Translation Tesselation by jahatch8

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2014-03-30 05:25

In collections Tesselation by Translation Tesselation by Translation

This example demonstrates how to create plane tesselation patterns using translation operations. Core math concepts include translation transformation, equilateral triangles, centroid, vector operations. Construction highlights Polygon, AttachCopyToView, Point, Vector, Translate commands/objects in GeoGebra. Suitable for high school mathematics teaching to understand geometric transformations and tesselation principles.

GeoGebra Commands & Parameters

Polygon(A, B, 4) → poly1, a, b, c, d, C, D
AttachCopyToView(PolyLine[(3.14, -4), (3.14, -4.12), (3.12, -4.18), (3.1, -4.28), (3.08, -4.34), (3.06, -4.4), (3.04, -4.46), (3.02, -4.58), (3, -4.68), (2.98, -4.74), (2.98, -4.82), (2.96, -4.88), (2.88, -4.88), (2.82, -4.9), (2.74, -4.9), (2.66, -4.9), (2.58, -4.92), (2.48, -4.92), (2.4, -4.92), (2.34, -4.94), (2.2600000000000002, -4.94), (2.18, -4.94), (2.1, -4.96), (2.06, -5.04), (2, -5.12), (1.96, -5.2), (1.9000000000000001, -5.28), (1.86, -5.34), (1.82, -5.4), (1.78, -5.46), (1.72, -5.5), (1.6600000000000001, -5.44), (1.62, -5.38), (1.56, -5.34), (1.54, -5.28), (1.52, -5.22), (1.58, -5.18), (1.62, -5.12), (1.68, -5.08), (1.72, -5.0200000000000005), (1.76, -4.96), (1.82, -4.94), (1.84, -4.88), (1.9000000000000001, -4.86), (1.96, -4.84), (2.02, -4.82), (2.08, -4.8), (2.14, -4.76), (2.2, -4.74), (2.2600000000000002, -4.7), (2.32, -4.68), (2.4, -4.64), (2.46, -4.6000000000000005), (2.44, -4.54), (2.38, -4.48), (2.32, -4.42), (2.2800000000000002, -4.36), (2.22, -4.34), (2.16, -4.28), (2.1, -4.22), (2.04, -4.2), (1.94, -4.14), (1.86, -4.1), (1.8, -4.0600000000000005), (1.72, -4.0200000000000005), (1.6600000000000001, -4), (1.6, -3.94), (1.54, -3.9), (1.48, -3.86), (1.52, -3.8000000000000003), (1.6, -3.7800000000000002), (1.6600000000000001, -3.7600000000000002), (1.72, -3.72), (1.78, -3.7), (1.84, -3.66), (1.9000000000000001, -3.64), (1.98, -3.6), (2.06, -3.58), (2.14, -3.54), (2.12, -3.48), (2.06, -3.46), (2, -3.44), (1.92, -3.38), (1.86, -3.3200000000000003), (1.8, -3.3000000000000003), (1.74, -3.24), (1.68, -3.2), (1.62, -3.14), (1.56, -3.1), (1.5, -3.04), (1.44, -3), (1.42, -2.94), (1.36, -2.96), (1.3, -2.98), (1.24, -3), (1.18, -3.02), (1.1, -3.02), (1.02, -3.04), (0.9400000000000001, -3.04), (0.86, -3.04), (0.8, -3.02), (0.72, -2.98), (0.66, -2.92), (0.6, -2.86), (0.56, -2.8000000000000003), (0.52, -2.72), (0.44, -2.62), (0.36, -2.56), (0.34, -2.5), (0.28, -2.44), (0.22, -2.42), (0.18, -2.48), (0.12, -2.54), (0.08, -2.6), (0.02, -2.64), (-0.02, -2.7), (-0.08, -2.74), (-0.14, -2.8000000000000003), (-0.2, -2.84), (-0.26, -2.86), (-0.34, -2.88), (-0.42, -2.88), (-0.5, -2.88), (-0.58, -2.88), (-0.66, -2.88), (-0.74, -2.92), (-0.78, -2.98), (-0.84, -3.02), (-0.9, -3.04), (-0.96, -3.08), (-0.98, -3.14), (-0.98, -3.22), (-0.98, -3.3000000000000003), (-0.96, -3.36), (-1.02, -3.42), (-1.08, -3.48), (-1.1400000000000001, -3.54), (-1.2, -3.58), (-1.26, -3.64), (-1.3, -3.7), (-1.32, -3.7600000000000002), (-1.28, -3.8200000000000003), (-1.26, -3.88), (-1.22, -3.94), true], 1, (-4.3, -7.96), (23.38, 6.3), (0, 713), (1384, 0)) → stroke1
