Minecraft Sphere

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2014-09-14 10:12

This example demonstrates the construction of a sphere in 3D space and its basic properties. It involves core mathematical concepts such as solid geometry, 3D shape construction, and coordinate geometry. The construction uses GeoGebra commands like Intersect, Circle, Polygon, Point, and Mirror. Suitable for high school mathematics teaching on solid geometry, geometric construction practice, and 3D shape visualization.

GeoGebra Commands & Parameters

Intersect(xAxis, yAxis) → A
Circle(A, 7) → c
Circle(A, 9.8) → d
Circle(A, 11.9) → e
Circle(A, 13.6) → f
Circle(A, 15) → g
Circle(A, 16.2) → h
Circle(A, 17.3) → k
Circle(A, 18.3) → p
Circle(A, 19.2) → q
Circle(A, 20) → r
Circle(A, 20.7) → s
Circle(A, 21.4) → t
Polygon(C, D, E, F) → poly1, c_1, d_1, e_1, f_1
Point(c) → P
Point(c) → A_1
Intersect(c, yAxis, 1) → F_1
Point(c) → K_1
Point(c) → T_1
Intersect(c, yAxis, 2) → B_2
Point(c) → F_2
Intersect(c, xAxis, 1) → K_2
Point(c) → P_2
Point(c) → U_2
Point(c) → Z_2
Polygon(B_2, C_2, K_2, L_2, M_2, N_2, O_2, P_2, Q_2, R_2, S_2, T_2, L, U_2, V_2, W_2, Z_2, A_3, K_1, B_3, C_3, D_3, E_3, D_2, F_3, G_3, H_3, I_3, J_3, K_3, L_3, M_3, N_3, E_2, F_2, G_2, H_2, I_2, J_2) → poly2, b_2, j_2, k_2, l_2, m_2, n_2, o_2, p_2, q_2, r_2, s_2, c_2, t_2, u_2, v_2, w_2, z_2, a_3, k_1, b_3, c_3, d_3, l, e_3, f_3, g_3, h_3, i_3, j_3, k_3, l_3, m_3, n_3, d_2, e_2, f_2, g_2, h_2, i_2
Point(yAxis) → O_3
Intersect(c, e_2, 1) → S_3
Intersect(c, i_3, 1) → T_3
Polygon(R_3, S_3, T_3, U_3, V_3, W_3, P_3, Q_3) → poly3, r_3, s_3, t_3, u_3, v_3, w_3, p_3, q_3
Intersect(c, a_3, 1) → Z_3
Polygon(T_3, Z_3, A_4, B_4, C_4, D_4, E_4, F_4) → poly4, t_1, z_3, a_4, b_4, c_4, d_4, e_4, f_4
Intersect(c, o_2, 1) → G_4
Polygon(Z_3, G_4, H_4, I_4, J_4, K_4, L_4, M_4) → poly5, z_1, g_4, h_4, i_4, j_4, k_4, l_4, m_4
Polygon(G_4, S_3, N_4, O_4, P_4, Q_4, R_4, S_4) → poly6, g_1, s_1, n_4, o_4, p_4, q_4, r_4, s_4
Point(r_3) → T_4
Point(s_1) → B_5
Polygon(T_4, U_4, V_4, W_4, Z_4, A_5, B_5, S_3) → poly7, t_4, u_4, v_4, w_4, z_4, a_5, b_5, s_5
Point(s_4) → C_5
Point(d) → F_5
Point(g_4) → I_5
Polygon(C_5, D_5, E_5, F_5, G_5, H_5, I_5, G_4) → poly8, c_5, d_5, e_5, f_5, g_5, h_5, i_5, g_6
Point(d) → M_5
Point(d) → O_5
Point(m_4) → P_5
