3.4.7 Museo de Onda: Azulejo 7

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2023-03-22 22:32

In collections geometriadinamica.es

This example demonstrates the geometric construction of complex tile patterns, highlighting symmetry and transformation. It involves core mathematical concepts like differential equations, conic sections, algebra, MCM and MCD, and the unit circle. Key GeoGebra commands used include Line, Point, OrthogonalLine, Intersect, Midpoint, Mirror, Min, Rotate, Vector, and Translate. Suitable for high school mathematics education, aiding students in understanding geometric transformations and symmetry in artistic design.

GeoGebra Commands & Parameters

Line(A, B) → b
Line(G, b) → e
Point(e) → J
OrthogonalLine(J, e) → h
OrthogonalLine(G, e) → f
Point(f) → H
OrthogonalLine(H, f) → g
Intersect(g, h) → E
Midpoint(E, H) → I
Midpoint(I, E) → B_1
Midpoint(G, J) → D
Midpoint(J, E) → F
Midpoint(H, G) → K
Midpoint(D, I) → L
Midpoint(K, L) → M
Midpoint(L, F) → N
Midpoint(F, J) → O
Midpoint(J, D) → P
Midpoint(G, D) → Q
Midpoint(K, G) → R
Midpoint(Q, M) → S
Midpoint(L, D) → T
Midpoint(P, N) → U
Midpoint(F, E) → V
Midpoint(K, H) → W
Midpoint(W, V) → Z
Midpoint(H, I) → A_1
Midpoint(N, B_1) → C_1
Midpoint(Z, W) → D_1
Midpoint(D, U) → E_1
Midpoint(U, J) → F_1
Midpoint(T, Q) → G_1
Midpoint(S, G) → H_1
Midpoint(S, K) → I_1
Midpoint(M, T) → J_1
Midpoint(T, N) → K_1
Midpoint(N, O) → L_1
Midpoint(F, C_1) → M_1
Midpoint(C_1, L) → N_1
Midpoint(L, D_1) → O_1
Midpoint(D_1, K) → P_1
Midpoint(H, D_1) → Q_1
Midpoint(D_1, I) → R_1
Midpoint(I, C_1) → S_1
Midpoint(C_1, E) → T_1
Mirror(F_1, h) → U_1
Mirror(L_1, h) → V_1
Mirror(M_1, h) → W_1
Mirror(T_1, h) → Z_1
Mirror(B_1, h) → A_2
Mirror(L_1, h) → C_2
Line(Q, A_2) → d
Line(F, d) → i
Line(C_1, d) → k
Line(S_1, k) → l
Line(R_1, L_1) → j
Line(D_1, j) → m
Line(M, j) → n
Line(I, j) → p
Line(S, A_1) → t
Line(E_1, N_1) → c_1
Line(F_1, M_1) → d_1
Line(G_1, R_1) → e_1
Line(W_1, P_1) → g_1
Line(Q_1, Z_1) → h_1
Mirror(T, m) → T'
Mirror(K_1, m) → I_2
Mirror(T, m) → T'_1
Mirror(L, m) → L'
Mirror(T, m) → T'_2
Mirror(U, m) → U'_1
Mirror(T, m) → T'_3
Point(b) → A1
Min(90, ((a - 1) * 90)) → r1
Rotate(T, ((-r1))°, T) → T'_7
Rotate(U'_1, ((-r1))°, T) → D_{12}
Rotate(T'_3, ((-r1))°, T) → E_{12}
Rotate(U, ((-r1))°, T) → U'_3
Rotate(T, ((-r1))°, T) → T'_8
Rotate(T, ((-r1))°, T'_8) → T'_9
Rotate(T'_2, ((-r1))°, T) → I_{12}
Rotate(T'_1, ((-r1))°, T) → T_{12}
Rotate(L', ((-r1))°, T) → L''_2
Rotate(L, ((-r1))°, T) → L'_2
Midpoint(C_1, E) → K_{20}
Rotate(U'_1, 270°, L') → D_{21}
