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正方锥体解剖

正方锥体解剖
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2017-08-09 08:24
三角函数解析几何立体几何几何作图
所属专题 GeoGebra 3D & AR: Geometry Resources & Challenges
本范例演示正方锥体的几何构造与基本属性。涉及的核心数学概念包括周长、立体几何、直角三角形、正方形、算术运算、二次方程、中位数、几何平均数。作图要点提炼自GeoGebra命令：交集、点、点在、锥体、射线、线段、中点、多边形、角、垂线；对象包括a, A, B, C, D, E, c, F, b, faceACBD_1, faceADF, faceACF, faceBCF, faceBDF, edgeAD_1, edgeAC_1, edgeBC_1, edgeBD_1, edgeDF, edgeAF, edgeCF, edgeBF, G, H, f, I, J, K, d, faceACBD, faceACK, faceBCK, faceBDK, faceADK, edgeAC, edgeBC, edgeBD, edgeAD, edgeAK, edgeCK。适合高中阶段学生或数学爱好者用于探索和理解立体几何构造。

GeoGebra 命令及参数

  1. Intersect(yAxis, xAxis) → D
  2. Point(zAxis) → E
  3. PointIn(c) → F
  4. Pyramid(D, A, C, B, F) → b, faceACBD_1, edgeDF, edgeAF, edgeCF, edgeBF, faceADF, faceACF, faceBCF, faceBDF, edgeAD_1, edgeAC_1, edgeBC_1, edgeBD_1
  5. Ray(G, H) → f
  6. Point(f) → I
  7. Point(edgeCF) → J
  8. Intersect(c, f) → K
  9. Pyramid(A, C, B, D, K) → d, faceACBD, edgeAK, edgeCK, edgeBK, edgeDK, faceACK, faceBCK, faceBDK, faceADK, edgeAC, edgeBC, edgeBD, edgeAD
  10. Segment(G, K) → h
  11. Midpoint(edgeBC) → M
  12. Segment(G, M) → j
  13. Segment(M, K) → k
  14. Polygon(G, M, K) → poly1, k_1, g, m
  15. Angle(M, G, K) → α
  16. OrthogonalLine(F, e) → i
  17. Intersect(i, e) → L
  18. Segment(F, L) → l
  19. Angle(F, L, A) → β
  20. Polygon(K, G, M) → poly2, m_1, k_2, g_1