Root Chakra: Geometric Construction Based on Pythagorean Theorem

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2020-03-22 15:11

① This GeoGebra example demonstrates a geometric figure named 'Root Chakra', composed of circles, line segments, and intersection points forming a symmetric mandala-like pattern that implicitly encodes the Pythagorean theorem. ② Core mathematical concepts include the Pythagorean theorem, unit circle, line segments, quadrilaterals, and intersection operations between circles and lines. ③ Construction highlights: using Circle, Intersect, and Line commands; objects include points A, B, C, etc., circles c, d, e, and lines, built through successive intersections to create a complex network. ④ Suitable for middle school geometry, visualizing the Pythagorean theorem, exploring symmetry and aesthetics in geometric patterns, and cross-disciplinary use in art or meditation-themed math education.

GeoGebra Commands & Parameters

Circle(A, B) → c
Circle(B, A) → d
Intersect(c, d, 1) → C
Circle(C, B) → e
Intersect(c, e, 2) → D
Circle(D, C) → f
Intersect(c, f, 2) → E
Circle(E, D) → g
Intersect(c, g, 2) → F
Circle(F, E) → h
Intersect(c, d, 2) → G
Circle(G, F) → k
Line(E, G) → i
Intersect(k, i, 2) → H
Circle(H, G) → p
Intersect(d, p, 2) → I
Circle(I, H) → q
Intersect(d, q, 1) → J
Circle(J, I) → r
Intersect(e, r, 1) → K
Circle(K, J) → s
Intersect(e, s, 1) → L
Circle(L, K) → t
Intersect(f, t, 1) → M
Circle(M, L) → c_1
Intersect(f, c_1, 1) → N
Circle(N, M) → d_1
Intersect(g, d_1, 1) → O
Circle(O, N) → e_1
Intersect(g, e_1, 1) → P
Circle(P, O) → f_1
Intersect(h, f_1, 1) → Q
Circle(Q, P) → g_1
Intersect(h, g_1, 1) → R
Circle(R, Q) → h_1
Intersect(k, p, 2) → S
Circle(S, R) → k_1
Intersect(p, k_1, 1) → B_1
Circle(B_1, H) → d_2
Intersect(p, q, 2) → C_1
Circle(C_1, I) → e_2
Intersect(q, r, 2) → D_1
Circle(D_1, J) → f_2
Intersect(r, s, 2) → E_1
Circle(E_1, K) → g_2
Intersect(s, t, 2) → F_1
Circle(F_1, L) → h_2
Intersect(t, c_1, 2) → G_1
Circle(G_1, M) → k_2
Intersect(c_1, d_1, 2) → H_1
Circle(H_1, N) → p_2
Intersect(d_1, e_1, 2) → I_1
Circle(I_1, O) → q_2
Intersect(e_1, f_1, 2) → J_1
Circle(J_1, P) → r_2
Intersect(f_1, g_1, 2) → K_1
Circle(K_1, Q) → s_2
Intersect(g_1, h_1, 2) → L_1
Circle(L_1, R) → t_2
Intersect(h_1, k_1, 2) → M_1
Circle(M_1, S) → c_3
Intersect(d_2, c_3, 1) → N_1
Circle(N_1, B_1) → d_3
Intersect(d_2, e_2, 2) → O_1
Circle(O_1, C_1) → e_3
Intersect(e_2, f_2, 2) → P_1
Circle(P_1, D_1) → f_3
Intersect(f_2, g_2, 2) → Q_1
Circle(Q_1, E_1) → g_3
Intersect(g_2, h_2, 2) → R_1
Circle(R_1, F_1) → h_3
Intersect(h_2, k_2, 2) → S_1
