Animated Demonstration of Geometry and Trigonometric Functions

GeoGebra Commands & Parameters

1. Segment(B, A) → i
2. Rotate(A, (a * π / 180), B) → A'
3. Ray(B, A') → g
4. Point(g) → C
5. Circle(C, 2) → e
6. Line(A, C) → l
7. Intersect(e, l, 2) → E
8. Ray(C, E) → m
9. Segment(B, C) → j
10. Angle(C, A, B) → ε
11. Rotate(C, ε / 2, A) → C'
12. Ray(A, C') → n_1
13. Segment(C, A) → h
14. Point(h) → D
15. Angle(B, D, A) → ζ
16. Rotate(B, ζ / 2, D) → B'_1
17. Ray(D, B'_1) → a_1
18. Intersect(n_1, a_1) → K
19. OrthogonalLine(K, i) → c
20. Intersect(c, i) → M
21. Circle(K, M) → c_1
22. Angle(C, D, B) → λ
23. Rotate(C, λ / 2, D) → C'_1
24. Ray(D, C'_1) → h_2
25. Angle(B, C, A) → κ
26. Rotate(B, κ / 2, C) → B'_2
27. Ray(C, B'_2) → g_2
28. Intersect(h_2, g_2) → L
29. OrthogonalLine(L, j) → d
30. Intersect(d, j) → N
31. Circle(L, N) → k_2
32. Min(Radius[c_1], Radius[k_2]) → o_1
33. Circle(C, (0.6 * o_1)) → d_4
34. Intersect(d_4, m, 1) → L_1
35. Circle(L_1, 1) → e_4
36. Intersect(e_4, m, 1) → M_1
37. Ray(L_1, M_1) → j_3
38. OrthogonalLine(L, h) → b_2
39. Intersect(b_2, h) → P
40. OrthogonalLine(K, h) → a_2
41. Intersect(h, a_2) → O
42. Angle(A, B, A') → α
43. Ray(B, A) → f
44. Segment(B, D) → k
45. Circle(A, 2) → p
46. Point(j_3) → G
47. OrthogonalLine(G, m) → n
48. Point(n) → F
49. Circle(G, 2) → q
50. Intersect(q, m, 2) → H
51. Intersect(q, n) → I, J
52. Angle(I, G, H) → β
53. Segment(A, K) → r
54. Segment(B, K) → s
55. Segment(B, L) → t
56. Segment(L, C) → b
57. Dilate(B, If[0 < u ≤ 1, 1 - u, 0], D) → B'
58. Segment(B, B') → g_1
59. Angle(D, A, K) → γ
60. Segment(D, K) → h_1
61. Angle(B, D, K) → δ
62. Min(r, h_1) → v
63. Circle(A, (0.3 * v)) → k_1
64. Circle(D, (0.3 * v)) → p_1
65. Intersect(k_1, h, 1) → Q
66. Intersect(k_1, r, 1) → R
67. Intersect(p_1, h_1) → T,
68. Intersect(p_1, k) → S,
69. CircleSector(A, Q, R) → q_1
70. CircleSector(D, S, T) → r_1
71. Dilate(D, If[1 < u ≤ 2, 2 - u, 0], K) → D'
72. Dilate(A, If[1 < u ≤ 2, 2 - u, 0], K) → A'_1
73. Segment(A, A'_1) → i_1
74. Segment(D, D') → j_1
75. Segment(D, L) → l_1
76. Segment(C, L) → m_1
77. Min(m_1, l_1) → w
78. Circle(C, (0.5 * w)) → s_1
79. Intersect(s_1, j, 1) → U
80. Intersect(s_1, m_1, 1) → V
81. Circle(D, (0.5 * w)) → t_1
82. Intersect(t_1, h) → W, Z
83. Intersect(t_1, l_1) → A_1,
84. CircleSector(D, W, A_1) → c_2
85. CircleSector(C, U, V) → d_2
86. Angle(C, A, C') → η
87. Angle(B, D, B'_1) → θ
88. Segment(A, K) → f_1
89. Segment(D, K) → b_1
90. Dilate(K, If[2 < u ≤ 3, 3 - u, 0], O) → K'
91. Segment(K, K') → d_1
92. Rotate(q_1, If[3 < u ≤ 4, ((u - 3) * γ), γ], A) → e_1
93. Rotate(r_1, If[4 < u ≤ 5, ((u - 4) * δ), δ], D) → e_2
94. Rotate(M, If[5 < u ≤ 7, ((u - 5) * π), (2 * π)], K) → M'
