GeoGebra Pentominoes

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2014-04-16 13:01

In collections Jessica's Fraction Book The Best Math Book in the World

This example demonstrates playing with pentominoes to solve geometric challenges using a slider to select different tasks. Core math concepts include geometric transformations, polygon assembly, and spatial reasoning. It uses commands like Circle, Point, Line, OrthogonalLine, Intersect, Vector, Translate, Segment, Polygon, Mirror. Suitable for middle school and above for geometry learning and spatial skills development.

GeoGebra Commands & Parameters

Circle(D, a) → c
Circle(D, (4 * a)) → k
Point(k) → M
Line(D, M) → d
OrthogonalLine(D, d) → e
Intersect(c, e, 2) → E
Intersect(c, e, 1) → F
Intersect(c, d, 1) → G
Intersect(c, d, 2) → H
Line(E, d) → f
Line(F, d) → g
Line(H, e) → h
Line(G, e) → i
Intersect(f, i) → I
Intersect(g, i) → J
Intersect(f, h) → K
Intersect(g, h) → L
Vector(J, L) → w
Vector(J, I) → z
Translate(K, w) → K'_1
Translate(L, w) → L'
Translate(K'_1, w) → K''_1
Translate(L', w) → L''
Translate(I, z) → I'_1
Translate(K, z) → K'
Vector(K, I) → j
Translate(I'_1, j) → I''_1
Translate(I, j) → I'
Point(d) → N
Circle(N, flipcircle) → p
Intersect(p, d, 1) → O
Intersect(p, d, 2) → P
Segment(O, P) → l
Point(l) → Q
Segment(O, Q) → m
Polygon(I''_1, I', I, J, L'', K''_1, K, K') → poly1, i'', i', i_1, j_1, l'', k'', k_1, k'
Mirror(I''_1, l) → I'''
Mirror(I'_1, l) → S
Mirror(K', l) → K''
Mirror(I', l) → I''
Polygon(I''', K'', L, L'', K''_1, I, J, I'') → poly2, i''', k''_1, l_1, l''_1, k''_2, i_2, j_2, i''_1
Circle(T, a) → r
Circle(T, (6 * a)) → s
Point(s) → U
Line(T, U) → t
OrthogonalLine(T, t) → a_1
Intersect(r, a_1, 2) → V
Intersect(r, t, 1) → W
Intersect(r, a_1, 1) → Z
Intersect(r, t, 2) → A_1
Line(V, t) → b_1
Line(Z, t) → c_1
Line(W, a_1) → d_1
Line(A_1, a_1) → e_1
Intersect(b_1, d_1) → B_1
Intersect(c_1, d_1) → C_1
Intersect(c_1, e_1) → D_1
Intersect(b_1, e_1) → E_1
Vector(C_1, D_1) → u
Vector(C_1, B_1) → v
Vector(E_1, D_1) → n
Vector(E_1, B_1) → q
Translate(D_1, Vector[(3 * u)]) → A
Translate(E_1, Vector[(3 * u)]) → B
Translate(B_1, v) → C
Translate(E_1, v) → R
Mirror(C, t) → C'
Mirror(R, t) → R'
Point(t) → F_1
Point(t) → G_1
Segment(F_1, G_1) → f_1
Point(f_1) → H_1
Segment(F_1, H_1) → g_1
Polygon(C, C_1, A, B, E_1, R) → poly3, c_2, c_3, a_2, b_2, e_2, r_1