Circle(S_1, G_1) → k_3
Intersect(k_2, p_2, 2) → T_1
Circle(T_1, H_1) → p_3
Intersect(p_2, q_2, 2) → U_1
Circle(U_1, I_1) → q_3
Intersect(q_2, r_2, 2) → V_1
Circle(V_1, J_1) → r_3
Intersect(r_2, s_2, 2) → W_1
Circle(W_1, K_1) → s_3
Intersect(s_2, t_2, 2) → Z_1
Circle(Z_1, L_1) → t_3
Intersect(t_2, c_3, 2) → A_2
Circle(A_2, M_1) → c_4
Intersect(c_3, d_3, 2) → B_2
Circle(B_2, N_1) → d_4
Intersect(d_2, d_3, 1) → C_2
Circle(C_2, O_1) → e_4
Intersect(e_2, e_3, 1) → D_2
Circle(D_2, P_1) → f_4
Intersect(f_2, f_3, 1) → E_2
Circle(E_2, Q_1) → g_4
Intersect(g_2, g_3, 1) → F_2
Circle(F_2, R_1) → h_4
Intersect(h_2, h_3, 1) → G_2
Circle(G_2, S_1) → k_4
Intersect(k_2, k_3, 1) → H_2
Circle(H_2, T_1) → p_4
Intersect(p_2, p_3, 1) → I_2
Circle(I_2, U_1) → q_4
Intersect(q_2, q_3, 1) → J_2
Circle(J_2, V_1) → r_4
Intersect(r_2, r_3, 1) → K_2
Circle(K_2, W_1) → s_4
Intersect(s_2, s_3, 1) → L_2
Circle(L_2, Z_1) → t_4
Intersect(t_3, c_4, 2) → M_2
Circle(M_2, A_2) → c_5
Intersect(c_4, d_4, 2) → N_2
Circle(N_2, B_2) → d_5
Intersect(d_3, e_4, 2) → O_2
Circle(O_2, C_2) → e_5
Intersect(e_3, f_4, 2) → P_2
Circle(P_2, D_2) → f_5
Intersect(f_3, g_4, 2) → Q_2
Circle(Q_2, E_2) → g_5
Intersect(g_3, h_4, 2) → R_2
Circle(R_2, F_2) → h_5
Intersect(h_3, k_4, 2) → S_2
Circle(S_2, G_2) → k_5
Intersect(k_3, p_4, 2) → T_2
Circle(T_2, H_2) → p_5
Intersect(p_3, q_4, 2) → U_2
Circle(U_2, I_2) → q_5
Intersect(q_3, r_4, 2) → V_2
Circle(V_2, J_2) → r_5
Intersect(r_3, s_4, 2) → W_2
Circle(W_2, K_2) → s_5
Intersect(s_3, t_4, 2) → Z_2
Circle(Z_2, L_2) → t_5
Intersect(t_3, c_5, 2) → A_3
Circle(A_3, M_2) → c_6
Intersect(c_5, d_5, 2) → B_3
Circle(B_3, N_2) → d_6
Intersect(d_4, e_5, 2) → C_3
Circle(C_3, O_2) → e_6
Intersect(e_4, f_5, 2) → D_3
Circle(D_3, P_2) → f_6
Intersect(f_4, g_5, 2) → E_3
Circle(E_3, Q_2) → g_6
Intersect(g_4, h_5, 2) → F_3
Circle(F_3, R_2) → h_6
Intersect(h_4, k_5, 2) → G_3
Circle(G_3, S_2) → k_6
Intersect(k_4, p_5, 2) → H_3
Circle(H_3, T_2) → p_6
Intersect(p_4, q_5, 2) → I_3
Circle(I_3, U_2) → q_6
Intersect(q_4, r_5, 2) → J_3
Circle(J_3, V_2) → r_6
Intersect(r_4, s_5, 2) → K_3
Circle(K_3, W_2) → s_6
Intersect(s_4, t_5, 2) → L_3
Circle(L_3, Z_2) → t_6
Intersect(t_4, c_6, 2) → M_3
Circle(M_3, A_3) → c_7
Intersect(c_6, d_6, 2) → N_3
Circle(N_3, B_3) → d_7
Intersect(d_5, e_6, 2) → O_3
Circle(O_3, C_3) → e_7
Intersect(e_5, f_6, 2) → P_3
Circle(P_3, D_3) → f_7
Intersect(f_5, g_6, 2) → Q_3
Circle(Q_3, E_3) → g_7
Intersect(g_5, h_6, 2) → R_3
Circle(R_3, F_3) → h_7
Intersect(h_5, k_6, 2) → S_3
Circle(S_3, G_3) → k_7
Intersect(k_5, p_6, 2) → T_3
Circle(T_3, H_3) → p_7
Intersect(p_5, q_6, 2) → U_3
