Tessellation by Translation by jahatch8 (2)

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2014-03-30 05:21

In collections Tesselation by Translation Tesselation by Translation

This example demonstrates the process of constructing a square tessellation through translation. Key mathematical concepts include translation transformation, angles, and geometric construction. Using GeoGebra commands such as Polygon, AttachCopyToView, Point, Vector, and Translate, the dynamic properties of translation transformation are showcased. Suitable for middle school and above students to learn about geometric transformations and tessellation patterns.

GeoGebra Commands & Parameters

Polygon(A, B, 4) → poly1, a, b, c, d, C, D
AttachCopyToView(PolyLine[(2.1, -3.38), (2.02, -3.38), (1.94, -3.38), (1.8800000000000001, -3.4), (1.82, -3.42), (1.76, -3.46), (1.68, -3.5), (1.62, -3.54), (1.56, -3.56), (1.52, -3.62), (1.48, -3.68), (1.46, -3.7600000000000002), (1.46, -3.86), (1.46, -3.94), (1.48, -4.0200000000000005), (1.4000000000000001, -4.0200000000000005), (1.32, -4.0200000000000005), (1.26, -4.04), (1.18, -4.04), (1.12, -4.0600000000000005), (1.06, -4.08), (0.98, -4.12), (0.9, -4.14), (0.84, -4.16), (0.78, -4.2), (0.74, -4.26), (0.72, -4.32), (0.64, -4.32), (0.62, -4.38), (0.56, -4.44), (0.5, -4.5200000000000005), (0.44, -4.5600000000000005), (0.42, -4.64), (0.42, -4.72), (0.4, -4.8), (0.36, -4.74), (0.36, -4.66), (0.36, -4.58), (0.34, -4.64), (0.3, -4.7), (0.28, -4.76), (0.26, -4.82), (0.24, -4.76), (0.22, -4.7), (0.22, -4.62), (0.2, -4.68), (0.18, -4.76), (0.16, -4.82), (0.14, -4.76), (0.14, -4.66), (0.16, -4.6000000000000005), (0.22, -4.54), (0.24, -4.48), (0.3, -4.46), (0.34, -4.4), (0.38, -4.34), (0.4, -4.28), (0.42, -4.2), (0.44, -4.14), (0.46, -4.08), (0.5, -4.0200000000000005), (0.56, -3.96), (0.6, -3.9), (0.66, -3.88), (0.72, -3.84), (0.78, -3.8200000000000003), (0.86, -3.8200000000000003), (0.9, -3.7600000000000002), (0.86, -3.7), (0.8, -3.68), (0.74, -3.66), (0.68, -3.62), (0.64, -3.56), (0.58, -3.5), (0.54, -3.42), (0.52, -3.36), (0.5, -3.3000000000000003), (0.48, -3.24), (0.48, -3.16), (0.48, -3.08), (0.5, -2.98), (0.52, -2.9), (0.44, -2.88), (0.34, -2.88), (0.26, -2.88), (0.2, -2.84), (0.18, -2.7800000000000002), (0.14, -2.72), (0.1, -2.66), (0.08, -2.6), (0.06, -2.54), (0.06, -2.46), (0.04, -2.4), (-0.04, -2.4), (-0.1, -2.38), (-0.16, -2.32), (-0.22, -2.2800000000000002), (-0.28, -2.24), (-0.34, -2.2), (-0.4, -2.18), (-0.46, -2.16), (-0.54, -2.18), (-0.6, -2.2), (-0.66, -2.22), (-0.72, -2.24), (-0.8, -2.24), (-0.84, -2.3000000000000003), (-0.88, -2.36), (-0.92, -2.42), (-0.98, -2.46), (-1.06, -2.5), (-1.12, -2.54), (-1.18, -2.56), (-1.2, -2.62), (-1.24, -2.68), (-1.26, -2.74), (-1.28, -2.8000000000000003), (-1.34, -2.86), (-1.3800000000000001, -2.92), (-1.44, -2.96), (-1.46, -3.02), (-1.52, -3.08), (-1.54, -3.14), (-1.58, -3.2), (-1.6, -3.2600000000000002), (-1.56, -3.3200000000000003), (-1.5, -3.36), true], 1, (-4.3, -7.96), (23.38, 6.3), (0, 713), (1384, 0)) → stroke1
Point(a) → E
Point(c) → F
Vector(E, F) → u
Translate(stroke1, u) → stroke1'
