MathPlotAI Logo MathPlotAI

Pyramidal Construction

Pyramidal Construction
Loading the math board and drawing, please wait…
2015-06-22 01:11
FunctionTrigonometrySolid GeometryParametric EquationGeometric Construction
This example demonstrates the deformation of a pyramid created by a single surface, involving core math concepts like solid geometry, trigonometry, function graphing, and parametric equations. It uses commands like Append, Function, CurveCartesian, Angle, Sequence, Polygon, Element, Surface in GeoGebra for construction, suitable for high school students and math enthusiasts exploring 3D graphics and dynamic transformations.

GeoGebra Commands & Parameters

  1. First({A, B, C, D, E, F, G, H, I, J, K, L}, n) → P_0
  2. Append(P_0, A) → P
  3. Function(Join[{{0, n}, Px}]) → fbx
  4. Function(Join[{{0, n}, Py}]) → fby
  5. CurveCartesian(fbx(t), fby(t), t, 0, n) → cb
  6. Angle((0, 0, 0), S, A) → α
  7. Sequence(Surface[(fbx(u) * (1 - v)) + (v * x(S)), (fby(u) * (1 - v)) + (v * y(S)), (ceil((v * m)) / m * z(S)), u, 0, U, v, ((i - 1) * V / m), (i * V / m)], i, 1, m) → liste1
  8. Sequence(CurveCartesian[(fbx(u) * (1 - v)) + (v * x(S)), (fby(u) * (1 - v)) + (v * y(S)), (ceil((v * m)) / m * z(S)), v, 0, V], u, 0, U, U / n) → liste3
  9. Sequence(CurveCartesian[(fbx(u) * (1 - v)) + (v * x(S)), (fby(u) * (1 - v)) + (v * y(S)), (ceil((v * m)) / m * z(S)), u, 0, U], v, 0, V, 1 / m) → liste2
  10. Polygon(P_0) → poly1
  11. Element({f1, f2, f3}, selec) → f
  12. Surface((((fbx(u) * (1 - v)) + (v * x(S))) * cos((w * v))) - (sin((w * v)) * ((fby(u) * (1 - v)) + (v * y(S)))), (((fbx(u) * (1 - v)) + (v * x(S))) * sin((w * v))) + (cos((w * v)) * ((fby(u) * (1 - v)) + (v * y(S)))), f(v), u, 0, U, v, 0.01, V) → d
  13. Surface((((fbx(u) * (1 - v)) + (v * x(S))) * cos((w * v))) - (sin((w * v)) * ((fby(u) * (1 - v)) + (v * y(S)))), (((fbx(u) * (1 - v)) + (v * x(S))) * sin((w * v))) + (cos((w * v)) * ((fby(u) * (1 - v)) + (v * y(S)))), f(v), u, 0, U, v, 0, V) → a
  14. Surface((((fbx(u) * (1 - v)) + (v * x(S))) * cos((w * v))) - (sin((w * v)) * ((fby(u) * (1 - v)) + (v * y(S)))), (((fbx(u) * (1 - v)) + (v * x(S))) * sin((w * v))) + (cos((w * v)) * ((fby(u) * (1 - v)) + (v * y(S)))), f(v), u, 0.03, U, v, 0, V) → b
  15. Sequence(CurveCartesian[(fbx(u) * (1 - v)) + (v * x(S)), (fby(u) * (1 - v)) + (v * y(S)), (ceil((v * m)) / m * z(S)), u, 0, U], v, 0.01, V, 1 / m) → liste4