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Logo Divinity

Logo Divinity
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2019-08-29 03:47
VectorFunctionGeometric Construction
This example demonstrates the geometric construction of a divine logo. It involves key mathematical concepts such as vectors, angles, area, functions, geometry, logarithms, perimeter, and fractions. Using GeoGebra commands like Vector, Rotate, Intersect, and Polygon, various parts of the logo can be constructed. Suitable for high school mathematics education and learning.

GeoGebra Commands & Parameters

  1. Vector(A, B) → u
  2. OrthogonalVector(u) → v
  3. Rotate(A, 75°, C) → A'
  4. Line(A', C) → h
  5. Line(H, h) → m
  6. Line(A, m) → t
  7. Line(A, B) → f
  8. Line(S, f) → f_1
  9. Line(C_1, f_1) → r_1
  10. OrthogonalLine(J, f) → l
  11. Intersect(m, l) → O
  12. Midpoint(H, O) → P
  13. Line(P, f) → a
  14. Intersect(t, a) → Q
  15. OrthogonalLine(D, f) → i
  16. Line(Z, h) → s_1
  17. Intersect(s_1, r_1) → E
  18. Intersect(s_1, f_1) → G_1
  19. OrthogonalLine(M, f) → p
  20. Line(N, f) → b
  21. Intersect(s_1, b) → H_1
  22. Intersect(f_1, t) → T
  23. Intersect(f_1, m) → B_1
  24. Circle(A, B) → c
  25. OrthogonalLine(A, f) → g
  26. Angle(A, C, A') → α
  27. OrthogonalLine(F, f) → j
  28. OrthogonalLine(H, f) → k
  29. OrthogonalLine(C, f) → n
  30. Circle(K_1, D_1) → c_1
  31. Line(G, t) → q
  32. Line(I, q) → r
  33. Line(K, r_1) → s
  34. Line(L, r) → d
  35. Line(R, s) → e
  36. Line(U, b) → g_1
  37. Intersect(t, s) → V
  38. Intersect(r, s) → W
  39. Intersect(q, e) → A_1
  40. Intersect(d, b) → E_1
  41. Intersect(q, b) → F_1
  42. Intersect(r, g_1) → I_1
  43. Polygon(V, W, I_1, E_1, F_1, A_1) → t1, h_1, i_1, j_1, k_1, l_1, m_1
  44. Vector(F_1, G) → w
  45. CurveCartesian(((1 - t)^(4) * M_1) + (((4 * (1 - t)^(3)) * t) * U_1) + (((6 * (1 - t)^(2)) * t^(2)) * Q_1) + (((4 * (1 - t)) * t^(3)) * O_1) + (t^(4) * J_1), t, 0, 1) → a_1
  46. CurveCartesian(((1 - t)^(4) * N_1) + (((4 * (1 - t)^(3)) * t) * U_1) + (((6 * (1 - t)^(2)) * t^(2)) * P_1) + (((4 * (1 - t)) * t^(3)) * O_1) + (t^(4) * L_1), t, 0, 1) → b_1