AttachCopyToView(PolyLine[(-1.5, -3.38), (-1.58, -3.38), (-1.6600000000000001, -3.38), (-1.74, -3.38), (-1.82, -3.38), (-1.86, -3.44), (-1.9000000000000001, -3.5), (-1.92, -3.44), (-1.92, -3.36), (-1.9000000000000001, -3.3000000000000003), (-1.96, -3.2800000000000002), (-2.04, -3.2800000000000002), (-2.08, -3.34), (-2.1, -3.4), (-2.1, -3.3200000000000003), (-2.06, -3.2600000000000002), (-2, -3.2), (-1.94, -3.16), (-1.8800000000000001, -3.14), (-1.82, -3.1), (-1.76, -3.08), (-1.7, -3.04), (-1.68, -2.96), (-1.6400000000000001, -2.9), (-1.6400000000000001, -2.82), (-1.62, -2.7600000000000002), (-1.6, -2.7), (-1.58, -2.64), (-1.54, -2.58), (-1.48, -2.52), (-1.46, -2.46), (-1.44, -2.4), (-1.42, -2.32), (-1.4000000000000001, -2.2600000000000002), (-1.36, -2.18), (-1.32, -2.12), (-1.26, -2.08), (-1.2, -2.04), (-1.1400000000000001, -2.02), (-1.08, -2), (-1.02, -1.98), (-0.96, -1.94), (-0.92, -1.8800000000000001), (-0.88, -1.82), (-0.8200000000000001, -1.78), (-0.78, -1.72), (-0.78, -1.6400000000000001), (-0.78, -1.56), (-0.78, -1.48), (-0.8, -1.42), (-0.86, -1.4000000000000001), (-0.92, -1.3800000000000001), (-0.98, -1.36), (-1.08, -1.36), (-1.18, -1.36), (-1.24, -1.3800000000000001), (-1.32, -1.4000000000000001), (-1.42, -1.42), (-1.52, -1.42), (-1.58, -1.44), (-1.6400000000000001, -1.46), (-1.7, -1.48), (-1.76, -1.5), (-1.82, -1.52), (-1.86, -1.6), (-1.8800000000000001, -1.6600000000000001), (-1.9000000000000001, -1.72), (-1.92, -1.78), (-1.92, -1.86), (-1.92, -1.94), (-1.84, -1.94), (-1.76, -1.94), (-1.68, -1.94), (-1.6, -1.94), (-1.54, -1.92), (-1.48, -1.8800000000000001), (-1.5, -1.94), (-1.54, -2), (-1.56, -2.06), (-1.58, -2.12), (-1.62, -2.18), (-1.6600000000000001, -2.24), (-1.68, -2.32), (-1.74, -2.34), (-1.8, -2.38), (-1.84, -2.32), (-1.84, -2.24), (-1.86, -2.18), (-1.9000000000000001, -2.24), (-1.94, -2.3000000000000003), (-1.96, -2.36), (-1.98, -2.3000000000000003), (-2, -2.22), (-2.04, -2.16), (-2.06, -2.1), (-2.08, -2.04), (-2.1, -1.98), (-2.1, -1.9000000000000001), (-2.1, -1.82), (-2.1, -1.74), (-2.12, -1.68), (-2.12, -1.58), (-2.12, -1.5), (-2.12, -1.42), (-2.12, -1.34), (-2.12, -1.24), (-2.1, -1.18), (-2.04, -1.1400000000000001), (-1.96, -1.12), (-1.9000000000000001, -1.1), (-1.82, -1.1), (-1.72, -1.1), (-1.6600000000000001, -1.08), (-1.58, -1.08), (-1.5, -1.08), (-1.44, -1.04), (-1.3800000000000001, -1.02), (-1.32, -0.96), (-1.3, -0.9), (-1.24, -0.86), (-1.18, -0.8200000000000001), (-1.1400000000000001, -0.76), (-1.06, -0.76), (-0.98, -0.76), (-0.9, -0.76), (-0.84, -0.74), (-0.78, -0.72), (-0.72, -0.7000000000000001), (-0.68, -0.64), (-0.62, -0.6), (-0.6, -0.54), (-0.58, -0.48), (-0.54, -0.42), (-0.52, -0.36), (-0.48, -0.3), (-0.42, -0.26), (-0.38, -0.2), (-0.34, -0.14), (-0.32, -0.08), (-0.3, 0), (-0.26, 0.08), (-0.24, 0.16), (-0.24, 0.24), (-0.24, 0.32), (-0.24, 0.4), (-0.24, 0.48), (-0.24, 0.56), (-0.3, 0.58), (-0.36, 0.62), (-0.42, 0.64), (-0.5, 0.64), (-0.56, 0.68), (-0.62, 0.7000000000000001), (-0.68, 0.66), (-0.74, 0.64), (-0.78, 0.58), (-0.8200000000000001, 0.52), (-0.88, 0.5), (-0.92, 0.44), (-0.98, 0.4), (-1.04, 0.36), (-1.12, 0.26), (-1.18, 0.22), (-1.24, 0.18), (-1.3, 0.16), (-1.3800000000000001, 0.16), (-1.44, 0.2), (-1.44, 0.28), true], 1, (-4.3, -7.96), (23.38, 6.3), (0, 713), (1384, 0)) → stroke2

AI Drawing Prompt Reference

Create a tessellation pattern using multiple squares through translation. Start by drawing a square, then translate one of its sides to create a new square, and repeat this process to form a complete tessellation pattern.

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