Polygon(C', R', D_1, A, B, B_1) → poly4, c', r', d_2, a_3, b_3, b_4
Circle(I_1, a) → h_1
Circle(I_1, (4 * a)) → p_1
Point(p_1) → J_1
Line(I_1, J_1) → m_1
OrthogonalLine(I_1, m_1) → n_1
Intersect(h_1, n_1, 2) → K_1
Intersect(h_1, m_1, 1) → L_1
Intersect(h_1, n_1, 1) → M_1
Intersect(h_1, m_1, 2) → N_1
Line(K_1, m_1) → q_1
Line(M_1, m_1) → s_1
Line(L_1, n_1) → t_1
Line(N_1, n_1) → f_2
Intersect(q_1, t_1) → O_1
Intersect(s_1, t_1) → P_1
Intersect(s_1, f_2) → Q_1
Intersect(q_1, f_2) → R_1
Vector(P_1, Q_1) → u_1
Vector(P_1, O_1) → v_1
Translate(Q_1, Vector[(2 * u_1)]) → T_1
Translate(R_1, u_1) → S_1
Translate(T_1, Vector[(2 * v_1)]) → U_1
Translate(S_1, v_1) → V_1
Translate(P_1, Vector[(-1 * v_1)]) → W_1
Translate(Q_1, Vector[(-1 * v_1)]) → Z_1
Polygon(Z_1, Q_1, T_1, U_1, V_1, S_1, O_1, W_1) → poly5, z_1, q_2, t_2, u_2, v_2, s_2, o_1, w_1
Mirror(W_1, m_1) → D_2
Mirror(Z_1, m_1) → E_2
Mirror(V_1, m_1) → F_2
Mirror(U_1, m_1) → G_2
Translate(T_1, v_1) → I_2
Point(m_1) → A_2
Point(m_1) → B_2
Point(m_1) → C_2
Segment(A_2, C_2) → g_2
Point(g_2) → H_2
Segment(H_2, A_2) → h_2
Translate(F_2, v_1) → J_2
Polygon(D_2, P_1, J_2, F_2, G_2, I_2, R_1, E_2) → poly6, d_3, p_2, j_3, f_3, g_3, i_3, r_2, e_3
Circle(K_2, a) → k_2
Circle(K_2, (4 * a)) → h_3
Point(h_3) → L_2
Line(K_2, L_2) → l_2
OrthogonalLine(K_2, l_2) → m_2
Intersect(k_2, m_2, 2) → M_2
Intersect(k_2, l_2, 1) → N_2
Intersect(k_2, m_2, 1) → O_2
Intersect(k_2, l_2, 2) → P_2
Line(M_2, l_2) → n_2
Line(O_2, l_2) → k_3
Line(N_2, m_2) → l_3
Line(P_2, m_2) → m_3
Intersect(n_2, l_3) → Q_2
Intersect(k_3, l_3) → R_2
Intersect(k_3, m_3) → S_2
Intersect(n_2, m_3) → T_2
Vector(R_2, S_2) → w_2
Vector(R_2, Q_2) → z_2
Translate(S_2, w_2) → U_2
Translate(U_2, w_2) → V_2
Translate(T_2, w_2) → W_2
Translate(W_2, w_2) → Z_2
Translate(T_2, z_2) → A_3
Translate(W_2, z_2) → B_3
Translate(U_2, Vector[(-1 * z_2)]) → C_3
Translate(V_2, Vector[(-1 * z_2)]) → D_3
Point(l_2) → E_3
Point(l_2) → F_3
Segment(E_3, F_3) → n_3
Point(n_3) → G_3
Segment(E_3, G_3) → p_3
Polygon(R_2, U_2, C_3, D_3, Z_2, W_2, B_3, A_3, T_2, Q_2) → poly7, r_3, q_3, u_3, c_4, d_4, z_3, w_3, b_5, a_4, t_3
Mirror(A_3, l_2) → H_3
Mirror(D_3, l_2) → I_3
Polygon(R_2, S_2, H_3, C_3, U_2, V_2, I_3, B_3, W_2, Q_2) → poly8, r_4, q_4, s_3, h_4, c_5, u_4, v_3, i_4, b_6, w_4
Circle(J_3, a) → e_4
Circle(J_3, (6 * a)) → f_4
Point(f_4) → K_3
Line(J_3, K_3) → g_4
OrthogonalLine(J_3, g_4) → j_4
