Tesselation by Translation

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2014-03-30 05:22

Polygon Vector

In collections Tesselation by Translation Tesselation by Translation

This example demonstrates how to create a tessellation of plane figures using translation operations. Key math concepts include translation, vectors, and polygon construction. The construction utilizes GeoGebra commands and objects like Polygon, AttachCopyToView, Point, Vector, and Translate to generate multiple copies of a shape through translation, forming a tessellated pattern. Suitable for high school students learning geometric transformations and spatial constructions.

GeoGebra Commands & Parameters

Polygon(A, B, 4) → poly1, a, b, c, d, C, D
AttachCopyToView(PolyLine[(3.66, -3.72), (3.58, -3.74), (3.52, -3.7600000000000002), (3.46, -3.8000000000000003), (3.4, -3.86), (3.36, -3.92), (3.34, -3.98), (3.3200000000000003, -4.04), (3.3200000000000003, -4.12), (3.3200000000000003, -4.2), (3.3200000000000003, -4.3), (3.3200000000000003, -4.38), (3.2600000000000002, -4.4), (3.16, -4.42), (3.1, -4.44), (3.04, -4.46), (2.98, -4.5), (2.92, -4.5200000000000005), (2.86, -4.5600000000000005), (2.8000000000000003, -4.6000000000000005), (2.74, -4.64), (2.72, -4.7), (2.66, -4.74), (2.62, -4.8), (2.56, -4.86), (2.54, -4.94), (2.48, -4.96), (2.4, -4.96), (2.32, -4.96), (2.24, -4.96), (2.18, -4.98), (2.12, -5.0200000000000005), (2.08, -5.08), (2.04, -5.14), (2, -5.2), (2, -5.1000000000000005), (2, -5.0200000000000005), (2, -4.94), (1.94, -4.98), (1.92, -5.04), (1.92, -5.12), (1.9000000000000001, -5.18), (1.8800000000000001, -5.24), (1.8800000000000001, -5.16), (1.8800000000000001, -5.08), (1.8800000000000001, -5), (1.8800000000000001, -4.92), (1.8800000000000001, -4.84), (1.94, -4.76), (2, -4.74), (2.06, -4.7), (2.14, -4.7), (2.22, -4.7), (2.3000000000000003, -4.7), (2.34, -4.64), (2.38, -4.5600000000000005), (2.42, -4.5), (2.48, -4.48), (2.5, -4.4), (2.54, -4.34), (2.6, -4.32), (2.66, -4.26), (2.72, -4.24), (2.62, -4.24), (2.52, -4.24), (2.44, -4.24), (2.38, -4.2), (2.3000000000000003, -4.18), (2.24, -4.16), (2.18, -4.1), (2.14, -4.04), (2.12, -3.98), (2.04, -3.96), (1.98, -3.94), (1.96, -3.88), (1.94, -3.8200000000000003), (1.92, -3.7600000000000002), (1.92, -3.68), (1.9000000000000001, -3.62), (1.9000000000000001, -3.54), (1.9000000000000001, -3.46), (1.92, -3.4), (1.86, -3.38), (1.78, -3.38), (1.7, -3.3200000000000003), (1.68, -3.2600000000000002), (1.6400000000000001, -3.18), (1.62, -3.12), (1.6, -3.06), (1.58, -3), (1.5, -2.96), (1.44, -2.94), (1.3800000000000001, -2.9), (1.36, -2.84), (1.32, -2.7600000000000002), (1.26, -2.68), (1.24, -2.62), (1.2, -2.56), (1.1400000000000001, -2.52), (1.1, -2.58), (1.04, -2.6), (0.96, -2.6), (0.9, -2.62), (0.8200000000000001, -2.58), (0.76, -2.56), (0.68, -2.56), (0.62, -2.6), (0.54, -2.64), (0.48, -2.66), (0.46, -2.72), (0.44, -2.7800000000000002), (0.4, -2.84), (0.36, -2.9), (0.3, -2.94), (0.28, -3), (0.26, -3.06), (0.2, -3.1), (0.2, -3.18), (0.18, -3.2600000000000002), (0.16, -3.3200000000000003), (0.12, -3.38), (0.06, -3.42), (0, -3.44), (-0.06, -3.46), (-0.12, -3.48), (-0.16, -3.54), (-0.18, -3.6), (-0.18, -3.68), (-0.16, -3.74), 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, v) → stroke1'
Translate(stroke1, u) → stroke1'_1