Polygon(Z_3, J_5, K_5, L_5, M_5, N_5, O_5, P_5) → poly9, z_5, j_5, k_5, l_5, m_5, n_5, o_5, p_5
Point(t_3) → Q_5
Point(d) → V_5
Polygon(Q_5, T_3, R_5, S_5, T_5, U_5, V_5) → poly10, q_5, t_5, r_5, s_6, t_6, u_5, v_5
Point(yAxis) → W_5
Point(e) → I_6
Point(yAxis) → J_6
Polygon(W_5, Z_5, I_6, J_6, A_6, B_6, C_6, D_6, E_6, F_6, G_6, H_6) → poly11, w_5, h_6, i_6, j_6, z_6, a_6, b_6, c_6, d_6, e_6, f_6, g_7
Mirror(W_5, a) → K_6
Mirror(Z_5, a) → L_6
Mirror(A_6, a) → M_6
Mirror(B_6, a) → N_6
Mirror(C_6, a) → O_6
Mirror(D_6, a) → P_6
Mirror(E_6, a) → Q_6
Mirror(F_6, a) → R_6
Mirror(G_6, a) → S_6
Mirror(H_6, a) → T_6
Mirror(I_6, a) → U_6
Mirror(J_6, a) → V_6
Polygon(K_6, L_6, U_6, V_6, M_6, N_6, O_6, P_6, Q_6, R_6, S_6, T_6) → poly11', k_6, t_7, u_6, v_6, l_6, m_6, n_6, o_6, p_6, q_6, r_6, s_7
Mirror(W_5, yAxis) → W_6
Mirror(Z_5, yAxis) → Z_6
Mirror(A_6, yAxis) → A_7
Mirror(B_6, yAxis) → B_7
Mirror(C_6, yAxis) → C_7
Mirror(D_6, yAxis) → D_7
Mirror(E_6, yAxis) → E_7
Mirror(F_6, yAxis) → F_7
Mirror(G_6, yAxis) → G_7
Mirror(H_6, yAxis) → H_7
Mirror(I_6, yAxis) → I_7
Mirror(J_6, yAxis) → J_7
Polygon(W_6, Z_6, I_7, J_7, A_7, B_7, C_7, D_7, E_7, F_7, G_7, H_7) → poly11'_1, w_6, h_7, i_7, j_7, z_7, a_7, b_7, c_7, d_7, e_7, f_7, g_8
Mirror(K_6, yAxis) → K_7
Mirror(L_6, yAxis) → L_7
Mirror(M_6, yAxis) → M_7
Mirror(N_6, yAxis) → N_7
Mirror(O_6, yAxis) → O_7
Mirror(P_6, yAxis) → P_7
Mirror(Q_6, yAxis) → Q_7
Mirror(R_6, yAxis) → R_7
Mirror(S_6, yAxis) → S_7
Mirror(T_6, yAxis) → T_7
Mirror(U_6, yAxis) → U_7
Mirror(V_6, yAxis) → V_7
Polygon(K_7, L_7, U_7, V_7, M_7, N_7, O_7, P_7, Q_7, R_7, S_7, T_7) → poly11'', k_7, t_8, u_7, v_7, l_7, m_7, n_7, o_7, p_7, q_7, r_7, s_8
Intersect(e, a, 1) → W_7
Polygon(W_7, Z_7, A_8, B_8, C_8, D_8, E_8, U_7, T_7, F_8) → poly12, w_7, f_8, z_8, a_8, b_8, c_8, d_8, e_8, u_1, t_9
Mirror(W_7, a) → G_8
Mirror(Z_7, a) → H_8
Mirror(A_8, a) → I_8
Mirror(B_8, a) → J_8
Mirror(C_8, a) → K_8
Mirror(D_8, a) → L_8
Mirror(E_8, a) → M_8
Mirror(U_7, a) → N_8
Mirror(T_7, a) → O_8
Mirror(F_8, a) → P_8
Polygon(G_8, H_8, I_8, J_8, K_8, L_8, M_8, N_8, O_8, P_8) → poly12', g_9, p_8, h_8, i_8, j_8, k_8, l_8, m_8, n_8, o_8
Mirror(J_8, yAxis) → Q_8
Mirror(G_8, yAxis) → R_8
Mirror(H_8, yAxis) → S_8
Mirror(I_8, yAxis) → T_8
Mirror(J_8, yAxis) → U_8
Mirror(K_8, yAxis) → V_8
Mirror(L_8, yAxis) → W_8
Mirror(M_8, yAxis) → Z_8
