Counting Squares in Parallelograms

GeoGebra Commands & Parameters

1. Point(xAxis) → A
2. Point(Ray[(0, 0), (1, 0)]) → B
3. PointIn(x ≥ 0 ∧ y ≥ 0 ∧ x ≤ x(B)) → C
4. Segment(C, D) → f
5. Intersect(eq1, f) → E
6. Segment(C, E) → g
7. Point(g) → F
8. Circle(H, Distance[A, G]) → e
9. Point(e) → I
10. Line(H, I) → h
11. OrthogonalLine(I, h) → i
12. Circle(I, Distance[G, F]) → k
13. Intersect(k, i, 2) → J
14. Line(J, h) → j
15. Circle(J, Distance[F, C]) → p
16. Intersect(p, j, 1) → K
17. Polygon(H, I, J, K) → q3, h_1, i_1, j_1, k_1
18. Circle(L, Distance[G, B]) → q
19. Point(q) → M
20. Line(L, M) → l
21. OrthogonalLine(L, l) → m
22. Circle(L, Distance[G, F]) → r
23. Intersect(r, m, 2) → N
24. Line(N, l) → n
25. Circle(N, Distance[F, D]) → s
26. Intersect(s, n, 2) → O
27. Polygon(L, M, O, N) → q4, l_1, m_1, o, n_1
28. Intersect(xAxis, yAxis) → P
29. Segment(P, C) → t
30. Segment(C, D) → p_1
31. Segment(D, B) → q_1
32. Segment(B, P) → r_1
33. Intersect(t, r_1) → Q
34. Polygon(Q, B, D, C) → q1, q_2, b, d, c
35. Segment(F, G) → a
36. RotateText(text1, pi / 2) → text2
37. Circle(R, a) → c_1
38. Point(c_1) → S
39. Line(R, S) → f_1
40. OrthogonalLine(R, f_1) → g_1
41. Circle(R, Distance[F, D]) → d_1
42. Intersect(d_1, g_1, 2) → T
43. Polygon(S, R, T) → t1, t_1, s_1, r_2