Symmetry
A pattern is symmetric if there is at least one symmetry
(rotation, translation, reflection, glide reflection)
that leaves the pattern unchanged.
Rotation
To rotate an object means to turn it around. Every rotation has a center and an angle.
Translation
To translate an object means to move it without rotating or reflecting it. Every translation has a direction and a distance.
Reflection
To reflect an object means to produce its mirror image. Every reflection has …
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…in both directions, you have made a symmetric pattern. You can translate the whole group ahead one person, and the procession will look the same. This pattern has an infinite number of symmetries, since you can translate forward by one person, two people, or three people, or backwards by the same numbers, or even by no people. There is one symmetry of this pattern for each integer (positive, negative, and zero whole numbers).
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