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Opening Boxes - Pyramids - Exploration

Opening Boxes - Pyramids - Exploration
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2022-10-18 16:30
TriangleSolid GeometryGeometric Construction
This example explores the nets of pyramids. Key mathematical concepts include solid geometry and geometric construction. Using GeoGebra commands such as PointIn, Polygon, Circle, etc., the net of a pyramid can be constructed. Suitable for middle school and above students to learn about the properties and nets of pyramids.

GeoGebra Commands & Parameters

  1. PointIn(xOyPlane) → A
  2. PointIn(xOyPlane) → B
  3. Polygon(A, B, 4, xOyPlane) → squa, segmAB, g, h, i, C, D
  4. Circle(Midpoint[A, B], (0.5 * Segment[A, B]), xOyPlane) → c
  5. Point(c) → E
  6. Polygon(A, B, E) → rightTri, e, a_1, b
  7. OrthogonalLine(Midpoint[A, B], segmAB, xOyPlane) → f
  8. Point(f) → P
  9. Polygon(A, B, P) → isoTri, p, a_2, b_1
  10. PointIn(xOyPlane) → F
  11. OrthogonalLine(F, Segment[A, F], xOyPlane) → j
  12. Point(j) → G
  13. OrthogonalLine(G, j, xOyPlane) → k
  14. OrthogonalLine(A, Segment[A, F], xOyPlane) → l
  15. Intersect(k, l) → H
  16. Polygon(A, F, G, H) → rect, a_3, f_1, g_1, h_1
  17. SelectedIndex(baseMenu) → is
  18. TriangleCenter(A, B, E, 1) → U_2
  19. OrthogonalLine(U_2, rightTri) → n
  20. Point(n) → V_2
  21. Pyramid(rightTri, V_2) → rightPir, face22, face24, face23, edge63, edge64, edge65
  22. TriangleCenter(A, B, P, 1) → I
  23. OrthogonalLine(I, isoTri) → q
  24. Point(q) → J
  25. Pyramid(isoTri, J) → isoPir, faceABJ, faceBJP, faceAJP, edgeAJ, edgeBJ, edgeJP
  26. Polygon(A, B, 4, xOyPlane) → poly1, r, s, t, a, K, L
  27. Segment(A, K) → d
  28. Segment(L, B) → i_1
  29. Intersect(d, i_1) → M
  30. OrthogonalLine(M, squa) → j_1
  31. Point(j_1) → N
  32. Pyramid(squa, N) → squaPir, faceABN, faceBCN, faceCDN, faceADN, edgeAN, edgeBN, edgeCN, edgeDN
  33. Midpoint(A, G) → O
  34. OrthogonalLine(O, rect) → k_1
  35. Point(k_1) → Q
  36. Pyramid(rect, Q) → rectPir, faceAFQ, faceFGQ, faceGHQ, faceAHQ, edgeAQ, edgeFQ, edgeGQ, edgeHQ
  37. Net(isoPir, open) → isoNet, R, faceRTW, edgeRS, edgeST, edgeRT, edgeRU, edgeSU, edgeSV, edgeTV, edgeTW, edgeRW, S, T, U, V, W, faceRST, faceRSU, faceSTV
  38. Net(rightPir, open) → rightNet, C_1, face3, edge1, edge5, edge2, edge3, edge6, edge7, edge8, edge9, edge4, D_1, E_1, F_1, G_1, H_1, face1, face2, face4
  39. Net(squaPir, open) → squaNet, C_2, face5, face7, face8, face6, edge10, edge14, edge17, edge11, edge12, edge15, D_2, edge16, edge18, edge19, edge20, edge21, edge13, E_2, F_2, G_2, H_2, I_2, J_2, face9
  40. Net(rectPir, open) → rectNet, O_2, face10, face12, face13, face11, edge22, edge26, edge29, edge23, edge24, edge27, P_2, edge28, edge30, edge31, edge32, edge33, edge25, Q_2, R_2, S_2, T_2, W_2, Z_2, face14
  41. Angle(B, E, A) → α

AI Drawing Prompt Reference

Draw an unfolded pyramid net, consisting of four triangles and four rectangles. Start with a square, then split it diagonally into two triangles, and extend each triangle upward to form the pyramid's sides. Ensure the drawing is clear and simple, suitable for educational purposes.
The prompt above was compiled from the original drawing commands and is for reference only.