Question

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a tessellation is an arrangement of repeating shapes that have what characteristic?

a. its pieces lie on top of each other to generate beautiful artwork.
b. its pieces always consist of regular shapes.
c. no spaces or overlaps exist between its pieces.
d. any spaces or overlaps are small and randomly shaped.

Explanation:

Define a tessellation

A tessellation (or tiling) of a flat surface is the covering of a plane using one or more geometric shapes, called tiles, with no overlaps and no gaps.

Evaluate the given options

• A is incorrect because overlapping pieces violate the definition of a tessellation.
• B is incorrect because tessellations can be made of irregular shapes (e.g., Escher-style tilings), not just regular shapes.
• C is correct because the defining characteristic of a tessellation is that there are no gaps (spaces) or overlaps between the tiles.
• D is incorrect because a true mathematical tessellation permits absolutely no spaces or overlaps, regardless of size.

Answer:

• (A) Its pieces lie on top of each other to generate beautiful artwork.
• (B) Its pieces always consist of regular shapes.
• (C) No spaces or overlaps exist between its pieces. (Correct answer)
• (D) Any spaces or overlaps are small and randomly shaped.