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Simple 3D Problems 2

Simple 3D Problems 2
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2014-08-18 10:00
VectorTrigonometrySolid GeometryGeometric Construction
In collections Graphs of power functions 2 Graphs of power functions
This example demonstrates the geometric construction and property analysis of a 3D shape combining a cube and a trapezoid in three-dimensional space. It involves core mathematical concepts such as trigonometry, quadratic functions, 3D vectors, translation, and solid geometry. The construction utilizes GeoGebra commands and objects like Circle, Point, Segment, Angle, Line, Polygon, PointIn, Intersect, Midpoint, Mirror, Vector, and Translate, as detailed in the construction summary. It is suitable for high school and above students learning about solid geometry, vectors, and transformations.

GeoGebra Commands & Parameters

  1. Circle(O, Radius) → axiscircle
  2. Point(axiscircle) → X
  3. Segment(O, X) → OY
  4. Point(axiscircle) → Z
  5. Angle(X, O, Z) → α
  6. Segment(O, Z) → OZ
  7. Point(axiscircle) → Y
  8. Segment(O, Y) → OX
  9. Line(A, OY) → CParallelCB
  10. Point(CParallelCB) → edgeXPt
  11. Segment(A, edgeXPt) → edgeX
  12. Line(A, OZ) → yaxis
  13. Point(yaxis) → edgeYPt
  14. Polygon(edgeYPt, A, edgeXPt) → MaxBase, MaxBaseEdge2, MaxBaseEdge1, MaxBaseEdge3
  15. PointIn(MaxBase) → D
  16. Line(A, D) → MaxBaseDivider
  17. Intersect(MaxBaseEdge3, MaxBaseDivider) → MaxBaseDividerPt
  18. Polygon(MaxBaseDividerPt, A, edgeXPt) → MaxBaseLowerHalf, MaxBaseLowerHalfEdge2, MaxBaseLowerHalfEdge1, MaxBaseLowerHalfEdge3
  19. PointIn(MaxBaseLowerHalf) → B
  20. Line(B, OZ) → BParallelZ
  21. Intersect(BParallelZ, edgeX) → B_X
  22. Line(B, OY) → BParallelX
  23. Midpoint(B, D) → MidPointBD
  24. Mirror(A, MidPointBD) → C
  25. Polygon(A, B, C, D) → Base, AB, BD, CD, AC
  26. PointIn(Base) → K
  27. Line(K, OX) → VerticalFromBase
  28. Point(VerticalFromBase) → VerticalFromBasePt
  29. Segment(K, VerticalFromBasePt) → MaxHeight
  30. Point(MaxHeight) → E
  31. Line(K, OZ) → KParallelZ
  32. Intersect(KParallelZ, BParallelX) → K_X
  33. Line(K, OY) → KParallelX
  34. Segment(A, edgeYPt) → edgeY
  35. Intersect(BParallelX, edgeY) → B_Z
  36. Intersect(KParallelX, edgeY) → K_Z
  37. Circle(B_S, LengthEB / Scale) → CircleAtB_S
  38. Circle(A_S, LengthEA / Scale) → CircleAtA_S
  39. Line(D, OZ) → CParallelZ
  40. Intersect(CParallelZ, edgeX) → C_X
  41. Line(D, OY) → CParallelX
  42. Intersect(CParallelX, edgeY) → C_Z
  43. Line(C, OZ) → DParallelZ
  44. Intersect(DParallelZ, CParallelCB) → D_X
  45. Line(C, OY) → DParallelX
  46. Intersect(DParallelX, yaxis) → D_Z
  47. Circle(A_P, LengthEA / Scale) → CircleAtA_P
  48. Circle(D_P, LengthEC / Scale) → CircleAtC_P
  49. Circle(B_R, LengthEB / Scale) → CircleAtB_R
  50. Point(OX) → RightAngleDistance
  51. Vector(O, RightAngleDistance) → u
  52. Translate(K, u) → DKA3
  53. Line(A, OX) → zaxis
  54. Point(zaxis) → edgeZPt
  55. Segment(A, edgeZPt) → edgeZ
  56. Segment(K, E) → KD
  57. Segment(A, E) → DA
  58. Segment(E, D) → DC
  59. Segment(E, B) → DB
  60. Segment(B_R, C_R) → BC_Q
