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Unfolding Pyramids

Unfolding Pyramids
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2022-11-11 22:22
PolygonSolid GeometryGeometric Construction
Explore the geometry of pyramids by unfolding and folding their nets. Change the dimensions of the pyramid to see how the net changes and understand its geometric properties. Core concepts include nets of solids, polygons, and solid geometry. Constructed using GeoGebra commands like Point, Circle, Ray, Sequence, Polygon, OrthogonalLine, Segment, Prism, Pyramid, Net, etc. Suitable for students in grades 6-8 to learn identifying nets of prisms, pyramids, cylinders, and cones.

GeoGebra Commands & Parameters

  1. Point(yAxis) → CA
  2. Point(yAxis) → CB
  3. Circle(CA, CB) → cCil
  4. Point(cCil) → C
  5. Ray(A, (x(A), y(A), 40)) → h
  6. Point(yAxis) → B
  7. Sequence(Rotate[C, ((t * 2) * pi / n), A], t, 1, n) → vert
  8. Polygon(vert) → poly
  9. OrthogonalLine(C, xOyPlane) → f
  10. Segment(HC, (x(C), y(C), 4)) → g
  11. Point(g) → E
  12. Prism(poly, Segment[C, E]) → a, F, face3, face4, face5, face6, face2, face13, face15, faceFGHIJK, edge1, edge2, G, edge3, edge4, edge5, edge6, edge13, edge16, edgeFG, edgeGH, edgeHI, edgeIJ, H, edgeJK, edgeFK, edge14, edge17, I, J, K, L, M, face1
  13. Point(Segment[(0, 0, 0.1), (0, 0, 4)]) → CD
  14. Pyramid(poly, CD) → b, face7, edge8, edge9, edge10, edge11, edge12, edge15, edge18, face9, face10, face11, face12, face8, face14, face16, edge7
  15. Net(a, (-open)) → prismNet, N, W, Z, A_1, B_1, C_1, D_1, E_1, F_1, G_1, H_1, O, I_1, J_1, K_1, L_1, M_1, N_1, O_1, P_1, Q_1, R_1, P, S_1, face17, face18, face19, face20, face21, face22, face23, face24, face34, Q, face35, edge19, edge20, edge21, edge22, edge23, edge24, edge25, edge26, edge27, R, edge28, edge29, edge30, edge31, edge32, edge33, edge34, edge35, edge36, edge37, S, edge38, edge39, edge40, edge41, edge42, edge43, edge44, edge45, edge70, edge71, T, edge72, edge73, edge74, edge75, edge76, edge77, edge78, edge79, edge80, edge81, U, V
  16. Net(b, (-open)) → pyrNet, T_1, E_2, F_2, G_2, H_2, I_2, J_2, K_2, face25, face26, face27, U_1, face28, face29, face30, face31, face32, face33, edge46, edge47, edge48, edge49, V_1, edge50, edge51, edge52, edge53, edge54, edge55, edge56, edge57, edge58, edge59, W_1, edge60, edge61, edge62, edge63, edge64, edge65, edge66, edge67, edge68, edge69, Z_1, A_2, B_2, C_2, D_2
  17. Random(3, 8) → nRand
  18. Circle(CA, CB) → d
  19. Cylinder(cCil, 3) → bCil, eCil, fCil
  20. Line(CC, xAxis) → aCil
  21. OrthogonalLine(CD, xOyPlane) → gCil
  22. Circle(gCil, CC) → kCil
  23. Rotate(Rotate[eCil, ϕCil, aCil], ϕCil, xAxis) → eeCil
  24. Rotate(Rotate[eCil, ϕCil, aCil], ϕCil, xAxis) → dCil
  25. Circle(CA, CB) → hCil
  26. If(abs(tCil) < 1, ((rCil * sin((-θCil))), ((rCil * (1 - cos((-θCil)))) * cos(ϕCil)) - (3 * sin(ϕCil)), (3 * cos(ϕCil)) + ((rCil * (1 - cos((-θCil)))) * sin(ϕCil))), ((-pi), (-3 * sin(ϕCil)), (3 * cos(ϕCil)))) → CE
