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Prism Nets Exploration

Prism Nets Exploration
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2022-10-18 16:18
Solid GeometryGeometric Construction
This example demonstrates the exploration of prism nets and their folding into 3D shapes. Core math concepts include prisms, line segments, quadratic equations, inequalities, percentages, and Poisson distribution. It is constructed using GeoGebra commands like PointIn, Polygon, Circle, Point, OrthogonalLine, Intersect, Segment, Prism, Net, SelectedIndex, making it suitable for high school students and math enthusiasts studying solid geometry.

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. OrthogonalLine(A, squa) → m
  18. Point(m) → I
  19. Segment(A, I) → hei
  20. Prism(squa, I) → squaPri, J, edgeBJ, edgeCK, edgeDL, edgeIJ, edgeJK, edgeKL, edgeIL, K, L, faceABJI, faceBCKJ, faceCDLK, faceADLI, faceIJKL, edgeAI_{1}
  21. Prism(rect, I) → rectPri, M, edgeFM, edgeGN, edgeHO, edgeIM, edgeMN, edgeNO, edgeIO, N, O, faceAFMI, faceFGNM, faceGHON, faceAHOI, faceIMNO, edgeAI_{2}
  22. Prism(isoTri, I) → isoPri, Q, edgeIQ, edgeQR, edgeIR, R, faceABQI, faceBPRQ, faceAIRP, faceIQR, edgeAI_{3}, edgeBQ, edgePR
  23. Prism(rightTri, I) → rightPri, S, edgeIS, edgeST, edgeIT, T, faceABSI, faceBETS, faceAETI, faceIST, edgeAI, edgeBS, edgeET
  24. Net(isoPri, open) → isoNet, U, F_1, faceUVW, face2, face4, face3, face1, edgeUV, edgeVW, edgeUW, edgeUZ, V, edge6, edge2, edge3, edge9, edge4, edge5, edge10, edge1, edge8, edge7, W, Z, A_1, B_1, C_1, D_1, E_1
  25. Net(rectPri, open) → rectNet, G_1, P_1, Q_1, R_1, S_1, T_1, face5, face6, face8, face9, face7, H_1, face10, edge11, edge15, edge18, edge12, edge13, edge23, edge16, edge17, edge26, I_1, edge19, edge20, edge27, edge21, edge22, edge28, edge14, edge25, edge29, edge24, J_1, K_1, L_1, M_1, N_1, O_1
  26. Net(rightPri, open) → rightNet, U_1, F_2, face11, face13, face15, face14, face12, edge30, edge34, edge31, edge32, V_1, edge39, edge35, edge36, edge42, edge37, edge38, edge43, edge33, edge41, edge40, W_1, Z_1, A_2, B_2, C_2, D_2, E_2
  27. Net(squaPri, open) → squaNet, G_2, P_2, Q_2, R_2, S_2, T_2, face16, face17, face19, face20, face18, H_2, face21, edge44, edge48, edge51, edge45, edge46, edge56, edge49, edge50, edge59, I_2, edge52, edge53, edge60, edge54, edge55, edge61, edge47, edge58, edge62, edge57, J_2, K_2, L_2, M_2, N_2, O_2
  28. SelectedIndex(baseMenu) → is

AI Drawing Prompt Reference

Draw a rectangular prism with a square base, four rectangular side faces, and two square bases. Start by drawing a square, then draw a vertical line from one of its vertices, which will be the height of the prism. Next, draw four rectangular faces using the endpoints of this line as the bases, connecting the square's vertices to the endpoints of the line. Finally, draw two square bases at the ends of the prism.
The prompt above was compiled from the original drawing commands and is for reference only.