Dice Multiplication: Combinations of 2–6 with GeoGebra

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2020-02-11 15:44

In collections Multiply with Dice

This GeoGebra example dynamically illustrates multiplication combinations using dice faces 2 through 6, revealing the interplay between numeric values and geometric transformations. Core concepts include combinatorics, probability, and parametric geometry. Construction employs GeoGebra commands such as Shuffle, Random, Rotate, Polygon, and Intersect, along with points, polygons, angles, and midpoints to generate an interactive multiplication visualization. It is suited for high school mathematics, probability units, and geometric exploration, serving as a tool for classroom demonstration and student-driven investigation of number-pattern geometry.

GeoGebra Commands & Parameters

Shuffle(dlist) → dl, {1, 7, 5, 4, 3, 9, 8, 6, 10, 2}
Element(dl, dsl) → dice
Shuffle(positionlist) → pl, {(20.841465339293297, 21.571366222300522), (2, 16), (13.792512983476586, 15.925190454706042), (14.879664839348814, 21.886990954650525), (4.53418750120986, 10.489431175344896), (8.35675370411544, 21.60643563700608), (2.184536715937622, 21.851921539944968), (20.701187680471076, 10.033528784172672), (7.865781898237659, 15.855051625294932), (19.75431348342107, 15.78491279588382)}
Element(pl, 1) → A
Element(pl, 2) → B
Element(pl, 3) → C
Element(pl, 4) → D
Element(pl, 5) → E
Element(pl, 6) → F
Element(pl, 7) → G
Element(pl, 8) → H
Element(pl, 9) → I
Element(pl, 10) → J
Circle(A, sd) → c
Circle(B, sd) → d
Circle(C, sd) → e
Circle(D, sd) → f
Circle(E, sd) → g
Circle(J, sd) → h
Circle(I, sd) → k
Circle(H, sd) → p
Circle(G, sd) → q
Random(90, 270) → a1
Circle(F, sd) → r
Point(c) → K
Point(d) → L
Point(e) → M
Point(f) → N
Point(g) → O
Rotate(K, a1°, A) → K'
Angle(K, A, K') → α
Polygon(A, K', 4) → poly1, i, j, l, m, P, Q
Random(0, 360) → a2
Random(0, 360) → a3
Random(0, 360) → a4
Random(0, 360) → a5
Random(0, 360) → a6
Random(0, 360) → a7
Random(0, 360) → a8
Random(0, 360) → a9
Random(0, 360) → a10
Point(r) → R
Point(q) → S
Point(p) → T
Point(k) → U
Point(h) → V
Rotate(L, a2°, B) → L'
Angle(L, B, L') → β
Rotate(M, a3°, C) → M'
Angle(M, C, M') → γ
Rotate(N, a4°, D) → N'
Angle(N, D, N') → δ
Rotate(O, a5°, E) → O'
Angle(O, E, O') → ε
Rotate(R, a6°, F) → R'
Angle(R, F, R') → ζ
Rotate(S, a7°, G) → S'
Angle(S, G, S') → η
Rotate(T, a8°, H) → T'
Angle(T, H, T') → θ
Rotate(U, a9°, I) → U'
Angle(U, I, U') → ι
Rotate(V, a10°, J) → V'
Angle(V, J, V') → κ
Polygon(B, L', 4) → poly2, n, s, t, a, W, Z
Polygon(C, M', 4) → poly3, b, f_1, g_1, h_1, A_1, B_1
Polygon(D, N', 4) → poly4, i_1, j_1, k_1, l_1, C_1, D_1
Polygon(E, O', 4) → poly5, m_1, n_1, p_1, q_1, E_1, F_1
Polygon(F, R', 4) → poly6, r_1, s_1, t_1, a_1, G_1, H_1
Polygon(G, S', 4) → poly7, b_1, c_1, d_1, e_1, I_1, J_1