Rotate(D_{21}, 270°, L') → G_{21}
Rotate(G_{21}, 270°, L') → M_{21}
Line(U'_1, D_{21}) → n_1
Mirror(U'_1, n_1) → V_{21}
Mirror(M_{21}, n_1) → D_{22}
Mirror(D_{21}, n_1) → M_{24}
Mirror(G_{21}, n_1) → P_{24}
Min(180, ((a - 1) * 180)) → r2
Min(270, ((a - 1) * 270)) → r3
Rotate(T, r1°, T) → T'_4
Rotate(T, r2°, T) → T'_5
Rotate(T, r3°, T) → T'_6
Rotate(L, r1°, T) → L'_1
Rotate(K_1, r1°, T) → Q_3
Rotate(L, r2°, T) → L'_3
Rotate(K_1, r2°, T) → Z_3
Rotate(L, r3°, T) → L'_4
Rotate(K_1, r3°, T) → H_4
Min(180, ((a - 5.5) * 180)) → r4
Intersect(t, i) → H_{15}
Midpoint(H_{15}, D) → J_{15}
Vector(S, D) → u
Vector(S, L) → w
Vector(U, P) → z
Vector(U, O) → u_1
Translate(pic1, u_1) → pic1'
Translate(pic1', z) → pic1''
Translate(pic1, z) → pic1'_1
Translate(pic1'_1, z) → pic2
Translate(pic2, z) → pic2'
Translate(pic2', z) → pic2''
Translate(pic2'', u_1) → pic2'''
Translate(pic2''', u_1) → pic3
Translate(pic2', u_1) → pic2''_1
Translate(pic2''_1, u_1) → pic4
Translate(pic2, u_1) → pic2'_1
Translate(pic3, u_1) → pic3'
Translate(pic3', u_1) → pic3''
Translate(pic4, u_1) → pic4'
Translate(pic4', u_1) → pic4''
Translate(pic2'_1, u_1) → pic5
Translate(pic5, u_1) → pic5'
Translate(pic5', u_1) → pic5''
Translate(pic1'', u_1) → pic1'''
Translate(pic1''', u_1) → pic6
Translate(pic6, u_1) → pic6'
Translate(pic1', u_1) → pic1''_1
Translate(pic1''_1, u_1) → pic7
Translate(pic7, u_1) → pic7'
Midpoint(Q, S) → C
Midpoint(S, M) → B_2
Midpoint(M, D_1) → D_2
Midpoint(D, T) → E_2
Midpoint(T, L) → F_2
Midpoint(L, Z) → G_2
Midpoint(G_1, J_1) → H_2
Midpoint(J_1, O_1) → J_2
Midpoint(O_1, R_1) → K_2
Midpoint(E_1, F_1) → L_2
Midpoint(U, N) → M_2
Midpoint(N, C_1) → N_2
Midpoint(T_1, M_1) → O_2
Midpoint(M_1, L_1) → P_2
Midpoint(L_1, F_1) → Q_2
Midpoint(J, O) → R_2
Midpoint(O, F) → S_2
Midpoint(F, V) → T_2
Line(E_2, i) → q
Line(C, d) → r
Line(B_2, k) → s
Line(S_2, p) → a_1
Line(Q_2, j) → b_1
Line(L_2, m) → f_1
Line(E_2, n) → i_1
Line(T_2, p) → j_1
Line(L_2, i) → k_1
Line(D_2, l) → l_1
Intersect(r, b_1) → U_2
Intersect(q, f_1) → V_2
Intersect(s, a_1) → W_2

AI Drawing Prompt Reference

Draw a complex tile pattern with multiple symmetric points and lines. Start by drawing two lines b and e, then take point J on e and draw two perpendicular lines h and f through J. Continue by finding midpoints of E and H, and so on, to construct multiple points. Finally, use mirroring operations to generate symmetric points and form a complex geometric pattern.

The prompt above was compiled from the original drawing commands and is for reference only.