Understanding Repeating Shapes and Patterns

The question describes a specific type of pattern created when a shape is used repeatedly to completely cover a flat surface, or plane, without leaving any gaps between the shapes and without any of the shapes overlapping each other.

What is a Tessellation?

This kind of pattern, where shapes fit together perfectly to tile a surface, is known as a tessellation. Think about tiles on a bathroom floor or a brick wall. These are real-world examples of tessellations. In a tessellation, the shapes meet exactly at their edges or vertices, leaving no empty space and not piling up on top of each other.

Mathematically, a tessellation is a partition of the plane into regions, where each region is a shape and the union of these regions is the entire plane, with no overlaps.

Why Tessellation Fits the Description

The definition provided in the question — "created when a shape is repeated over and over again covering a plane without any gaps or overlaps" — precisely matches the definition of a tessellation. The repeated shape covers the entire area (the plane) without leaving gaps or having overlaps, which are the key characteristics of a tessellation.

Evaluating Other Options

Let's consider why the other options are not correct:

• Data handling: This term refers to the process of collecting, organizing, analyzing, and presenting data. It has nothing to do with geometric shapes or patterns covering a plane.
• Circle: A circle is a single geometric shape. While circles can be used in patterns, a simple repetition of circles alone will always leave gaps between them, so a single shape like a circle by itself cannot form a tessellation unless combined with other shapes (like in certain complex patterns).
• Asymmetric: This describes a property of a shape or pattern — that it does not have symmetry. While shapes used in tessellations can be symmetric or asymmetric, the term "asymmetric" describes a characteristic of the shape itself, not the process of covering a plane by repeating shapes without gaps or overlaps.

Based on the description given, the correct term for a pattern created by repeating a shape to cover a plane without gaps or overlaps is a tessellation.