Polygon(H, T', 4) → poly8, f_2, g_2, h_2, i_2, K_1, L_1
Polygon(I, U', 4) → poly9, j_2, k_2, l_2, m_2, M_1, N_1
Polygon(J, V', 4) → poly10, n_2, p_2, q_2, r_2, O_1, P_1
Circle(J, O_1) → c_2
Circle(H, K_1) → d_2
Circle(G, I_1) → e_2
Circle(F, G_1) → s_2
Circle(E, E_1) → t_2
Circle(D, C_1) → c_3
Circle(C, A_1) → d_3
Circle(B, W) → e_3
Circle(I, M_1) → f_3
Circle(A, P) → g_3
Midpoint(K', Q) → Q_1
Midpoint(Q_1, Q) → R_1
Midpoint(K', Q_1) → S_1
Midpoint(B, W) → T_1
Midpoint(T_1, W) → U_1
Midpoint(B, T_1) → V_1
Midpoint(C, A_1) → W_1
Midpoint(C, W_1) → Z_1
Midpoint(W_1, A_1) → A_2
Midpoint(D, C_1) → B_2
Midpoint(D, B_2) → C_2
Midpoint(B_2, C_1) → D_2
Midpoint(E, E_1) → E_2
Midpoint(E_2, E_1) → F_2
Midpoint(E, E_2) → G_2
Midpoint(F, G_1) → H_2
Midpoint(H_2, G_1) → I_2
Midpoint(F, H_2) → J_2
Midpoint(G, I_1) → K_2
Midpoint(G, K_2) → L_2
Midpoint(I_1, K_2) → M_2
Midpoint(H, K_1) → N_2
Midpoint(H, N_2) → O_2
Midpoint(N_2, K_1) → P_2
Midpoint(J, O_1) → Q_2
Midpoint(J, Q_2) → R_2
Midpoint(Q_2, O_1) → S_2
Midpoint(M_1, I) → T_2
Midpoint(M_1, T_2) → U_2
Midpoint(T_2, I) → V_2
Element(dl, dsl) → dn
Textfield(kiddice) → InputBox1
Textfield(kiddots) → InputBox2
Intersect(j, l) → E_3
Intersect(t, a) → F_3
Intersect(g_1, h_1) → G_3
Intersect(k_1, l_1) → H_3
Intersect(p_1, q_1) → I_3
Intersect(t_1, a_1) → J_3
Intersect(d_1, e_1) → K_3
Intersect(h_2, i_2) → L_3
Intersect(l_2, m_2) → M_3
Intersect(n_2, p_2) → N_3
Intersect(q_2, r_2) → O_3
Midpoint(A, Q_1) → P_3
Midpoint(Q_1, E_3) → Q_3
Midpoint(F_3, T_1) → R_3
Midpoint(L', T_1) → S_3
Midpoint(M', W_1) → T_3
Midpoint(W_1, G_3) → U_3
Midpoint(H_3, B_2) → V_3
Midpoint(B_2, N') → W_3
Midpoint(E_2, I_3) → Z_3
Midpoint(E_2, O') → A_4
Midpoint(R', H_2) → B_4
Midpoint(H_2, J_3) → C_4
Midpoint(K_2, S') → D_4
Midpoint(K_3, K_2) → E_4
Midpoint(L_3, N_2) → F_4
Midpoint(N_2, T') → G_4
Midpoint(U', T_2) → H_4
Midpoint(T_2, M_3) → I_4
Midpoint(N_3, Q_2) → J_4
Midpoint(Q_2, O_3) → K_4
Midpoint(Q_3, R_1) → B_3
Midpoint(S_1, P_3) → C_3
Midpoint(S_3, U_1) → D_3
Midpoint(V_1, R_3) → L_4
Midpoint(V_3, C_2) → M_4
Midpoint(D_2, W_3) → N_4
Midpoint(A_2, U_3) → O_4
Midpoint(T_3, Z_1) → P_4
Midpoint(U_2, I_4) → Q_4
Midpoint(H_4, V_2) → R_4
Midpoint(C_4, J_2) → S_4
Midpoint(I_2, B_4) → T_4
Midpoint(P_2, G_4) → U_4
Midpoint(F_4, O_2) → V_4
Midpoint(E_4, M_2) → W_4
Midpoint(L_2, D_4) → Z_4
Midpoint(K_4, S_2) → A_5
Midpoint(F_2, A_4) → B_5
Midpoint(Z_3, G_2) → C_5
Midpoint(R_2, J_4) → D_5

AI Drawing Prompt Reference

Draw a combination of two dice with faces numbered 2 to 6. First, randomly generate the positions of the two dice, then draw circles around the centers of each die. Next, randomly rotate the circles and generate new polygons through rotation to show the multiplication combinations of the two dice.

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