Point(a) → E
Vector(E, F) → u
Translate(stroke1, u) → stroke1'
AttachCopyToView(PolyLine[(-1.2, -3.94), (-1.26, -4), (-1.3, -4.0600000000000005), (-1.34, -4.12), (-1.3800000000000001, -4.18), (-1.4000000000000001, -4.12), (-1.42, -4.0600000000000005), (-1.46, -4), (-1.5, -3.92), (-1.54, -3.86), (-1.58, -3.8000000000000003), (-1.62, -3.74), (-1.6, -3.64), (-1.54, -3.58), (-1.48, -3.54), (-1.42, -3.5), (-1.3800000000000001, -3.44), (-1.34, -3.36), (-1.34, -3.2800000000000002), (-1.32, -3.22), (-1.32, -3.14), (-1.3, -3.06), (-1.28, -3), (-1.28, -2.92), (-1.28, -2.84), (-1.28, -2.7600000000000002), (-1.22, -2.72), (-1.16, -2.7), (-1.08, -2.68), (-1.02, -2.62), (-0.96, -2.58), (-0.88, -2.5), (-0.8, -2.42), (-0.74, -2.38), (-0.66, -2.34), (-0.6, -2.3000000000000003), (-0.54, -2.2600000000000002), (-0.48, -2.22), (-0.42, -2.2), (-0.36, -2.16), (-0.3, -2.14), (-0.32, -2.08), (-0.36, -2.02), (-0.38, -1.96), (-0.44, -1.9000000000000001), (-0.48, -1.84), (-0.54, -1.78), (-0.6, -1.72), (-0.64, -1.6600000000000001), (-0.66, -1.6), (-0.72, -1.6600000000000001), (-0.74, -1.72), (-0.78, -1.8), (-0.84, -1.86), (-0.9, -1.9000000000000001), (-0.96, -1.94), (-1.02, -2), (-1.06, -2.06), (-1, -2.08), (-0.9400000000000001, -2.04), (-0.86, -2.02), (-0.78, -2.02), (-0.72, -2), (-0.66, -1.98), (-0.6, -1.96), (-0.58, -2.02), (-0.58, -2.1), (-0.6, -2.16), (-0.62, -2.22), (-0.7000000000000001, -2.22), (-0.78, -2.22), (-0.86, -2.22), (-0.92, -2.24), (-1, -2.2600000000000002), (-1.06, -2.2800000000000002), (-1.12, -2.3000000000000003), (-1.2, -2.3000000000000003), (-1.26, -2.32), (-1.34, -2.32), (-1.3800000000000001, -2.24), (-1.3800000000000001, -2.16), (-1.3800000000000001, -2.08), (-1.4000000000000001, -2.02), (-1.4000000000000001, -1.94), (-1.42, -1.8800000000000001), (-1.42, -1.8), (-1.36, -1.76), (-1.28, -1.68), (-1.22, -1.6400000000000001), (-1.16, -1.6), (-1.12, -1.54), (-1.08, -1.48), (-1.06, -1.42), (-1.04, -1.32), (-1.02, -1.26), (-1, -1.2), (-0.96, -1.12), (-0.9400000000000001, -1.06), (-0.86, -1.06), (-0.8, -1.08), (-0.72, -1.1), (-0.64, -1.12), (-0.58, -1.1400000000000001), (-0.52, -1.18), (-0.46, -1.22), (-0.38, -1.24), (-0.32, -1.26), (-0.26, -1.28), (-0.22, -1.22), (-0.2, -1.16), (-0.16, -1.08), (-0.12, -1.02), (-0.08, -0.96), (-0.04, -0.88), (0, -0.8200000000000001), (0.06, -0.78), (0.12, -0.7000000000000001), (0.16, -0.64), (0.22, -0.58), (0.28, -0.52), (0.32, -0.46), (0.38, -0.4), (0.44, -0.38), (0.5, -0.32), (0.56, -0.28), (0.6, -0.22), (0.6, -0.12), (0.64, 0.02), (0.64, 0.1), (0.68, 0.18), (0.7000000000000001, 0.26), (0.72, 0.34), (0.76, 0.42), (0.78, 0.52), (0.8200000000000001, 0.58), (0.84, 0.66), (0.86, 0.72), (0.78, 0.72), (0.7000000000000001, 0.72), (0.62, 0.76), (0.56, 0.8), (0.48, 0.8200000000000001), (0.4, 0.84), (0.34, 0.86), (0.28, 0.9), (0.22, 0.92), (0.16, 0.9400000000000001), (0.08, 0.96), (0.02, 0.98), (-0.06, 0.98), (-0.14, 0.96), (-0.2, 0.92), (-0.26, 0.86), (-0.28, 0.8), (-0.34, 0.76), (-0.38, 0.68), (-0.42, 0.62), (-0.46, 0.56), (-0.48, 0.5), (-0.54, 0.46), (-0.6, 0.44), (-0.68, 0.44), (-0.76, 0.44), (-0.84, 0.44), (-0.9, 0.42), (-0.98, 0.42), (-1.04, 0.4), (-1.12, 0.4), true], 1, (-4.3, -7.96), (23.38, 6.3), (0, 713), (1384, 0)) → stroke2