Mirror(N_8, yAxis) → A_9
Mirror(O_8, yAxis) → B_9
Mirror(P_8, yAxis) → C_9
Polygon(R_8, S_8, T_8, U_8, V_8, W_8, Z_8, A_9, B_9, C_9) → poly12'', r_8, c_9, s_9, t_{10}, u_8, v_8, w_8, z_9, a_9, b_9
Mirror(R_8, a) → D_9
Mirror(S_8, a) → E_9
Mirror(T_8, a) → F_9
Mirror(U_8, a) → G_9
Mirror(V_8, a) → H_9
Mirror(W_8, a) → I_9
Mirror(Z_8, a) → J_9
Mirror(A_9, a) → K_9
Mirror(B_9, a) → L_9
Mirror(C_9, a) → M_9
Polygon(D_9, E_9, F_9, G_9, H_9, I_9, J_9, K_9, L_9, M_9) → poly12''', d_9, m_9, e_9, f_9, g_{10}, h_9, i_9, j_9, k_9, l_9
Point(yAxis) → N_9
Point(f) → Q_9
Point(f) → V_9
Point(f) → D_{10}
Polygon(W_5, N_9, W_9, Z_9, A_{10}, B_{10}, C_{10}, D_{10}, E_{10}, F_{10}, G_{10}, H_{10}, O_9, I_{10}, J_{10}, K_{10}, L_{10}, M_{10}, P_9, Q_9, R_9, S_9, T_9, U_9, V_9) → poly13, w_1, v_9, w_9, z_{10}, a_{10}, b_{10}, c_{10}, d_{10}, e_{10}, f_{10}, g_{11}, n_9, h_{10}, i_{10}, j_{10}, k_{10}, l_{10}, m_{10}, o_9, p_9, q_9, r_9, s_{10}, t_{11}, u_9
Mirror(W_5, a) → N_{10}
Mirror(N_9, a) → O_{10}
Mirror(O_9, a) → P_{10}
Mirror(P_9, a) → Q_{10}
Mirror(Q_9, a) → R_{10}
Mirror(R_9, a) → S_{10}
Mirror(S_9, a) → T_{10}
Mirror(T_9, a) → U_{10}
Mirror(U_9, a) → V_{10}
Mirror(V_9, a) → W_{10}
Mirror(W_9, a) → Z_{10}
Mirror(Z_9, a) → A_{11}
Mirror(A_{10}, a) → B_{11}
Mirror(B_{10}, a) → C_{11}
Mirror(C_{10}, a) → D_{11}
Mirror(D_{10}, a) → E_{11}
Mirror(E_{10}, a) → F_{11}
Mirror(F_{10}, a) → G_{11}
Mirror(G_{10}, a) → H_{11}
Mirror(H_{10}, a) → I_{11}
Mirror(I_{10}, a) → J_{11}
Mirror(J_{10}, a) → K_{11}
Mirror(K_{10}, a) → L_{11}
Mirror(L_{10}, a) → M_{11}
Mirror(M_{10}, a) → N_{11}
Polygon(N_{10}, O_{10}, Z_{10}, A_{11}, B_{11}, C_{11}, D_{11}, E_{11}, F_{11}, G_{11}, H_{11}, I_{11}, P_{10}, J_{11}, K_{11}, L_{11}, M_{11}, N_{11}, Q_{10}, R_{10}, S_{10}, T_{10}, U_{10}, V_{10}, W_{10}) → poly13', n_{10}, w_{10}, z_{11}, a_{11}, b_{11}, c_{11}, d_{11}, e_{11}, f_{11}, g_{12}, h_{11}, o_{10}, i_{11}, j_{11}, k_{11}, l_{11}, m_{11}, n_{11}, p_{10}, q_{10}, r_{10}, s_{11}, t_{12}, u_{10}, v_{10}
Mirror(N_{10}, yAxis) → O_{11}
Mirror(O_{10}, yAxis) → P_{11}
Mirror(P_{10}, yAxis) → Q_{11}
Mirror(Q_{10}, yAxis) → R_{11}
Mirror(R_{10}, yAxis) → S_{11}
Mirror(S_{10}, yAxis) → T_{11}
Mirror(T_{10}, yAxis) → U_{11}
Mirror(U_{10}, yAxis) → V_{11}
Mirror(V_{10}, yAxis) → W_{11}
Mirror(W_{10}, yAxis) → Z_{11}
Mirror(Z_{10}, yAxis) → A_{12}