Circle(U_3, I_3) → q_7
Intersect(q_5, r_6, 2) → V_3
Circle(V_3, J_3) → r_7
Intersect(r_5, s_6, 2) → W_3
Circle(W_3, K_3) → s_7
Intersect(s_5, t_6, 2) → Z_3
Circle(Z_3, L_3) → t_7
Intersect(t_5, c_7, 2) → A_4
Circle(A_4, M_3) → c_8
Intersect(c_6, c_7, 1) → B_4
Circle(B_4, N_3) → d_8
Intersect(d_5, d_6, 1) → C_4
Circle(C_4, O_3) → e_8
Intersect(e_5, e_6, 1) → D_4
Circle(D_4, P_3) → f_8
Intersect(f_5, f_6, 1) → E_4
Circle(E_4, Q_3) → g_8
Intersect(g_5, g_6, 1) → F_4
Circle(F_4, R_3) → h_8
Intersect(h_5, h_6, 1) → G_4
Circle(G_4, S_3) → k_8
Intersect(k_5, k_6, 1) → H_4
Circle(H_4, T_3) → p_8
Intersect(p_5, p_6, 1) → I_4
Circle(I_4, U_3) → q_8
Intersect(q_5, q_6, 1) → J_4
Circle(J_4, V_3) → r_8
Intersect(r_5, r_6, 1) → K_4
Circle(K_4, W_3) → s_8
Intersect(s_5, s_6, 1) → L_4
Circle(L_4, Z_3) → t_8
Intersect(t_5, t_6, 1) → M_4
Circle(M_4, A_4) → c_9
Intersect(c_7, c_8, 1) → N_4
Circle(N_4, B_4) → d_9
Intersect(d_7, e_8, 2) → O_4
Circle(O_4, C_4) → e_9
Intersect(e_6, e_7, 1) → P_4
Circle(P_4, D_4) → f_9
Intersect(f_6, f_7, 1) → Q_4
Circle(Q_4, E_4) → g_9
Intersect(g_6, g_7, 1) → R_4
Circle(R_4, F_4) → h_9
Intersect(h_6, h_7, 1) → S_4
Circle(S_4, G_4) → k_9
Intersect(k_6, k_7, 1) → T_4
Circle(T_4, H_4) → p_9
Intersect(p_6, p_7, 1) → U_4
Circle(U_4, I_4) → q_9
Intersect(q_6, q_7, 1) → V_4
Circle(V_4, J_4) → r_9
Intersect(r_6, r_7, 1) → W_4
Circle(W_4, K_4) → s_9
Intersect(s_6, s_7, 1) → Z_4
Circle(Z_4, L_4) → t_9
Intersect(t_6, t_7, 1) → A_5
Circle(A_5, M_4) → c_{10}
Intersect(c_8, d_9, 2) → B_5
Circle(B_5, N_4) → d_{10}
Intersect(d_7, e_9, 2) → C_5
Circle(C_5, O_4) → e_{10}
Intersect(e_7, f_9, 2) → D_5
Circle(D_5, P_4) → f_{10}
Intersect(f_7, g_9, 2) → E_5
Circle(E_5, Q_4) → g_{10}
Intersect(g_7, h_9, 2) → F_5
Circle(F_5, R_4) → h_{10}
Intersect(h_7, k_9, 2) → G_5
Circle(G_5, S_4) → k_{10}
Intersect(k_7, p_9, 2) → H_5
Circle(H_5, T_4) → p_{10}
Intersect(p_7, q_9, 2) → I_5
Circle(I_5, U_4) → q_{10}
Intersect(q_7, r_9, 2) → J_5
Circle(J_5, V_4) → r_{10}
Intersect(r_7, s_9, 2) → K_5
Circle(K_5, W_4) → s_{10}
Intersect(s_7, t_9, 2) → L_5
Circle(L_5, Z_4) → t_{10}
Intersect(t_7, c_{10}, 2) → M_5
Circle(M_5, A_5) → c_{11}
Intersect(c_9, d_{10}, 2) → T
Circle(T, B_5) → p_1
Intersect(d_8, e_{10}, 2) → U
Circle(U, C_5) → q_1
Intersect(e_8, f_{10}, 2) → V
Circle(V, D_5) → r_1
Intersect(f_8, g_{10}, 2) → W
Circle(W, E_5) → s_1
Intersect(g_8, h_{10}, 2) → Z
Circle(Z, F_5) → t_1
Intersect(h_8, k_{10}, 2) → A_1
Circle(A_1, G_5) → c_2
Intersect(k_8, p_{10}, 2) → N_5
Circle(N_5, H_5) → d_{11}
Intersect(p_8, q_{10}, 2) → O_5
Circle(O_5, I_5) → e_{11}
Intersect(q_8, r_{10}, 2) → P_5
