(A, C) → j
  23. Segment(A, B) → k
  24. Segment(C, C_1) → l
  25. Segment(C_1, E) → m
  26. Segment(A, B) → p
  27. Segment(B, H) → q
  28. Segment(H, E) → r
  29. Segment(H, G) → s
  30. Segment(B, F) → t
  31. Segment(G, C_1) → d_1
  32. Segment(F, G) → i_1
  33. Segment(F, C) → j_1
  34. Polygon(A, B, F', D') → poly7, a_4, b_3, f', d'
  35. Polygon(E, A, D'', C') → poly8, e_3, a_5, d'', c'
  36. Polygon(B, F'', G', H) → poly9, b_4, f'', g', h_3
  37. Polygon(H, G'', C''', E) → poly10, h_4, g'', c''', e_4
  38. Polygon(A_2, B_2, G'', C''') → poly11, a_6, b_5, g''_1, c'''_1