Tessellation by Translation by jahatch8 (4)

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2014-03-30 05:22

In collections Tesselation by Translation Tesselation by Translation

This example demonstrates the process of creating a tessellation through translation. Key mathematical concepts include translation transformation, coordinate systems, and rational numbers. Using GeoGebra commands such as Polygon, AttachCopyToView, Point, Vector, and Translate, the transformation of shapes through translation can be created. Suitable for middle school and above students to learn about geometric transformations and tessellations.

GeoGebra Commands & Parameters

Polygon(A, B, 4) → poly1, a, b, c, d, C, D
AttachCopyToView(PolyLine[(2.32, -3.66), (2.2600000000000002, -3.68), (2.2, -3.72), (2.16, -3.7800000000000002), (2.14, -3.84), (2.1, -3.92), (2.1, -4), (2.1, -4.08), (2.08, -4.14), (2.08, -4.22), (2, -4.24), (1.92, -4.24), (1.84, -4.24), (1.76, -4.24), (1.7, -4.28), (1.62, -4.3), (1.54, -4.32), (1.48, -4.34), (1.42, -4.36), (1.36, -4.42), (1.3, -4.5), (1.24, -4.5600000000000005), (1.2, -4.62), (1.18, -4.68), (1.16, -4.74), (1.08, -4.74), (1, -4.74), (0.9400000000000001, -4.78), (0.9, -4.84), (0.86, -4.9), (0.8, -4.92), (0.78, -4.98), (0.76, -5.04), (0.76, -4.96), (0.76, -4.88), (0.76, -4.8), (0.72, -4.86), (0.7000000000000001, -4.92), (0.68, -4.98), (0.64, -4.92), (0.64, -4.84), (0.64, -4.74), (0.68, -4.68), (0.74, -4.62), (0.8, -4.58), (0.86, -4.5600000000000005), (0.9400000000000001, -4.5600000000000005), (0.96, -4.5), (0.98, -4.42), (1, -4.36), (1.02, -4.3), (1.06, -4.24), (1.12, -4.22), (1.18, -4.16), (1.24, -4.14), (1.3, -4.1), (1.36, -4.0600000000000005), (1.42, -4.04), (1.48, -3.98), (1.54, -3.94), (1.6, -3.9), (1.54, -3.88), (1.46, -3.88), (1.3800000000000001, -3.88), (1.3, -3.88), (1.22, -3.88), (1.1400000000000001, -3.86), (1.08, -3.84), (1.08, -3.7600000000000002), (1.08, -3.68), (1.02, -3.62), (1.02, -3.54), (1.02, -3.46), (1.02, -3.38), (1.02, -3.2800000000000002), (1.04, -3.2), (0.98, -3.2600000000000002), (0.92, -3.3000000000000003), (0.84, -3.3000000000000003), (0.76, -3.3000000000000003), (0.72, -3.24), (0.72, -3.16), (0.72, -3.06), (0.68, -3), (0.68, -2.9), (0.62, -2.88), (0.56, -2.94), (0.5, -2.96), (0.42, -2.96), (0.36, -2.98), (0.28, -2.96), (0.26, -2.9), (0.22, -2.84), (0.22, -2.7600000000000002), (0.16, -2.7800000000000002), (0.1, -2.8000000000000003), (0.04, -2.82), (-0.04, -2.82), (-0.06, -2.7600000000000002), (-0.08, -2.7), (-0.1, -2.64), (-0.12, -2.58), (-0.16, -2.64), (-0.22, -2.68), (-0.28, -2.72), (-0.34, -2.74), (-0.42, -2.74), (-0.46, -2.68), (-0.48, -2.62), (-0.5, -2.56), (-0.52, -2.5), (-0.54, -2.56), (-0.58, -2.62), (-0.64, -2.68), (-0.7000000000000001, -2.74), (-0.78, -2.74), (-0.8200000000000001, -2.68), (-0.86, -2.62), (-0.88, -2.68), (-0.92, -2.74), (-0.9400000000000001, -2.8000000000000003), (-0.9400000000000001, -2.88), (-0.96, -2.94), (-0.98, -3), (-1.02, -3.06), (-1.08, -3.12), (-1.1, -3.18), (-1.12, -3.24), (-1.18, -3.2800000000000002), (-1.22, -3.34), (-1.28, -3.38), (-1.32, -3.44), (-1.36, -3.5), (-1.42, -3.54), (-1.48, -3.58), (-1.48, -3.66), (-1.4000000000000001, -3.66), (-1.32, -3.66), (-1.26, -3.68), 