Circle(P_5, J_5) → f_{11}
Intersect(r_8, s_{10}, 2) → Q_5
Circle(Q_5, K_5) → g_{11}
Intersect(s_8, t_{10}, 2) → R_5
Circle(R_5, L_5) → h_{11}
Intersect(t_8, c_{11}, 2) → S_5
Circle(S_5, M_5) → k_{11}
Intersect(c_{10}, p_1, 2) → T_5
Circle(T_5, T) → p_{11}
Intersect(d_9, q_1, 2) → U_5
Circle(U_5, U) → q_{11}
Intersect(e_9, r_1, 2) → V_5
Circle(V_5, V) → r_{11}
Intersect(f_9, s_1, 2) → W_5
Circle(W_5, W) → s_{11}
Intersect(g_9, t_1, 2) → Z_5
Circle(Z_5, Z) → t_{11}
Intersect(h_9, c_2, 2) → A_6
Circle(A_6, A_1) → c_{12}
Intersect(k_9, d_{11}, 2) → B_6
Circle(B_6, N_5) → d_{12}
Intersect(p_9, e_{11}, 2) → C_6
Circle(C_6, O_5) → e_{12}
Intersect(q_9, f_{11}, 2) → D_6
Circle(D_6, P_5) → f_{12}
Intersect(r_9, g_{11}, 2) → E_6
Circle(E_6, Q_5) → g_{12}
Intersect(s_9, h_{11}, 2) → F_6
Circle(F_6, R_5) → h_{12}
Intersect(t_9, k_{11}, 2) → G_6
Circle(G_6, S_5) → k_{12}
Intersect(c_{11}, p_{11}, 2) → H_6
Circle(H_6, T_5) → p_{12}
Intersect(d_{10}, q_{11}, 2) → I_6
Circle(I_6, U_5) → q_{12}
Intersect(e_{10}, r_{11}, 2) → J_6
Circle(J_6, V_5) → r_{12}
Intersect(f_{10}, s_{11}, 2) → K_6
Circle(K_6, W_5) → s_{12}
Intersect(g_{10}, t_{11}, 2) → L_6
Circle(L_6, Z_5) → t_{12}
Intersect(h_{10}, c_{12}, 2) → M_6
Circle(M_6, A_6) → c_{13}
Intersect(k_{10}, d_{12}, 2) → N_6
Circle(N_6, B_6) → d_{13}
Intersect(p_{10}, e_{12}, 2) → O_6
Circle(O_6, C_6) → e_{13}
Intersect(q_{10}, f_{12}, 2) → P_6
Circle(P_6, D_6) → f_{13}
Intersect(r_{10}, g_{12}, 2) → Q_6
Circle(Q_6, E_6) → g_{13}
Intersect(s_{10}, h_{12}, 2) → R_6
Circle(R_6, F_6) → h_{13}
Intersect(t_{10}, k_{12}, 2) → S_6
Circle(S_6, G_6) → k_{13}
Intersect(c_{11}, k_{11}, 1) → T_6
Circle(T_6, H_6) → p_{13}
Intersect(d_{10}, p_1, 1) → U_6
Circle(U_6, I_6) → q_{13}
Intersect(e_{10}, q_1, 1) → V_6
Circle(V_6, J_6) → r_{13}
Intersect(f_{10}, r_1, 1) → W_6
Circle(W_6, K_6) → s_{13}
Intersect(g_{10}, s_1, 1) → Z_6
Circle(Z_6, L_6) → t_{13}
Intersect(h_{10}, t_1, 1) → A_7
Circle(A_7, M_6) → c_{14}
Intersect(k_{10}, c_2, 1) → B_7
Circle(B_7, N_6) → d_{14}
Intersect(p_{10}, d_{11}, 1) → C_7
Circle(C_7, O_6) → e_{14}
Intersect(q_{10}, e_{11}, 1) → D_7
Circle(D_7, P_6) → f_{14}
Intersect(r_{10}, g_{13}, 2) → E_7
Circle(E_7, Q_6) → g_{14}
Intersect(s_{10}, g_{11}, 1) → F_7
Circle(F_7, R_6) → h_{14}
Intersect(t_{10}, h_{11}, 1) → G_7
Circle(G_7, S_6) → k_{14}
Intersect(k_{11}, k_{12}, 1) → H_7
Circle(H_7, T_6) → p_{14}
Intersect(p_1, p_{11}, 1) → I_7
Circle(I_7, U_6) → q_{14}
Intersect(q_1, q_{11}, 1) → J_7
Circle(J_7, V_6) → r_{14}
Intersect(r_1, r_{11}, 1) → K_7
Circle(K_7, W_6) → s_{14}
Intersect(s_1, s_{11}, 1) → L_7
Circle(L_7, Z_6) → t_{14}
