![]() Which transformations can be used to create frieze patterns? Used first the translation is easy to see with the repeating octagon. ![]() Video quote: Although this pattern looks confusing it is quite simple when broken into the operators. There are four types of rigid motions that we will consider: translation, rotation, reflection, and glide reflection. A composition of reflections over parallel lines has the same effect as a translation (twice the distance between the parallel lines). What is a composition of transformations?Ī composition of transformations is a combination of two or more transformations, each performed on the previous image. ![]() Some images are just one reflection away from their pre-images other images (in translation and rotation problems) are two reflections away. What is a glide reflection A combination of?Ĭan a glide reflection have two translations?Īnd because you can produce the translation part with two reflections, you can achieve a glide reflection with three reflections. In a glide reflection, the order in which the transformations are performed does not affect the final image. Note : Because a glide reflection is a composition of a translation and a reflection, this theorem implies that glide reflections are isometries. The composition of two (or more) isometries is an isometry. What is the composition of two glide reflections?
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