Net of a Square Pyramid by Edward Knote

GeoGebra Commands & Parameters

1. Point(Circle[A, l]) → B
2. Segment(A, B) → a
3. Line(A, B) → b_2
4. Circle(B, 3 * l / 4.5) → c
5. Intersect(c, b_2, 2) → C
6. Rotate(C, 30*°, B) → C'
7. Line(C', b_2) → d
8. Segment(B, C') → e
9. Line(A, e) → f
10. Intersect(d, f) → D
11. Polygon(A, B, C', D) → poly1, a_1, b_1, c', d_1
12. Segment(A, C') → g
13. Segment(D, B) → h_1
14. Intersect(g, h_1) → E
15. OrthogonalLine(E, a_1) → i
16. Circle(E, h) → k
17. Intersect(k, i, 2) → F
18. Segment(B, F) → j
19. Segment(C', F) → l_5
20. Segment(F, D) → m
21. Segment(F, A) → n
22. Segment(E, F) → p
23. Segment(A, D) → q
24. Midpoint(b_1) → G
25. Segment(G, F) → r
26. Angle(G, E, F) → α
27. Segment(E, G) → t
28. Line(E, G) → c_1
29. Circle(G, F) → f_1
30. Intersect(f_1, c_1, 2) → H
31. Intersect(c_1, d_1) → I
32. Circle(I, F) → g_1
33. Intersect(g_1, c_1, 1) → J
34. Vector(F, J) → u
35. Point(c') → L
36. Circle(L, F) → q_1
37. Vector(F, H) → w
38. Midpoint(A, B) → K
39. Line(K, E) → e_1
40. Circle(K, h) → p_1
41. Intersect(e_1, c') → M
42. Circle(M, h) → r_1
43. Intersect(r_1, e_1, 2) → N
44. Intersect(p_1, e_1, 1) → O
45. Vector(F, N) → v
46. Vector(F, O) → z
47. Translate(F, Vector[z * o]) → F'_1
48. Translate(F, Vector[u * (o - 1)]) → F'_2
49. Translate(F, Vector[v * (o - 2)]) → F'_3
50. Translate(F, Vector[w * (o - 3)]) → F'
51. Segment(F, N) → s
52. LineBisector(s) → a_2
53. Intersect(a_2, c') → P
54. CircleArc(P, N, F) → c_2
55. Ray(P, F'_3) → d_2
56. Intersect(c_2, d_2, 1) → Q
57. Segment(F, O) → e_2
58. LineBisector(e_2) → f_2
59. Intersect(f_2, a_1) → R
60. CircleArc(R, F, O) → g_2
61. Ray(R, F'_1) → h_2
62. Intersect(g_2, h_2, 1) → S
63. CircleArc(I, F, J) → k_2
64. CircleArc(G, H, F) → p_2
65. Ray(I, F'_2) → i_2
66. Intersect(k_2, i_2, 1) → T
67. Ray(G, F') → j_2
68. Intersect(p_2, j_2, 1) → U
69. Circle(I, E) → s_1
70. OrthogonalLine(I, a_1) → i_1
71. Intersect(s_1, i_1, 2) → V
72. Intersect(s_1, i_1, 1) → W
73. OrthogonalLine(V, i_1) → j_1
74. OrthogonalLine(W, i_1) → k_1
75. OrthogonalLine(G, k_1) → l_1
76. Intersect(j_1, l_1) → Z
77. Intersect(k_1, l_1) → A_1
78. Midpoint(V, Z) → B_1
79. Midpoint(A_1, W) → C_1
80. Circle(B_1, r) → t_1
81. Circle(C_1, r) → q_2
82. OrthogonalLine(B_1, k_1) → m_1
83. Intersect(t_1, m_1, 1) → D_1
84. Intersect(q_2, m_1, 2) → E_1
85. Vector(C', Z) → u_1
86. Vector(B, A_1) → v_1
87. Vector(N, D_1) → w_1
88. Vector(O, E_1) → z_1
89. Translate(N, Vector[w_1 * (o - 4)]) → N'
90. Translate(O, Vector[z_1 * (o - 4)]) → O'
91. Translate(B, Vector[v_1 * (o - 4)]) → B'
92. Translate(A, Vector[v_1 * (o - 4)]) → A'
93. Translate(C', Vector[u_1 * (o - 4)]) → C''
