Mondrian Art Fractions: Color Area Proportions as Fractions

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2020-08-06 05:00

This GeoGebra example demonstrates how changing the proportions of red, white, blue, and yellow regions in a Mondrian-style partition affects their corresponding fractions of the total area. It focuses on reasoning about fraction/percentage equivalence and checking that the sum of all colored parts matches the whole, as well as comparing how one color’s area relates to another. The construction uses core commands from the provided construction summary: Polygon and Point to define the outer shape and key vertices, Line to create the partition lines, and Intersect to compute intersection points that determine the boundaries of each colored region (e.g., objects like A, B, poly1, C, D, E and their numbered variants). Suitable for middle/high school learners and for classroom interactive activities on fraction modeling through geometry, area proportion, and visual verification.

GeoGebra Commands & Parameters

Polygon(A, B, 4) → poly1, a, b, c, d, C, D
Point(c) → E
Line(E, b) → e
Polygon(A_1, B_1, 4) → poly1_1, a_1, b_1, c_1, d_1, C_1, D_1
Point(c) → F
Line(F, e) → f
Point(c) → G
Line(G, b) → g
Point(c) → H
Line(H, b) → h
Point(c) → I
Line(I, b) → i
Point(c) → J
Line(J, b) → j
Point(c) → K
Line(K, b) → k
Point(b) → L
Line(L, c) → l
Point(b) → M
Line(M, c) → m
Point(b) → N
Line(N, c) → n
Point(b) → O
Line(O, c) → p
Point(b) → P
Line(P, c) → q
Point(b) → Q
Line(Q, a) → r
Point(b) → R
Line(R, a) → s
Intersect(j, l) → S
Intersect(j, m) → T
Intersect(j, n) → U
Intersect(j, p) → V
Intersect(j, q) → W
Intersect(r, j) → Z
Intersect(s, j) → F_1
Intersect(s, poly1) → G_1, H_1
Intersect(h, s) → I_1
Intersect(r, h) → J_1
Intersect(h, q) → K_1
Intersect(h, poly1) → L_1, M_1
Intersect(p, h) → N_1
Intersect(h, n) → O_1
Intersect(h, m) → P_1
Intersect(h, l) → Q_1
Intersect(e, l) → R_1
Intersect(e, m) → S_1
Intersect(e, n) → T_1
Intersect(e, p) → U_1
Intersect(e, q) → V_1
Intersect(e, r) → W_1
Intersect(e, s) → Z_1
Intersect(s, g) → A_2
Intersect(r, g) → B_2
Intersect(g, q) → C_2
Intersect(p, g) → D_2
Intersect(n, g) → E_2
Intersect(g, m) → F_2
Intersect(g, l) → G_2
Intersect(f, l) → H_2
Intersect(f, poly1) → I_2, J_2
Intersect(m, f) → K_2
Intersect(f, n) → L_2
Intersect(p, poly1) → M_2, N_2
Intersect(p, f) → O_2
Intersect(f, poly1) → P_2, Q_2
Intersect(q, f) → R_2
Intersect(r, f) → S_2
Intersect(s, f) → T_2
Intersect(s, i) → U_2
Intersect(r, i) → V_2
Intersect(q, i) → W_2
Intersect(p, i) → Z_2
Intersect(n, poly1) → A_3, B_3
Intersect(i, poly1) → C_3, D_3
Intersect(n, i) → E_3
Intersect(i, m) → F_3
Intersect(i, l) → G_3
Intersect(l, k) → H_3
Intersect(m, k) → I_3
Intersect(n, k) → J_3
Intersect(p, k) → K_3
Intersect(q, k) → L_3
Intersect(r, poly1) → M_3, N_3
Intersect(r, poly1) → O_3, P_3
Intersect(k, r) → Q_3
Intersect(k, s) → R_3
Intersect(m, d) → S_3
Intersect(l, d) → T_3
Intersect(q, d) → U_3
Intersect(e, a) → V_3
Intersect(j, a) → W_3
Intersect(e, poly1) → Z_3, A_4
Intersect(g, a) → B_4
Intersect(k, a) → C_4
Polygon(C, L, S, J) → poly2, c_2, l_1, s_1, j_1
Polygon(L, M, T, S) → poly3, l_2, m_1, t, s_2
Polygon(M, N, U, T) → poly4, m_2, n_1, u, t_1
Polygon(N, O, V, U) → poly5, n_2, o, v, u_1
Polygon(O, P, W, V) → poly6, o_1, p_1, w, v_1
Polygon(P, Q, Z, W) → poly7, p_2, q_1, z, w_1
Polygon(Q, R, F_1, Z) → poly8, q_2, r_1, f_1, z_1
Polygon(R, B, W_3, F_1) → poly9, r_2, b_2, w_3, f_2
Polygon(W_3, F_1, I_1, L_1) → poly10, w_2, f_3, i_1, l_3
Polygon(F_1, Z, J_1, I_1) → poly11, f_4, z_2, j_2, i_2
Polygon(W, Z, J_1, K_1) → poly12, w_4, z_3, j_3, k_1
Polygon(W, K_1, N_1, V) → poly13, w_5, k_2, n_3, v_2
Polygon(V, U, O_1, N_1) → poly14, v_3, u_2, o_2, n_4
Polygon(U, T, P_1, O_1) → poly15, u_3, t_2, p_3, o_3