  61. Circle(C_R, LengthED / Scale) → CircleAtD_R
  62. Intersect(CircleAtB_R, CircleAtD_R) → E_R, D_{Q'}, ,
  63. Segment(C_R, E_R) → DC_Q
  64. Segment(E_R, B_R) → DB_Q
  65. Intersect(CircleAtA_S, CircleAtB_S) → E_S, T_{R'}, ,
  66. Segment(E_S, A_S) → AC_R
  67. Segment(A_S, B_S) → AB_R
  68. Segment(B_S, E_S) → BC_R
  69. Circle(K, KVertical) → CircleAtK
  70. Circle(B, BAnglePoint1) → CircleAtB
  71. Circle(D, 0.5) → CircleAtC
  72. Circle(A, 0.5) → CircleAtA
  73. Intersect(CircleAtC_P, CircleAtA_P) → E_P, D_{P'}, ,
  74. Segment(E_P, A_P) → DA_P
  75. Segment(E_P, D_P) → DC_P
  76. Segment(A_P, D_P) → AC_P
  77. Midpoint(A, D) → MidPointAD
  78. Midpoint(A_S, E_S) → MidPointEA_S
  79. Midpoint(A, B) → MidPointAB
  80. Midpoint(A_S, B_S) → MidPointAB_S
  81. Midpoint(B_S, E_S) → MidPointEB_S
  82. Midpoint(E_R, C_R) → MidPointEC_R
  83. Midpoint(E, D) → MidPointED
  84. Midpoint(E, B) → MidPointEB
  85. Midpoint(B_R, C_R) → MidPointBC_R
  86. Midpoint(B_R, E_R) → MidPointEB_R
  87. Midpoint(E, K) → MidPointEK
  88. Midpoint(A, E) → MidPointEA
  89. Midpoint(A_P, D_P) → MidPointAD_P
  90. Midpoint(E_P, A_P) → MidPointAE_P
  91. Midpoint(E_P, D_P) → MidPointDE_P
  92. Angle(E_P, A_P, D_P) → DAC_P
  93. Angle(A_P, D_P, E_P) → DCA_P
  94. Angle(E_R, C_R, B_R) → DCB_Q
  95. Angle(C_R, B_R, E_R) → DBC_Q
  96. Segment(C, E) → ED
  97. Angle(B_S, A_S, E_S) → TAB_R
  98. Angle(E_S, B_S, A_S) → TBA_R
  99. Segment(A_T, K_T) → AK_S
  100. Segment(K_T, E_T) → TK_S
  101. Segment(E_T, A_T) → TA_S
  102. Angle(E_T, K_T, A_T) → TKA_S
  103. Circle(D_Q, LengthED / Scale) → CircleAtD_Q
  104. Circle(C_Q, LengthEC / Scale) → CircleAtC_Q
  105. Intersect(CircleAtD_Q, CircleAtC_Q) → E_1, E_Q, ,
  106. Segment(C_Q, D_Q) → CD_Q
  107. Segment(D_Q, E_Q) → TD_Q
  108. Segment(E_Q, C_Q) → TC_Q
  109. Angle(E_Q, D_Q, C_Q) → TDC_Q
  110. Angle(D_Q, C_Q, E_Q) → TCD_Q
  111. Midpoint(E, C) → MidPointEC
  112. Midpoint(B, C) → MidPointBC
  113. Midpoint(E_Q, D_Q) → MidPointED_Q
  114. Midpoint(C_Q, D_Q) → MidPointCD_Q
  115. Midpoint(E_Q, C_Q) → MidPointEC_Q
  116. Midpoint(C, D) → MidPointCD
  117. Segment(A, K) → AK
  118. Midpoint(A, K) → MidPointAK
  119. Midpoint(E_T, K_T) → MidPointEK_T
  120. Midpoint(A_T, K_T) → MidPointAK_T
  121. Midpoint(E_T, A_T) → MidPointEA_T
  122. Intersect(CircleAtK, KD) → EKA_1,
  123. Intersect(CircleAtK, AK) → EKA_2,
  124. Line(EKA_2, KD) → ParallelEK
  125. Line(EKA_1, AK) → ParallelAK
  126. Intersect(ParallelAK, ParallelEK) → EKA_3
  127. Segment(EKA_2, EKA_3) → EKA_{L1}
  128. Segment(EKA_3, EKA_1) → EKA_{L2}
  129. Midpoint(A, C) → MidPointAC

AI Drawing Prompt Reference

Draw a 3D shape combining a cube and a trapezoid, showing its construction and properties. Start by drawing a circle and marking points on it, then connect these points to the center to form line segments. Use these segments and points to construct angles, and based on this, draw parallel lines and triangles. Next, create new points and polygons using midpoints and mirror operations, finally forming the combined shape of the cube and trapezoid, with key points and lines labeled.
The prompt above was compiled from the original drawing commands and is for reference only.