Identify the symmetry in the frieze pattern. translation symmetry translation symmetry and glide reflection symmetry glide reflection symmetry none
The Correct Answer and Explanation is:
Correct Answer: Translation symmetry and glide reflection symmetry
Explanation
A frieze pattern is a design that repeats itself in a strip along one direction—in most cases, horizontally. These patterns are commonly seen in architectural borders, tile designs, and decorative bands. Mathematically, frieze patterns can have up to seven different types of symmetries, including translation, glide reflection, reflection, and rotation.
In this case, the frieze pattern contains translation symmetry and glide reflection symmetry. Let’s break down what each means:
- Translation Symmetry:
This is the most basic symmetry in frieze patterns. A pattern has translation symmetry if you can shift (or “translate”) it along the horizontal axis by a certain distance and the pattern looks the same. Every frieze pattern has translation symmetry by definition, because they all repeat continuously in one direction. - Glide Reflection Symmetry:
Glide reflection combines two transformations: a translation along a line followed by a reflection over that same line. If you glide (shift) the pattern a certain distance and then reflect it over a horizontal axis, and the pattern matches exactly, it has glide reflection symmetry. This symmetry is common in patterns where shapes seem to alternate direction or “flip” as they repeat.
Some frieze patterns have only translation symmetry, while others have combinations like reflection, rotation, or glide reflection. The presence of both translation and glide reflection symmetry means the pattern repeats by shifting and flipping, but it doesn’t necessarily include vertical or horizontal reflection symmetry on its own.
To identify these symmetries, one must observe the motif’s repetition: if it moves forward and flips consistently, glide reflection is present; if it just repeats in the same orientation, only translation is present. Since this pattern includes both movements, it has translation symmetry and glide reflection symmetry.