94. Translate(D, Vector[u_1 * (o - 4)]) → D'
95. If(o < 1, S, If[o < 4, O, If[o < 5, O', E_1]]) → F_1
96. If(o < 1, F, If[o < 2, T, J]) → G_1
97. If(o < 3, F, If[o < 4, U, H]) → H_1
98. If(o < 2, F, If[o < 3, Q, If[o < 4, N, If[o < 5, N', D_1]]]) → I_1
99. If(o < 4, A, If[o < 5, A', W]) → J_1
100. If(o < 4, B, If[o < 5, B', A_1]) → K_1
101. If(o < 4, C', If[o < 5, C'', Z]) → L_1
102. If(o < 4, D, If[o < 5, D', V]) → M_1
103. Polygon(F_1, J_1, K_1) → poly2, k_3, f_3, j_3
104. Polygon(L_1, H_1, K_1) → poly3, k_4, l_2, h_3
105. Polygon(L_1, I_1, M_1) → poly4, m_2, l_3, i_3
106. Polygon(M_1, G_1, J_1) → poly5, j_4, m_3, g_3
107. Intersect(m, j_3) → N_1
108. Segment(I_1, N_1) → n_1
109. Intersect(j_3, i_3) → O_1
110. Intersect(c', i_3) → Q_1
111. Intersect(c', i_3) → R_1
112. Intersect(c', i_3) → S_1
113. Intersect(c', i_3) → U_1
114. Intersect(c', i_3) → A_2
115. Intersect(l_2, i_3) → B_2
116. Segment(B_2, O_1) → n_2
117. Segment(B_2, M_1) → r_2
118. Midpoint(M_1, L_1) → C_2
119. Midpoint(L_1, K_1) → D_2
120. Midpoint(K_1, J_1) → E_2
121. Midpoint(J_1, M_1) → F_2
122. Segment(G_1, F_2) → s_2
123. Segment(C_2, I_1) → t_2
124. Segment(D_2, H_1) → a_3
125. Segment(E_2, F_1) → b_3
126. Polygon(J_1, M_1, L_1, K_1) → poly6, j_5, m_4, l_4, k_5
127. Intersect(j_3, d_1) → P_1
128. Segment(P_1, M_1) → c_3
129. Midpoint(p) → V_1
130. OrthogonalLine(V_1, p) → d_3
131. Point(d_3) → W_1
132. Vector(W_1, V_1) → u_2
133. Midpoint(r) → T_1
134. Midpoint(a_3) → Z_1
135. Point(a_2) → G_2
136. Vector(G_2, T_1) → v_2
137. Vector(G_2, Z_1) → w_2
138. Point(Circle[H_2, l]) → I_2
139. Segment(H_2, I_2) → e_3
140. Line(H_2, I_2) → b
141. Circle(I_2, 3 * l / 4.5) → p_3
142. Intersect(p_3, b, 2) → J_2
143. Rotate(J_2, 30*°, I_2) → K_2
144. Segment(I_2, K_2) → n_3
145. Line(K_2, b) → q_3
146. Line(H_2, n_3) → r_3
147. Intersect(q_3, r_3) → L_2
148. Segment(H_2, K_2) → s_3
149. Segment(I_2, L_2) → t_3
150. Intersect(s_3, t_3) → M_2
151. Circle(M_2, h) → c_4
152. OrthogonalLine(M_2, b) → a_4
153. Intersect(c_4, a_4, 2) → N_2
154. Polygon(H_2, N_2, I_2) → poly7, i_4, h_4, n_4
155. Polygon(I_2, N_2, K_2) → poly8, k_6, i_5, n_5
156. Polygon(H_2, L_2, K_2, I_2) → poly9, h_5, l_6, k_7, i_6
157. Polygon(H_2, N_2, L_2) → poly10, l_7, h_6, n_6
158. Polygon(L_2, N_2, K_2) → poly11, k_8, l_8, n_7
159. Midpoint(k_7) → O_2
160. Segment(M_2, O_2) → b_4
161. Segment(M_2, N_2) → d_4
162. Segment(N_2, O_2) → e_4
163. Angle(O_2, M_2, N_2) → β
164. Midpoint(N_2, M_2) → P_2
165. Midpoint(O_2, N_2) → Q_2
166. Line(P_2, Q_2) → f_4
167. Circle(P_2, l) → g_4
168. Intersect(g_4, f_4, 1) → R_2
169. Intersect(g_4, f_4, 2) → S_2
170. Vector(R_2, P_2) → z_2
171. Vector(S_2, Q_2) → u_3
172. Midpoint(b_3) → V_2