Transformations, Symmetries, and Tilings

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Transformations, Symmetries, and Tilings

Rigid Motions And Similarity Transformations

Four Basic Rigid Motions

Glide-Reflections

Combines both a slide and reflection.

Reflections

AKA flip, a reflection is determined by a line in the plane.

Rotaions

AKA turn, one point is held fixed and the remaining points are turned about the center of the rotation the same number of degrees.

Translations

AKA slide, all points of the plane are moved the same distance in the same direction.

Transformation of the Plane

A one-to-one set correspondence of the set of points in the plane onto itself.

Rigid motion of plane

A transformation of the plane

Main topic