Intersect(t_1, t_{11}, 1) → M_7
Circle(M_7, A_7) → c_{15}
Intersect(c_2, c_{12}, 1) → N_7
Circle(N_7, B_7) → d_{15}
Intersect(d_{11}, d_{12}, 1) → O_7
Circle(O_7, C_7) → e_{15}
Intersect(e_{11}, e_{12}, 1) → P_7
Circle(P_7, D_7) → f_{15}
Intersect(f_{11}, f_{12}, 1) → Q_7
Circle(Q_7, E_7) → g_{15}
Intersect(g_{11}, g_{12}, 1) → R_7
Circle(R_7, F_7) → h_{15}
Intersect(h_{11}, h_{12}, 1) → S_7
Circle(S_7, G_7) → k_{15}
Intersect(p_{11}, p_{12}, 1) → T_7
Circle(T_7, I_7) → p_{15}
Intersect(q_{11}, q_{12}, 1) → U_7
Circle(U_7, J_7) → q_{15}
Intersect(r_{11}, r_{12}, 1) → V_7
Circle(V_7, K_7) → r_{15}
Intersect(s_{11}, s_{12}, 1) → W_7
Circle(W_7, L_7) → s_{15}
Intersect(t_{11}, t_{12}, 1) → Z_7
Circle(Z_7, M_7) → t_{15}
Intersect(c_{12}, c_{13}, 1) → A_8
Circle(A_8, N_7) → c_{16}
Intersect(d_{12}, d_{13}, 1) → B_8
Circle(B_8, O_7) → d_{16}
Intersect(e_{12}, e_{13}, 1) → C_8
Circle(C_8, P_7) → e_{16}
Intersect(f_{12}, f_{13}, 1) → D_8
Circle(D_8, Q_7) → f_{16}
Intersect(g_{12}, g_{13}, 1) → E_8
Circle(E_8, R_7) → g_{16}
Intersect(h_{12}, h_{13}, 1) → F_8
Circle(F_8, S_7) → h_{16}
Intersect(k_{12}, k_{13}, 1) → G_8
Circle(G_8, H_7) → k_{16}
Intersect(p_{12}, p_{15}, 2) → H_8
Circle(H_8, T_7) → p_{16}
Intersect(q_{12}, q_{15}, 2) → I_8
Circle(I_8, U_7) → q_{16}
Intersect(r_{12}, r_{15}, 2) → J_8
Circle(J_8, V_7) → r_{16}
Intersect(s_{12}, s_{15}, 2) → K_8
Circle(K_8, W_7) → s_{16}
Intersect(t_{12}, t_{15}, 2) → L_8
Circle(L_8, Z_7) → t_{16}
Intersect(c_{13}, c_{16}, 2) → M_8
Circle(M_8, A_8) → c_{17}
Intersect(d_{13}, d_{16}, 2) → N_8
Circle(N_8, B_8) → d_{17}
Intersect(e_{13}, e_{16}, 2) → O_8
Circle(O_8, C_8) → e_{17}
Intersect(f_{13}, f_{16}, 2) → P_8
Circle(P_8, D_8) → f_{17}
Intersect(g_{13}, g_{16}, 2) → Q_8
Circle(Q_8, E_8) → g_{17}
Intersect(h_{13}, h_{16}, 2) → R_8
Circle(R_8, F_8) → h_{17}
Intersect(k_{13}, k_{16}, 2) → S_8
Circle(S_8, G_8) → k_{17}

AI Drawing Prompt Reference

Draw a symmetric mandala-like geometric pattern named 'Root Chakra', based on the Pythagorean theorem. Start with two equal circles intersecting, then repeatedly draw new circles centered at their intersection points, generating a chain of circles and points around the circumference. Connect selected points with a line, then use its intersections with circles as new centers to continue adding circles, building a layered network of arcs, segments, and intersection points. The final figure is a highly symmetric composition of interlocking circles, lines, and points, subtly encoding the Pythagorean relationship.

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