Polygon(T, S, Q_1, P_1) → poly16, t_3, s_3, q_3, p_4
Polygon(S, J, H, Q_1) → poly17, s_4, j_4, h_1, q_4
Polygon(Q_1, R_1, E, H) → poly18, q_5, r_3, e_2, h_2
Polygon(Q_1, P_1, S_1, R_1) → poly19, q_6, p_5, s_5, r_4
Polygon(P_1, O_1, T_1, S_1) → poly20, p_6, o_4, t_4, s_6
Polygon(O_1, N_1, U_1, T_1) → poly21, o_5, n_5, u_4, t_5
Polygon(N_1, K_1, V_1, U_1) → poly22, n_6, k_3, v_4, u_5
Polygon(K_1, J_1, W_1, V_1) → poly23, k_4, j_5, w_6, v_5
Polygon(J_1, I_1, Z_1, W_1) → poly24, j_6, i_3, z_4, w_7
Polygon(I_1, L_1, V_3, Z_1) → poly25, i_4, l_4, v_6, z_5
Polygon(V_3, B_4, A_2, Z_1) → poly26, v_7, b_4, a_2, z_6
Polygon(Z_1, W_1, B_2, A_2) → poly27, z_7, w_8, b_3, a_3
Polygon(W_1, V_1, C_2, B_2) → poly28, w_9, v_8, c_3, b_5
Polygon(V_1, C_2, D_2, U_1) → poly29, v_9, c_4, d_2, u_6
Polygon(U_1, T_1, E_2, D_2) → poly30, u_7, t_6, e_3, d_3
Polygon(T_1, S_1, F_2, E_2) → poly31, t_7, s_7, f_5, e_4
Polygon(S_1, R_1, G_2, F_2) → poly32, s_8, r_5, g_2, f_6
Polygon(R_1, E, G, G_2) → poly33, r_6, e_5, g_1, g_3
Polygon(G_2, H_2, F, G) → poly34, g_4, h_3, f_7, g_5
Polygon(G_2, F_2, K_2, H_2) → poly35, g_6, f_8, k_5, h_4
Polygon(F_2, E_2, L_2, K_2) → poly36, f_9, e_6, l_5, k_6
Polygon(E_2, D_2, O_2, L_2) → poly37, e_7, d_4, o_6, l_6
Polygon(D_2, C_2, R_2, O_2) → poly38, d_5, c_5, r_7, o_7
Polygon(C_2, B_2, S_2, R_2) → poly39, c_6, b_6, s_9, r_8
Polygon(B_2, A_2, T_2, S_2) → poly40, b_7, a_4, t_8, s_{10}
Polygon(A_2, B_4, I_2, T_2) → poly41, a_5, b_8, i_5, t_9
Polygon(I_2, C_3, U_2, T_2) → poly42, i_6, c_7, u_8, t_{10}
Polygon(T_2, S_2, V_2, U_2) → poly43, t_{11}, s_{11}, v_{10}, u_9
Polygon(S_2, R_2, W_2, V_2) → poly44, s_{12}, r_9, w_{10}, v_{11}
Polygon(R_2, O_2, Z_2, W_2) → poly45, r_{10}, o_8, z_8, w_{11}
Polygon(O_2, L_2, E_3, Z_2) → poly46, o_9, l_7, e_8, z_9
Polygon(L_2, E_3, F_3, K_2) → poly47, l_8, e_9, f_{10}, k_7
Polygon(K_2, F_3, G_3, H_2) → poly48, k_8, f_{11}, g_7, h_5
Polygon(H_2, G_3, I, F) → poly49, h_6, g_8, i_7, f_{12}
Polygon(G_3, H_3, K, I) → poly50, g_9, h_7, k_9, i_8
Polygon(G_3, F_3, I_3, H_3) → poly51, g_{10}, f_{13}, i_9, h_8
Polygon(E_3, J_3, I_3, F_3) → poly52, e_{10}, j_7, i_{10}, f_{14}
Polygon(E_3, Z_2, K_3, J_3) → poly53, e_{11}, z_{10}, k_{10}, j_8
Polygon(Z_2, W_2, L_3, K_3) → poly54, z_{11}, w_{12}, l_9, k_{11}
Polygon(W_2, V_2, Q_3, L_3) → poly55, w_{13}, v_{12}, q_7, l_{10}
Polygon(V_2, U_2, R_3, Q_3) → poly56, v_{13}, u_{10}, r_{11}, q_8
Polygon(U_2, C_3, C_4, R_3) → poly57, u_{11}, c_8, c_9, r_{12}
Polygon(C_4, R_3, G_1, A) → poly58, c_{10}, r_{13}, g_{11}, a_6
Polygon(R_3, Q_3, M_3, G_1) → poly59, r_{14}, q_9, m_3, g_{12}
Polygon(Q_3, M_3, U_3, L_3) → poly60, q_{10}, m_4, u_{12}, l_{11}
Polygon(L_3, K_3, N_2, U_3) → poly61, l_{12}, k_{12}, n_7, u_{13}
Polygon(K_3, J_3, B_3, N_2) → poly62, k_{13}, j_9, b_9, n_8
Polygon(J_3, I_3, S_3, B_3) → poly63, j_{10}, i_{11}, s_{13}, b_{10}
Polygon(I_3, H_3, T_3, S_3) → poly64, i_{12}, h_9, t_{12}, s_{14}
Polygon(H_3, K, D, T_3) → poly65, h_{10}, k_{14}, d_6, t_{13}

AI Drawing Prompt Reference

Draw a Mondrian-style partition: start with a closed polygon as the outer frame, then split its interior into several adjacent regions using a set of straight partition lines. First define the outer polygon by its key vertices. Choose internal points and draw lines through them along a consistent set of directions (linked to the chosen base directions) so that the partition lines intersect. Compute all relevant intersection points and use those points to form the boundaries of each region. The result should be multiple neighboring polygonal areas whose relative sizes can be compared as fractions/percentages of the total area, focusing on how one part’s area relates to another and that all colored parts fit together within the original outer polygon.

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