Intersect(e_4, j_4, 2) → L_3
Intersect(e_4, g_4, 1) → M_3
Intersect(e_4, j_4, 1) → N_3
Intersect(e_4, g_4, 2) → O_3
Line(L_3, g_4) → k_4
Line(N_3, g_4) → l_4
Line(M_3, j_4) → m_4
Line(O_3, j_4) → n_4
Intersect(k_4, m_4) → P_3
Intersect(l_4, m_4) → Q_3
Intersect(l_4, n_4) → R_3
Intersect(k_4, n_4) → S_3
Vector(Q_3, R_3) → v_4
Vector(Q_3, P_3) → z_4
Translate(R_3, v_4) → T_3
Translate(T_3, v_4) → U_3
Translate(U_3, v_4) → V_3
Translate(S_3, v_4) → W_3
Translate(W_3, v_4) → Z_3
Translate(Z_3, v_4) → A_4
Translate(S_3, z_4) → B_4
Translate(W_3, z_4) → C_4
Mirror(B_4, g_4) → D_4
Mirror(C_4, g_4) → E_4
Point(g_4) → G_4
Point(g_4) → H_4
Segment(G_4, H_4) → p_4
Point(p_4) → I_4
Segment(G_4, I_4) → s_4
Polygon(Q_3, V_3, A_4, W_3, C_4, B_4, S_3, P_3) → poly9, q_5, v_5, a_5, w_5, c_6, b_7, s_5, p_5
Polygon(P_3, A_4, V_3, T_3, E_4, D_4, R_3, Q_3) → poly10, p_6, a_6, v_6, t_4, e_5, d_5, r_5, q_6
Circle(J_4, a) → f_5
Circle(J_4, (4 * a)) → g_5
Point(g_5) → K_4
Line(J_4, K_4) → h_5
OrthogonalLine(J_4, h_5) → i_5
Intersect(f_5, i_5, 2) → L_4
Intersect(f_5, i_5, 1) → M_4
Intersect(f_5, h_5, 1) → N_4
Intersect(f_5, h_5, 2) → O_4
Line(L_4, h_5) → j_5
Line(M_4, h_5) → k_5
Line(N_4, i_5) → l_5
Line(O_4, i_5) → m_5
Intersect(j_5, l_5) → P_4
Intersect(k_5, l_5) → Q_4
Intersect(k_5, m_5) → R_4
Intersect(j_5, m_5) → S_4
Vector(Q_4, P_4) → u_5
Vector(Q_4, R_4) → z_5
Translate(R_4, z_5) → T_4
Translate(T_4, z_5) → U_4
Translate(P_4, u_5) → V_4
Translate(V_4, z_5) → W_4
Translate(W_4, z_5) → Z_4
Translate(T_4, u_5) → A_5
Translate(U_4, u_5) → B_5
Point(h_5) → C_5
Point(h_5) → D_5
Mirror(V_4, h_5) → E_5
Mirror(W_4, h_5) → F_5
Mirror(Z_4, h_5) → G_5
Segment(C_5, D_5) → n_5
Point(n_5) → H_5
Segment(C_5, H_5) → t_5
Polygon(V_4, Q_4, U_4, B_5, A_5, Z_4) → poly11, v_7, q_7, u_6, b_8, a_7, z_6
Polygon(P_4, B_5, U_4, T_4, G_5, E_5) → poly12, p_7, b_9, u_7, t_6, g_6, e_6
Circle(I_5, a) → d_6
Circle(I_5, (8 * a)) → f_6
Point(f_6) → J_5
Line(I_5, J_5) → h_6
OrthogonalLine(I_5, h_6) → i_6
Intersect(d_6, i_6, 2) → K_5
Intersect(d_6, h_6, 1) → L_5
Intersect(d_6, i_6, 1) → M_5
Intersect(d_6, h_6, 2) → N_5
Line(K_5, h_6) → j_6
Line(M_5, h_6) → k_6
Line(L_5, i_6) → l_6
Line(N_5, i_6) → m_6
Intersect(j_6, l_6) → O_5
Intersect(k_6, l_6) → P_5
Intersect(k_6, m_6) → Q_5
Intersect(j_6, m_6) → R_5
Vector(P_5, Q_5) → w_6
Translate(Q_5, Vector[(4 * w_6)]) → S_5
Translate(R_5, Vector[(4 * w_6)]) → T_5