AttachCopyToView(PolyLine[(-0.1, -3.72), (-0.18, -3.72), (-0.24, -3.74), (-0.3, -3.7800000000000002), (-0.34, -3.84), (-0.36, -3.9), (-0.36, -3.98), (-0.36, -4.0600000000000005), (-0.4, -4), (-0.42, -3.92), (-0.48, -3.96), (-0.48, -4.04), (-0.52, -3.98), (-0.52, -3.9), (-0.52, -3.8200000000000003), (-0.52, -3.74), (-0.48, -3.68), (-0.46, -3.62), (-0.44, -3.56), (-0.44, -3.48), (-0.42, -3.42), (-0.4, -3.36), (-0.38, -3.3000000000000003), (-0.32, -3.2800000000000002), (-0.28, -3.22), (-0.22, -3.18), (-0.2, -3.12), (-0.14, -3.08), (-0.12, -3.02), (-0.06, -2.98), (-0.04, -2.92), (-0.02, -2.84), (0, -2.7800000000000002), (0.04, -2.72), (0.08, -2.66), (0.12, -2.6), (0.14, -2.54), (0.18, -2.48), (0.24, -2.44), (0.3, -2.4), (0.36, -2.36), (0.42, -2.32), (0.44, -2.2600000000000002), (0.5, -2.24), (0.54, -2.18), (0.54, -2.08), (0.58, -2.02), (0.58, -1.94), (0.58, -1.86), (0.56, -1.78), (0.54, -1.72), (0.48, -1.6600000000000001), (0.42, -1.6400000000000001), (0.36, -1.62), (0.3, -1.6), (0.22, -1.6), (0.14, -1.6), (0.06, -1.6), (0, -1.6400000000000001), (-0.04, -1.7), (-0.06, -1.76), (-0.08, -1.82), (-0.1, -1.8800000000000001), (-0.12, -1.94), (-0.16, -2), (-0.18, -2.08), (-0.18, -2.16), (-0.2, -2.22), (-0.22, -2.2800000000000002), (-0.16, -2.2600000000000002), (-0.14, -2.2), (-0.1, -2.12), (-0.08, -2.06), (-0.02, -2), (0.04, -1.96), (0.12, -1.92), (0.18, -1.8800000000000001), (0.24, -1.9000000000000001), (0.24, -1.98), (0.22, -2.04), (0.16, -2.1), (0.12, -2.18), (0.1, -2.24), (0.04, -2.2800000000000002), (-0.04, -2.32), (-0.1, -2.38), (-0.16, -2.42), (-0.2, -2.48), (-0.22, -2.54), (-0.28, -2.56), (-0.36, -2.56), (-0.42, -2.52), (-0.46, -2.46), (-0.48, -2.4), (-0.5, -2.34), (-0.5, -2.2600000000000002), (-0.5, -2.14), (-0.5, -2.06), (-0.5, -1.98), (-0.5, -1.9000000000000001), (-0.48, -1.84), (-0.44, -1.78), (-0.42, -1.7), (-0.38, -1.6400000000000001), (-0.32, -1.56), (-0.3, -1.48), (-0.28, -1.42), (-0.26, -1.36), (-0.24, -1.3), (-0.18, -1.28), (-0.12, -1.26), (-0.06, -1.24), (0, -1.22), (0.08, -1.22), (0.16, -1.22), (0.24, -1.22), (0.32, -1.22), (0.38, -1.26), (0.46, -1.26), (0.54, -1.22), (0.6, -1.18), (0.64, -1.12), (0.66, -1.06), (0.72, -1.02), (0.78, -0.96), (0.84, -0.9400000000000001), (0.9, -0.88), (0.96, -0.84), (1, -0.78), (1.04, -0.72), (1.06, -0.66), (1.08, -0.6), (1.08, -0.52), (1.1, -0.46), (1.1400000000000001, -0.4), (1.16, -0.34), (1.18, -0.28), (1.2, -0.22), (1.22, -0.16), (1.16, -0.12), (1.1400000000000001, -0.06), (1.12, 0), (1.1, 0.08), (1.1, 0.16), (1.1, 0.24), (1.08, 0.3), (1.06, 0.36), (1.04, 0.42), (1.02, 0.48), (1.02, 0.56), (1, 0.62), (1, 0.7000000000000001), (0.9400000000000001, 0.68), (0.88, 0.66), (0.84, 0.6), (0.8200000000000001, 0.54), (0.8, 0.48), (0.76, 0.42), (0.7000000000000001, 0.38), (0.64, 0.36), (0.58, 0.34), (0.52, 0.28), (0.5, 0.22), (0.48, 0.16), (0.46, 0.1), (0.4, 0.06), (0.34, 0.02), (0.28, 0), (0.22, -0.02), (0.14, -0.02), (0.06, -0.02), (-0.02, -0.02), (-0.08, 0), true], 1, (-4.3, -7.96), (23.38, 6.3), (0, 713), (1384, 0)) → stroke2
Point(d) → G
Point(b) → H
Vector(G, H) → w
Translate(stroke2, w) → stroke2'

AI Drawing Prompt Reference

Draw a plane figure consisting of a quadrilateral, then create multiple copies of it through translation operations to form a tessellation pattern. Start by drawing a quadrilateral, then identify its two opposite vertices and draw a vector from one vertex to the other. Use this vector to translate the quadrilateral, creating the first copy. Next, use one of the sides of the quadrilateral as a vector to translate the first copy, creating the second copy. Finally, combine all three shapes to form a continuous tessellation pattern.

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