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[(-1.28, -3.6), (-1.3, -3.68), (-1.34, -3.74), (-1.4000000000000001, -3.7600000000000002), (-1.46, -3.7800000000000002), (-1.54, -3.7800000000000002), (-1.6, -3.72), (-1.62, -3.66), (-1.6400000000000001, -3.72), (-1.6400000000000001, -3.8000000000000003), (-1.7, -3.84), (-1.74, -3.7800000000000002), (-1.76, -3.72), (-1.76, -3.64), (-1.76, -3.56), (-1.76, -3.48), (-1.72, -3.4), (-1.7, -3.34), (-1.6400000000000001, -3.3200000000000003), (-1.56, -3.3200000000000003), (-1.54, -3.2600000000000002), (-1.52, -3.2), (-1.5, -3.14), (-1.48, -3.08), (-1.46, -3.02), (-1.44, -2.96), (-1.42, -2.9), (-1.3800000000000001, -2.84), (-1.36, -2.7800000000000002), (-1.34, -2.72), (-1.28, -2.66), (-1.22, -2.62), (-1.16, -2.56), (-1.12, -2.5), (-1.08, -2.44), (-1.02, -2.38), (-0.96, -2.32), (-0.92, -2.2600000000000002), (-0.88, -2.2), (-0.8200000000000001, -2.18), (-0.76, -2.14), (-0.7000000000000001, -2.1), (-0.68, -2.04), (-0.64, -1.98), (-0.62, -1.92), (-0.6, -1.86), (-0.58, -1.8), (-0.56, -1.74), (-0.56, -1.6600000000000001), (-0.62, -1.6), (-0.68, -1.56), (-0.74, -1.5), (-0.84, -1.5), (-0.92, -1.5), (-1, -1.5), (-1.08, -1.5), (-1.1400000000000001, -1.54), (-1.2, -1.6), (-1.26, -1.6600000000000001), (-1.28, -1.72), (-1.3, -1.78), (-1.36, -1.82), (-1.42, -1.86), (-1.46, -1.92), (-1.48, -1.98), (-1.48, -2.06), (-1.5, -2.12), (-1.48, -2.18), (-1.42, -2.2), (-1.36, -2.22), (-1.36, -2.14), (-1.36, -2.06), (-1.36, -1.98), (-1.3, -1.94), (-1.22, -1.94), (-1.22, -2.02), (-1.2, -2.08), (-1.1400000000000001, -2.04), (-1.12, -1.96), (-1.1, -1.9000000000000001), (-1.06, -1.96), (-1.06, -2.04), (-1.06, -2.12), (-1.08, -2.2), (-1.12, -2.2600000000000002), (-1.18, -2.2800000000000002), (-1.24, -2.32), (-1.3, -2.34), (-1.36, -2.36), (-1.42, -2.38), (-1.5, -2.38), (-1.56, -2.4), (-1.6400000000000001, -2.4), (-1.6600000000000001, -2.34), (-1.68, -2.2600000000000002), (-1.7, -2.2), (-1.72, -2.12), (-1.72, -2.04), (-1.72, -1.96), (-1.72, -1.8800000000000001), (-1.72, -1.8), (-1.6600000000000001, -1.76), (-1.62, -1.7), (-1.56, -1.6600000000000001), (-1.5, -1.6), (-1.46, -1.54), (-1.44, -1.48), (-1.42, -1.42), (-1.3800000000000001, -1.36), (-1.36, -1.3), (-1.3, -1.24), (-1.24, -1.2), (-1.18, -1.18), (-1.1, -1.18), (-1.04, -1.1400000000000001), (-0.98, -1.12), (-0.9, -1.12), (-0.8200000000000001, -1.12), (-0.76, -1.1), (-0.7000000000000001, -1.06), (-0.66, -1), (-0.62, -0.9400000000000001), (-0.56, -0.9), (-0.5, -0.88), (-0.42, -0.84), (-0.36, -0.78), (-0.32, -0.7000000000000001), (-0.26, -0.64), (-0.22, -0.58), (-0.18, -0.52), (-0.12, -0.48), (-0.06, -0.42), (0, -0.36), (0.06, -0.32), (0.1, -0.26), (0.12, -0.16), (0.14, -0.06), (0.18, 0), (0.24, 0.06), (0.18, 0.1), (0.12, 0.12), (0.06, 0.14), (0, 0.18), (-0.02, 0.24), (-0.08, 0.26), (-0.16, 0.26), (-0.24, 0.26), (-0.3, 0.28), (-0.32, 0.34), (-0.38, 0.38), (-0.42, 0.32), (-0.46, 0.26), (-0.52, 0.22), (-0.58, 0.18), (-0.64, 0.14), (-0.7000000000000001, 0.12), (-0.76, 0.08), (-0.8200000000000001, 0.02), (-0.9, -0.02), (-0.9400000000000001, -0.08), (-1.02, -0.08), (-1.08, -0.1), (-1.16, -0.1), 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'

AI Drawing Prompt Reference

Create a pattern made of multiple small rectangles arranged in a seamless repeating pattern through translation. First, draw a quadrilateral, then translate it, draw another quadrilateral, translate it again, and finally combine these two translated quadrilaterals to form a complete pattern.

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