Polygon(P_5, S_5, T_5, O_5) → poly13, p_8, s_6, t_7, o_5
Circle(U_5, a) → r_6
Circle(U_5, (4 * a)) → c_7
Point(c_7) → V_5
Line(U_5, V_5) → n_6
OrthogonalLine(U_5, n_6) → d_7
Intersect(r_6, d_7, 2) → W_5
Intersect(r_6, d_7, 1) → Z_5
Intersect(r_6, n_6, 1) → A_6
Intersect(r_6, n_6, 2) → B_6
Line(W_5, n_6) → e_7
Line(Z_5, n_6) → f_7
Line(A_6, d_7) → g_7
Line(B_6, d_7) → h_7
Intersect(e_7, g_7) → C_6
Intersect(f_7, g_7) → D_6
Intersect(f_7, h_7) → E_6
Intersect(e_7, h_7) → F_6
Vector(D_6, E_6) → w_7
Vector(D_6, C_6) → z_7
Vector(F_6, E_6) → i_7
Translate(E_6, i_7) → G_6
Translate(G_6, w_7) → H_6
Translate(H_6, z_7) → I_6
Translate(I_6, w_7) → J_6
Translate(J_6, z_7) → K_6
Translate(F_6, w_7) → L_6
Translate(L_6, z_7) → M_6
Translate(F_6, z_7) → N_6
Polygon(D_6, E_6, F_6, C_6, G_6, H_6, I_6, J_6, K_6, L_6, M_6, N_6) → poly14, d_8, n_7, f_8, c_8, e_8, g_8, h_8, i_8, j_7, k_7, l_7, m_7
Circle(O_6, a) → r_7
Circle(O_6, (4 * a)) → s_7
Point(s_7) → P_6
Line(O_6, P_6) → a_8
OrthogonalLine(O_6, a_8) → j_8
Intersect(r_7, j_8, 2) → Q_6
Intersect(r_7, a_8, 1) → R_6
Intersect(r_7, j_8, 1) → S_6
Intersect(r_7, a_8, 2) → T_6
Line(Q_6, a_8) → k_8
Line(S_6, a_8) → l_8
Line(R_6, j_8) → m_8
Line(T_6, j_8) → n_8
Intersect(k_8, m_8) → U_6
Intersect(l_8, m_8) → V_6
Intersect(l_8, n_8) → W_6
Intersect(k_8, n_8) → Z_6
Vector(V_6, W_6) → u_8
Vector(V_6, U_6) → v_8
Translate(W_6, Vector[(2 * u_8)]) → A_7
Translate(Z_6, Vector[(2 * u_8)]) → B_7
Translate(U_6, Vector[(2 * v_8)]) → C_7
Translate(Z_6, Vector[(2 * v_8)]) → D_7
Polygon(V_6, A_7, B_7, Z_6, D_7, C_7) → poly15, v_9, a_9, b_{10}, z_8, d_9, c_9
Circle(E_7, a) → q_8
Circle(E_7, (4 * a)) → r_8
Point(r_8) → F_7
Line(E_7, F_7) → s_8
OrthogonalLine(E_7, s_8) → t_8
Intersect(q_8, t_8, 2) → G_7
Intersect(q_8, s_8, 1) → H_7
Intersect(q_8, t_8, 1) → I_7
Intersect(q_8, s_8, 2) → J_7
Line(G_7, s_8) → e_9
Line(I_7, s_8) → f_9
Line(H_7, t_8) → g_9
Line(J_7, t_8) → h_9
Intersect(e_9, g_9) → K_7
Intersect(f_9, g_9) → L_7
Intersect(f_9, h_9) → M_7
Intersect(e_9, h_9) → N_7
Vector(L_7, M_7) → w_8
Vector(L_7, K_7) → u_9
Translate(M_7, Vector[(2 * w_8)]) → O_7
Translate(N_7, Vector[(2 * w_8)]) → P_7
Translate(N_7, w_8) → Q_7
Translate(N_7, Vector[(2 * u_9)]) → R_7
Translate(Q_7, Vector[(2 * u_9)]) → S_7
Polygon(L_7, O_7, P_7, Q_7, S_7, R_7, N_7, K_7) → poly16, l_9, o_7, p_9, q_9, s_9, r_9, n_9, k_9
Circle(T_7, a) → t_9
Circle(T_7, (2 * a)) → c_{10}
