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Cornucopia in Geometry

Cornucopia in Geometry
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2020-06-14 00:27
FunctionSolid GeometryGeometric Construction
This example demonstrates the Cornucopia shape in geometry. It involves key concepts such as geometry, surface, and differential equations. Using GeoGebra commands like Surface, Sequence, Cone, etc., complex geometric shapes can be constructed. Suitable for high school and above students or teachers.

GeoGebra Commands & Parameters

  1. Surface(x(A) + ((a * (1 + sin(i) + (r(i) * cos(j)))) * cos(i)), y(A) + ((b + (r(i) * cos(j))) * sin(i)), z(A) + (r(i) * sin(j)), i, 0.5, 3.092, j, 0, t) → d
  2. Sequence(CurveCartesian[x(A) + ((a * (1 + sin(i) + (r(i) * cos(j)))) * cos(i)), y(A) + ((b + (r(i) * cos(j))) * sin(i)), z(A) + (r(i) * sin(j)), j, 0, t], i, 0.5, h, h / 10) → liste3
  3. Sequence(CurveCartesian[x(A) + ((a * (1 + sin(i) + (r(i) * cos(j)))) * cos(i)), y(A) + ((b + (r(i) * cos(j))) * sin(i)), z(A) + (r(i) * sin(j)), i, 0.5, 3.092], j, 0, t, t / n) → liste1
  4. Cone(H, H + (-0.02, -0.21, 0), 0.055) → e, p, i
  5. Vector(H, H + (0.07, -0.3, 0)) → u
  6. Join(Sequence[Sequence[(x(A) + ((a * (1 + sin(i) + (r(i) * cos(j)))) * cos(i)), y(A) + ((b + (r(i) * cos(j))) * sin(i)), z(A) + (r(i) * sin(j))), i, 0.5, 0.5], j, 0, t, t / n]) → liste2
  7. Sequence(Segment[I, Element[liste2, i]], i, 1, Length[liste2]) → liste4
  8. Sphere(J, 0.3) → j
  9. Point(Circle[P, Distance[O, P], Segment[O, P]]) → Q
  10. Cube(O, P, Q) → m, S, faceQSWV, faceTUVW, arêteOS, arêteOP, arêtePQ, arêteQS, arêteOT, arêteSW, arêteTW, arêteTU, T, arêtePU, arêteUV, arêteQV, arêteVW, U, V, W, faceOPQS, faceOSWT, faceOPUT, facePQVU
  11. Polygon(N, A_1, Z) → poly1, z_1, n_1, a_1
  12. Midpoint(n_1) → K
  13. Midpoint(N, K) → L
  14. Pyramid(A_1, Z, N, M) → l, face1, arêteMN, face3, faceMNZ, face2, arête2, arêteNZ, arête1, arête3, arêteMZ
  15. Cylinder(D_1, C_1, 0.2) → o, q, s, v
  16. Cone(E_1, F_1, 0.2) → w, c_1, b_1
  17. Plane(J_1, I_1, K_1) → p_1
  18. PointIn(p_1) → G_1
  19. PointIn(p_1) → H_1
  20. Conic(G_1, H_1, J_1, I_1, K_1) → d_1