95. CircleArc(K, M, M') → f_2
96. Angle(B, C, B'_2) → μ
97. Angle(C, D, C'_1) → ν
98. Dilate(D, If[7 < u ≤ 8, 8 - u, 0], L) → D'_1
99. Dilate(C, If[7 < u ≤ 8, 8 - u, 0], L) → C'_2
100. Segment(D, D'_1) → i_2
101. Segment(C, C'_2) → j_2
102. Dilate(L, If[8 < u ≤ 9, 9 - u, 0], P) → L'
103. Segment(L, L') → l_2
104. Rotate(c_2, If[9 < u ≤ 10, ((u - 9) * λ / 2), λ / 2], D) → p_2
105. Rotate(d_2, If[10 < u ≤ 11, ((u - 10) * κ / 2), κ / 2], C) → q_2
106. Rotate(N, If[11 < u ≤ 13, ((u - 11) * π), (2 * π)], L) → N'
107. CircleArc(L, N, N') → r_2
108. Dilate(B, If[13 < u ≤ 14, 14 - u, 0], K) → B'_3
109. Segment(B, K) → m_2
110. Segment(B, L) → n_2
111. Min(m_2, n_2) → o
112. Circle(K, (0.6 * o_1)) → s_2
113. Circle(L, (0.6 * o_1)) → t_2
114. Angle(K, O, A) → ο
115. Angle(C, P, L) → ι
116. Intersect(s_2, m_2, 1) → B_1
117. Intersect(s_2, i_1, 1) → C_1
118. CircleSector(K, B_1, C_1) → c_3
119. Intersect(t_2, j_2, 1) → D_1
120. Intersect(t_2, n_2, 1) → E_1
121. CircleSector(L, D_1, E_1) → d_3
122. Segment(B, B'_3) → f_3
123. Dilate(B, If[13 < u ≤ 14, 14 - u, 0], L) → B'_4
124. Segment(B, B'_4) → g_3
125. Angle(B_1, K, C_1) → ξ
126. Angle(E_1, L, D_1) → ρ
127. Rotate(B_1, If[14 < u ≤ 15, ((u - 14) * ξ), ξ], K) → F_1
128. CircleSector(K, B_1, F_1) → e_3
129. Rotate(E_1, If[14 < u ≤ 15, ((-(u - 14)) * ρ), (-ρ)], L) → G_1
130. CircleSector(L, G_1, E_1) → h_3
131. Point(n) → I_1
132. Dilate(K, If[15.5 < u ≤ 16.5, 16.5 - u, 0], G) → K'_1
133. Vector(K, K'_1) → u_1
134. Translate(c_3, u_1) → k_3
135. Line(G, i_1) → i_3
136. Point(i_3) → H_1
137. Angle(H_1, G, I_1) → σ
138. Rotate(k_3, If[16.5 < u ≤ 17.5, ((u - 16.5) * σ), σ], G) → p_3
139. CircleArc(K, B_1, C_1) → q_3
140. Circle(G, (0.6 * o_1)) → r_3
141. Intersect(r_3, n, 2) → K_1
142. Circle(K_1, (0.6 * o_1)) → s_3
143. Intersect(s_3, n, 2) → J_1
144. Dilate(L, If[17.5 < u ≤ 18.5, 18.5 - u, 0], J_1) → L'_1
145. Vector(L, L'_1) → v_1
146. Translate(d_3, v_1) → t_3
147. CircleArc(L, D_1, E_1) → c_4
148. Ray(C, L_1) → l_3
149. Line(J_1, j_2) → m_3
150. Rotate(B, ρ, K) → B'_5
151. Rotate(B'_3, ρ, K) → N_1
152. Rotate(B, σ, K) → B'_6
153. Rotate(B'_3, σ, K) → O_1
154. Segment(B'_6, O_1) → n_3
155. Line(J_1, n_3) → a_3
156. Point(a_3) → P_1
157. Line(J_1, g_3) → b_3
158. Point(b_3) → Q_1
159. Angle(Q_1, J_1, P_1) → τ
160. Rotate(t_3, If[18.5 < u ≤ 19.5, ((u - 18.5) * τ), τ], J_1) → f_4
161. Dilate(J_1, If[19.5 < u ≤ 20.5, 20.5 - u, 0], G) → R_1
162. Vector(J_1, R_1) → w_1
163. Translate(f_4, w_1) → g_4
164. Point(n) → S_1
165. Ray(G, S_1) → h_4
166. Line(C, G) → i_4
167. Point(i_4) → T_1
168. Ray(G, T_1) → j_4
169. Polygon(A, C, B) → poly1, b_4, a_4, c_5
170. Point(j_4) → U_1
171. Point(h_4) → V_1
172. Angle(V_1, G, U_1) → υ