Point(c_{10}) → U_7
Line(T_7, U_7) → i_9
OrthogonalLine(T_7, i_9) → j_9
Intersect(t_9, j_9, 2) → V_7
Intersect(t_9, i_9, 1) → W_7
Intersect(t_9, j_9, 1) → Z_7
Intersect(t_9, i_9, 2) → A_8
Line(V_7, i_9) → m_9
Line(Z_7, i_9) → a_{10}
Line(W_7, j_9) → d_{10}
Line(A_8, j_9) → e_{10}
Intersect(m_9, d_{10}) → B_8
Intersect(a_{10}, d_{10}) → C_8
Intersect(a_{10}, e_{10}) → D_8
Intersect(m_9, e_{10}) → E_8
Vector(C_8, D_8) → w_9
Vector(C_8, B_8) → z_9
Vector(E_8, D_8) → u_{10}
Vector(E_8, B_8) → v_{10}
Translate(D_8, w_9) → F_8
Translate(F_8, z_9) → G_8
Translate(G_8, z_9) → H_8
Translate(E_8, z_9) → I_8
Translate(B_8, z_9) → J_8
Translate(J_8, v_{10}) → K_8
Translate(C_8, v_{10}) → L_8
Polygon(L_8, F_8, H_8, I_8, E_8, B_8, J_8, K_8) → poly17, l_{10}, f_{10}, h_{10}, i_{10}, e_{11}, b_{11}, j_{10}, k_{10}
Circle(M_8, a) → g_{10}
Circle(M_8, (2 * a)) → p_{10}
Point(p_{10}) → N_8
Line(M_8, N_8) → m_{10}
OrthogonalLine(M_8, m_{10}) → n_{10}
Intersect(g_{10}, n_{10}, 2) → O_8
Intersect(g_{10}, m_{10}, 1) → P_8
Intersect(g_{10}, n_{10}, 1) → Q_8
Intersect(g_{10}, m_{10}, 2) → R_8
Line(O_8, m_{10}) → q_{10}
Line(Q_8, m_{10}) → r_{10}
Line(P_8, n_{10}) → s_{10}
Line(R_8, n_{10}) → t_{10}
Intersect(q_{10}, s_{10}) → S_8
Intersect(r_{10}, s_{10}) → T_8
Intersect(r_{10}, t_{10}) → U_8
Intersect(q_{10}, t_{10}) → V_8
Vector(T_8, U_8) → w_{10}
Vector(V_8, S_8) → z_{10}
Vector(T_8, S_8) → u_{11}
Vector(V_8, U_8) → v_{11}
Translate(U_8, w_{10}) → W_8
Translate(V_8, w_{10}) → Z_8
Translate(V_8, u_{11}) → A_9
Translate(S_8, u_{11}) → B_9
Translate(S_8, z_{10}) → C_9
Translate(C_9, u_{11}) → D_9
Translate(D_9, u_{11}) → E_9
Translate(B_9, u_{11}) → F_9
Polygon(T_8, W_8, Z_8, V_8, A_9, B_9, F_9, E_9, C_9, S_8) → poly18, t_{11}, s_{11}, w_{11}, z_{11}, v_{12}, a_{11}, b_{12}, f_{11}, e_{12}, c_{11}
Polygon(G_9, H_9, J_9, I_9) → poly19, g_{11}, h_{11}, j_{11}, i_{11}
Polygon(G_9, L_9, K_9, M_9) → poly20, g_{12}, l_{11}, k_{11}, m_{11}

AI Drawing Prompt Reference

Draw a geometric shape composed of multiple pentominoes. Start by drawing a circle c, then a larger circle k, and select point M from it. Draw a line d through M and its perpendicular line e, intersecting circle c at points E and F. Continue by drawing lines f, g, h, and i, and points, using translations and reflections to form two pentominoes poly1 and poly2.

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