Mirror(A_{11}, yAxis) → B_{12}
Mirror(B_{11}, yAxis) → C_{12}
Mirror(C_{11}, yAxis) → D_{12}
Mirror(D_{11}, yAxis) → E_{12}
Mirror(E_{11}, yAxis) → F_{12}
Mirror(F_{11}, yAxis) → G_{12}
Mirror(G_{11}, yAxis) → H_{12}
Mirror(H_{11}, yAxis) → I_{12}
Mirror(I_{11}, yAxis) → J_{12}
Mirror(J_{11}, yAxis) → K_{12}
Mirror(K_{11}, yAxis) → L_{12}
Mirror(L_{11}, yAxis) → M_{12}
Mirror(M_{11}, yAxis) → N_{12}
Mirror(N_{11}, yAxis) → O_{12}
Polygon(O_{11}, P_{11}, A_{12}, B_{12}, C_{12}, D_{12}, E_{12}, F_{12}, G_{12}, H_{12}, I_{12}, J_{12}, Q_{11}, K_{12}, L_{12}, M_{12}, N_{12}, O_{12}, R_{11}, S_{11}, T_{11}, U_{11}, V_{11}, W_{11}, Z_{11}) → poly13'', o_{11}, z_{12}, a_{12}, b_{12}, c_{12}, d_{12}, e_{12}, f_{12}, g_{13}, h_{12}, i_{12}, p_{11}, j_{12}, k_{12}, l_{12}, m_{12}, n_{12}, o_{12}, q_{11}, r_{11}, s_{12}, t_{13}, u_{11}, v_{11}, w_{11}
Mirror(O_{11}, a) → P_{12}
Mirror(P_{11}, a) → Q_{12}
Mirror(Q_{11}, a) → R_{12}
Mirror(R_{11}, a) → S_{12}
Mirror(S_{11}, a) → T_{12}
Mirror(T_{11}, a) → U_{12}
Mirror(U_{11}, a) → V_{12}
Mirror(V_{11}, a) → W_{12}
Mirror(W_{11}, a) → Z_{12}
Mirror(Z_{11}, a) → A_{13}
Mirror(A_{12}, a) → B_{13}
Mirror(B_{12}, a) → C_{13}
Mirror(C_{12}, a) → D_{13}
Mirror(D_{12}, a) → E_{13}
Mirror(E_{12}, a) → F_{13}
Mirror(F_{12}, a) → G_{13}
Mirror(G_{12}, a) → H_{13}
Mirror(H_{12}, a) → I_{13}
Mirror(I_{12}, a) → J_{13}
Mirror(J_{12}, a) → K_{13}
Mirror(K_{12}, a) → L_{13}
Mirror(L_{12}, a) → M_{13}
Mirror(M_{12}, a) → N_{13}
Mirror(N_{12}, a) → O_{13}
Mirror(O_{12}, a) → P_{13}
Polygon(P_{12}, Q_{12}, B_{13}, C_{13}, D_{13}, E_{13}, F_{13}, G_{13}, H_{13}, I_{13}, J_{13}, K_{13}, R_{12}, L_{13}, M_{13}, N_{13}, O_{13}, P_{13}, S_{12}, T_{12}, U_{12}, V_{12}, W_{12}, Z_{12}, A_{13}) → poly13''', p_{12}, a_{13}, b_{13}, c_{13}, d_{13}, e_{13}, f_{13}, g_{14}, h_{13}, i_{13}, j_{13}, q_{12}, k_{13}, l_{13}, m_{13}, n_{13}, o_{13}, p_{13}, r_{12}, s_{13}, t_{14}, u_{12}, v_{12}, w_{12}, z_{13}

AI Drawing Prompt Reference

Draw a sphere in 3D space by constructing multiple circles with varying radii from a central point, then build a mesh surface for the sphere using polygons formed by the intersections of these circles, highlighting the sphere's geometric properties and coordinate relationships.

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