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Quirinus Puzzle

Quirinus Puzzle
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2018-01-08 01:08
Coordinate GeometryParametric EquationGeometric Construction
This is a lovely paradox puzzle that demonstrates the concepts of area and similarity transformation. Using GeoGebra, we can construct a series of geometric shapes, including circles, polygons, and parametric curves. The example involves core math concepts such as similarity, area calculation, and percentages. Suitable for middle school and above students to learn geometric construction and related concepts.

GeoGebra Commands & Parameters

  1. Point(Circle[O, 1 + o]) → P
  2. Segment(O, P) → g_1
  3. Segment(A, B) → f
  4. Polygon(A, B, 4) → poly1, g, h, i, j, C_1, D_1
  5. Segment(E, F) → k
  6. Segment(C, D) → l
  7. Segment(G, H) → m
  8. Polygon(E, F, 4) → poly2, n, p, q, r, I, J
  9. Polygon(C, D, 4) → poly3, s, t, a, b, K, L
  10. Polygon(G, H, 4) → poly4, c, d, e, f_1, M, N
  11. Point(Circle[Q, 1 + o]) → R
  12. Segment(Q, R) → h_1
  13. Point(Circle[S, 1 + o]) → T
  14. Segment(S, T) → i_1
  15. Point(Circle[U, 1 + o]) → V
  16. Segment(U, V) → j_1
  17. Point(Circle[W, 1 - o]) → Z
  18. Segment(W, Z) → k_1
  19. Point(Circle[A_1, 1 - o]) → B_1
  20. Segment(A_1, B_1) → l_1
  21. Point(Circle[E_1, 1 - o]) → F_1
  22. Segment(E_1, F_1) → m_1
  23. Point(Circle[G_1, 1 - o]) → H_1
  24. Polygon(O, P, P + u_1) → t1, p_1, i_2, j_2
  25. Segment(G_1, H_1) → n_1
  26. Polygon(Q, R, R + OrthogonalVector[h_1] / (1 + o)) → t2, q_1, r_1, k_2
  27. Polygon(S, T, T + OrthogonalVector[i_1] / (1 + o)) → t3, s_1, t_1, l_2
  28. Polygon(U, V, V + OrthogonalVector[j_1] / (1 + o)) → t4, a_1, m_2, n_2
  29. Polygon(W, Z, Z - OrthogonalVector[k_1] / (1 - o)) → t5, b_1, p_2, q_2
  30. Polygon(A_1, B_1, B_1 - OrthogonalVector[l_1] / (1 - o)) → t6, c_1, r_2, s_2
  31. Polygon(E_1, F_1, F_1 - OrthogonalVector[m_1] / (1 - o)) → t7, d_1, e_1, f_2
  32. Polygon(G_1, H_1, H_1 - OrthogonalVector[n_1] / (1 - o)) → t8, g_2, h_2, t_2
  33. Circle(I_1, (j_2 + f_2) / sqrt(2)) → c_2