Point(d) → G
Point(b) → H
Vector(G, H) → v
Translate(stroke2, v) → stroke2'
Vector(A, D) → w
Translate(stroke1, w) → stroke1'_1
Translate(stroke1', w) → stroke1''
Translate(stroke2, w) → stroke2'_1
Translate(stroke2', w) → stroke2''
Translate(B, w) → B'
Translate(C, w) → C'
Translate(E, w) → E'
Translate(F, w) → F'
Translate(G, w) → G'
Translate(H, w) → H'
Point(stroke1') → I
Point(stroke1') → J
Point(stroke1') → K
Point(stroke1') → L
Point(stroke1') → M
Point(stroke1'_1) → N
Point(stroke1') → O
Point(stroke1') → P
Point(stroke1') → Q
Point(stroke1') → R
Point(stroke1') → S
Point(stroke1') → T
Point(stroke1'_1) → U
Point(stroke1') → V
Point(stroke1') → W
Point(stroke1') → Z
Point(stroke2') → A_1
Point(stroke2') → B_1
Point(stroke2') → C_1
Point(stroke2') → D_1
Point(stroke2') → E_1
Point(stroke2') → F_1
Point(stroke2') → G_1
Point(stroke2') → H_1
Point(stroke2') → I_1
Point(stroke2') → J_1
Point(stroke2') → K_1
Point(stroke2') → L_1
Point(stroke2') → M_1
Point(stroke2') → P_1
Point(stroke2') → Q_1
Point(stroke2') → R_1
Point(stroke2') → S_1
Point(stroke2') → T_1
Point(stroke1) → U_1
Point(stroke1) → V_1
Point(stroke1) → W_1
Point(stroke1) → Z_1
Point(stroke1) → A_2
Point(stroke1) → B_2
Point(stroke1) → C_2
Point(stroke1) → D_2
Point(stroke1) → E_2
Point(stroke1) → F_2
Point(stroke1) → G_2
Point(stroke1) → H_2
Point(stroke1) → J_2
Point(stroke1) → K_2
Point(stroke1) → L_2
Point(stroke2) → M_2
Point(stroke2) → O_2
Point(stroke2) → P_2
Point(stroke2) → Q_2
Point(stroke2) → S_2
Point(stroke2) → T_2
Point(stroke2) → U_2
Point(stroke2) → V_2
Point(stroke2) → W_2
Point(stroke2) → Z_2
Point(stroke2) → B_3
Point(stroke2) → C_3
Point(stroke2) → D_3
Point(stroke2) → E_3
Point(stroke2) → F_3
Polygon(D, I, R, S, T, U, V, W, Z, H, C, A_1, J, B_1, C_1, D_1, E_1, F_1, G_1, H_1, I_1, J_1, K_1, K, M_1, N_1, O_1, P_1, Q_1, R_1, S_1, T_1, B, U_1, L, V_1, W_1, Z_1, A_2, B_2, C_2, D_2, E_2, F_2, G_2, M, H_2, I_2, J_2, K_2, L_2, A, M_2, N_2, O_2, P_2, N, Q_2, R_2, S_2, T_2, U_2, V_2, W_2, Z_2, A_3, B_3, O, F, E', D_3, E_3, F_3, P, Q) → poly2, d_1, q, r, s, t, u_1, v_1, w_1, z, h, c_1, i, a_1, b_1, c_2, d_2, e_1, f_1, g_1, h_1, i_1, j_1, j, k_1, m_1, n_1, o_1, p_1, q_1, r_1, s_1, t_1, b_2, k, u_2, v_2, w_2, z_1, a_2, b_3, c_3, d_3, e_2, f_2, l, g_2, h_2, i_2, j_2, k_2, l_2, a_3, m_2, n_2, o_2, m, p_2, q_2, r_2, s_2, t_2, u_3, v_3, w_3, z_2, a_4, n, b_4, f, e', d_4, e_3, f_3, o, p

AI Drawing Prompt Reference

Draw a plane tesselation pattern composed of multiple quadrilaterals connected through translation operations. Start by drawing a quadrilateral, then draw a curve starting from one of its vertices. Next, create a vector from the curve's starting point and use it to translate the quadrilateral, forming a new one. Repeat this process, using the vertices and vectors of the newly formed quadrilaterals to create more, ultimately creating a complete tesselation pattern.

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