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WhatsApp Logo Geometric Construction

WhatsApp Logo Geometric Construction
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2019-09-21 02:02
CircleVectorTrigonometryCoordinate GeometryGeometric Construction
This example demonstrates how to construct the WhatsApp logo using GeoGebra, focusing on 2D geometry. Key math concepts include vectors, angles, circles, geometric constructions, and rotations. The construction involves commands like Vector, OrthogonalVector, Midpoint, Mirror, Polygon, Line, OrthogonalLine, Intersect, Circle, Rotate, LineBisector, CircleArc, and CurveCartesian. Suitable for high school mathematics education or geometric drawing learning.

GeoGebra Commands & Parameters

  1. Vector(A, B) → u
  2. OrthogonalVector(u) → v
  3. Midpoint(C, B) → D
  4. Mirror(A, D) → A'
  5. Polygon(C, A', B, A) → q1, c, a', b, a
  6. Mirror(E, D) → E'
  7. Line(E, b) → f
  8. Line(E', c) → g
  9. OrthogonalLine(D, f) → h
  10. Intersect(h, f) → F
  11. Circle(D, F) → d
  12. Circle(D, G) → e
  13. Rotate(G, (-(30°)), D) → G'
  14. Rotate(G', (-(20°)), D) → G''
  15. LineBisector(G'', G') → i
  16. Rotate(F, (-(28°)), D) → F'
  17. Mirror(F', i) → F''
  18. Line(I, f) → j
  19. Intersect(i, j) → J
  20. Line(G, f) → k
  21. Intersect(i, k) → K
  22. Polygon(G', G'', K) → t1, k_1, g', g''
  23. Polygon(F', F'', J) → t2, j_1, f', f''
  24. Mirror(i, h) → i'
  25. Rotate(i', 15°, D) → i''
  26. Mirror(H, i) → H'
  27. Mirror(P, i) → P'
  28. Polygon(H, P, R, Q) → q2, h_1, p, r, q
  29. Mirror(H, i) → H'_1
  30. Mirror(P, i) → P'_1
  31. Mirror(R, i) → R'
  32. Mirror(Q, i) → Q'
  33. Polygon(H'_1, P'_1, R', Q') → q2', h'_1, p'_1, r', q'
  34. Intersect(i, g) → S
  35. CircleArc(S, R, R') → s
  36. Mirror(T, i) → T'
  37. Polygon(R, Q, T, T', Q', R') → poly1, r_1, q_1, t, t', m, n
  38. Polygon(H, Q, T) → t3, t_1, h_2, q_2
  39. Mirror(H, i) → H'_2
  40. Mirror(Q, i) → Q'_1
  41. Mirror(T, i) → T'_1
  42. Polygon(H'_2, Q'_1, T'_1) → t3', t'_1, h'_2, q'_1
  43. CurveCartesian(((1 - t)^(5) * P) + (((5 * (1 - t)^(4)) * t) * O) + (((10 * (1 - t)^(3)) * t^(2)) * L) + (((10 * (1 - t)^(2)) * t^(3)) * U) + (((5 * (1 - t)) * t^(4)) * N) + (t^(5) * P'), t, 0, 1) → l