MathPlotAI Logo MathPlotAI

Scutoides Geometric Construction

Scutoides Geometric Construction
Loading the math board and drawing, please wait…
2018-07-31 12:07
Coordinate GeometrySolid GeometryCalculusGeometric Construction
In collections From POST-IT to 3D PRINTING: playing with squares and cubes
This example demonstrates the construction and properties of a novel geometric shape, the Scutoides. It involves core mathematical concepts such as area, inequalities, differential and integral calculus, and conic sections. The construction utilizes various GeoGebra commands and objects including orthogonal lines, intersections, segments, points, circles, rotations, polygons, point-in-object, orthogonal planes, midpoints, lines, rays, splines, surfaces, and Cartesian curves. It is suitable for high school and advanced learners exploring applications of solid geometry and calculus.

GeoGebra Commands & Parameters

  1. OrthogonalLine(A, xOyPlane) → l
  2. OrthogonalLine(P, xOyPlane) → f
  3. Intersect(f, a) → Q
  4. Segment(P, Q) → g
  5. Point(g) → R
  6. Circle(zAxis, A) → d
  7. Rotate(A, (2 * π / n), zAxis) → A'
  8. Polygon(A, A', n, xOyPlane) → pol1, i, C, D, B_1, D_1, F_1, j, k, m, p, t_1, b_1, d_1, B
  9. Intersect(zAxis, a) → E
  10. PointIn(a) → F
  11. Circle(zAxis, F) → e
  12. Rotate(F, (2 * π / (n + 1)), zAxis) → F'
  13. Polygon(F, F', n + 1, a) → pol2, q, G, H, I, J, C_1, E_1, G_1, r, s, t, b, f_1, a_1, c_1, e_1
  14. OrthogonalPlane(R, g) → o
  15. Midpoint(q) → K
  16. Line(K, D) → g_1
  17. Intersect(g_1, o) → L
  18. Intersect(zAxis, o) → M
  19. Ray(M, L) → h_1
  20. Point(h_1) → N
  21. Polygon(F, N, F') → t1, f', f_2, n_1
  22. Segment(N, D) → i_1
  23. Line(J, C) → j_1
  24. Line(I, B) → k_1
  25. Line(H, A') → l_1
  26. Line(G, A) → m_1
  27. Intersect(k_1, o) → O
  28. Intersect(j_1, o) → S
  29. Intersect(l_1, o) → T
  30. Intersect(m_1, o) → U
  31. Ray(M, T) → p_1
  32. Ray(M, O) → q_1
  33. Ray(M, S) → r_1
  34. Ray(M, U) → s_1
  35. Point(s_1) → V
  36. Point(p_1) → W
  37. Point(q_1) → Z
  38. Point(r_1) → A_1
  39. Spline({H, W, A'}, 3) → c2
  40. Spline({I, Z, B}, 3) → c3
  41. Spline({J, A_1, C}, 3) → c4
  42. Spline({G, V, A}, 3) → c1
  43. Surface((k * c1(t)) + ((1 - k) * c2(t)), k, 0, 1, t, 0, 1) → s1
  44. Surface((k * c3(t)) + ((1 - k) * c2(t)), k, 0, 1, t, 0, 1) → s3
  45. Surface((k * c3(t)) + ((1 - k) * c4(t)), k, 0, 1, t, 0, 1) → s2
  46. CurveCartesian(F + (t * (N - F)), t, 0, 1) → c5
  47. CurveCartesian(F' + (t * (N - F')), t, 0, 1) → c6
  48. CurveCartesian(N + (t * (D - N)), t, 0, 1) → c7
  49. Surface((k * c4((u * t))) + ((1 - k) * c5(t)), k, 0, 1, t, 0, 1) → s4
  50. Surface((k * c4(((1 - u) * t) + u)) + ((1 - k) * c7(t)), k, 0, 1, t, 0, 1) → s5
  51. Surface((k * c1(((1 - u) * t) + u)) + ((1 - k) * c7(t)), k, 0, 1, t, 0, 1) → s7
  52. Surface((k * c1((u * t))) + ((1 - k) * c6(t)), k, 0, 1, t, 0, 1) → s6