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Pyramid and Midpoint Construction

Pyramid and Midpoint Construction
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2019-01-25 22:40
CirclePolygonCoordinate GeometrySolid GeometryGeometric Construction
In collections Polyeder, whose coordinates are golden numbers
This example demonstrates how to construct geometric figures related to pyramids using basic elements such as midpoints, circles, polygons, and line segments. The core mathematical concepts involved include midpoint, circle, polygon, rhombus, logarithm, set theory, and cube. The construction highlights the use of GeoGebra commands/objects like Midpoint, Circle, Polygon, and Segment. Suitable for high school and above learners to understand geometric constructions and spatial geometric relationships.

GeoGebra Commands & Parameters

  1. Midpoint(P_2, P_3) → M_{23}
  2. Midpoint(P_0, P_1) → M_{01}
  3. Circle((0, 0), r) → c
  4. Polygon(P_0, I_{01}, P_4) → D_1, f, g, h_1
  5. Polygon(I_{01}, P_1, P_4) → D_2, p_4, p_{51}, p_1
  6. Midpoint(P_1, P_2) → M_{12}
  7. Midpoint(P_3, P_0) → M_{03}
  8. Polygon(I_1, P_1, P_4) → D_3, i, p_{61}, j
  9. Polygon(I_1, P_2, P_4) → D_4, k, l, p_2
  10. Polygon(P_2, I_{23}, P_4) → D_5, m, n, p_{71}
  11. Segment(P_0, P_4) → s
  12. Polygon(I_{23}, P_3, P_4) → D_6, p, q, p_3
  13. Polygon(P_3, I_{12}, P_4) → D_7, t, a_1, p_{81}
  14. Polygon(I_{12}, P_0, P_4) → D_8, b, d, p_0
  15. Segment(O, P_4) → hh
  16. Segment(P_0, P_3) → aa