  27. If(abs(tCil) < 1, ((rCil * sin(θCil)), ((rCil * (1 - cos(θCil))) * cos(ϕCil)) - (3 * sin(ϕCil)), (3 * cos(ϕCil)) + ((rCil * (1 - cos(θCil))) * sin(ϕCil))), (pi, (-3 * sin(ϕCil)), (3 * cos(ϕCil)))) → CF
  28. If(abs(tCil) < 1, ((rCil * sin((-θCil))), ((rCil * (1 - cos((-θCil)))) * cos(ϕCil)), ((rCil * (1 - cos((-θCil)))) * sin(ϕCil))), ((-pi), 0, 0)) → CG
  29. If(abs(tCil) < 1, ((rCil * sin(θCil)), ((rCil * (1 - cos(θCil))) * cos(ϕCil)), ((rCil * (1 - cos(θCil))) * sin(ϕCil))), (pi, 0, 0)) → CH
  30. Segment(CE, CG) → mCil
  31. Segment(CF, CH) → nCil
  32. Line((0, 1, 0), zAxis) → pCil
  33. Circle(pCil, CB) → qCil
  34. Circle(pCil, CB) → sCil
  35. OrthogonalLine((1, 0, 0), xOyPlane) → aCon
  36. Circle(aCon, (0, 0, 0)) → cCon
  37. Point(aCon) → KA
  38. Intersect(xAxis, aCon) → KB
  39. Cone(KB, KA, 1) → bCon, dCon, eCon
  40. Intersect(yAxis, xAxis) → KC
  41. Segment(KC, KA) → lCon
  42. Distance(KB, KC) → rCon
  43. Angle(KA, KC, KB) → α
  44. Rotate(KA, (abs(tCil) * α), yAxis) → KAA
  45. OrthogonalLine(KAA, xOyPlane) → fCon
  46. Intersect(fCon, xOyPlane) → KBB
  47. Rotate(KC, bet / 2, fCon) → KCC
  48. Rotate(KC, ((-bet)) / 2, fCon) → KCR
  49. CircumcircleArc(KCC, KC, KCR) → gCon
  50. Distance(KAA, KBB) → hCon
  51. Distance(KBB, KCC) → rcCon
  52. Surface(((kCon - ((v * rcCon) * cos((u * bet / 2)))) * cos(ϕCon)) - (((1 - v) * hCon) * sin(ϕCon)), ((v * rcCon) * sin((u * bet / 2))), (((1 - v) * hCon) * cos(ϕCon)) + ((kCon - ((v * rcCon) * cos((u * bet / 2)))) * sin(ϕCon)), u, -1, 1, v, 0, 1) → jCon
  53. CurveCartesian(((kCon - (rcCon * cos((u * bet / 2)))) * cos(ϕCon)), (rcCon * sin((u * bet / 2))), ((kCon - (rcCon * cos((u * bet / 2)))) * sin(ϕCon)), u, -1, 1) → mCon
  54. Segment(KE, KF) → nCon
  55. Segment(KD, KF) → pCon
  56. If(abs(tCil) < 1, CurveCartesian[(rCil * sin((u * θCil))), ((rCil * (1 - cos((u * θCil)))) * cos(ϕCil)) - (3 * sin(ϕCil)), (3 * cos(ϕCil)) + ((rCil * (1 - cos((u * θCil)))) * sin(ϕCil)), u, -1, 1], CurveCartesian[(pi * u), (-3 * sin(ϕCil)), (3 * cos(ϕCil)), u, -1, 1]) → jCil
  57. If(abs(tCil) < 1, CurveCartesian[(rCil * sin((u * θCil))), ((rCil * (1 - cos((u * θCil)))) * cos(ϕCil)), ((rCil * (1 - cos((u * θCil)))) * sin(ϕCil)), u, -1, 1], CurveCartesian[(pi * u), 0, 0, u, -1, 1]) → lCil
  58. If(abs(tCil) < 1, Surface[(rCil * sin((u * θCil))), ((rCil * (1 - cos((u * θCil)))) * cos(ϕCil)) - (v * sin(ϕCil)), (v * cos(ϕCil)) + ((rCil * (1 - cos((u * θCil)))) * sin(ϕCil)), u, -1, 1, v, 0, 3], Surface[(pi * u), ((-v) * sin(ϕCil)), (v * cos(ϕCil)), u, -1, 1, v, 0, 3]) → iCil
  59. Sequence((6, 7) + (t / 5 * ((9, 7) - (6, 7))), t, 0, 5) → fakeCursorGrid
  60. Element(fakeCursorGrid, n - 2) → PSLI

AI Drawing Prompt Reference

Draw the net of a square pyramid. Start by creating a square base and a vertex, then use rotation and unfolding to generate the net. Make sure the four edges of the base and the lines connecting them to the vertex are correctly connected to form a complete net.
The prompt above was compiled from the original drawing commands and is for reference only.