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Translation geometry reflection9/12/2023 ![]() Maybe some people consider glide reflections special for that reason. The inverting rigid motions that are not reflections are glide reflections. ![]() In the past, I independently thought all by myself about how it's interesting that not all inverting rigid motions are reflections. We develop a framework that allows one to describe the birational geometry of Calabi-Yau pairs (X, D). I'm guessing that sometimes people make the assumption that all inverting rigid motions are reflections, and when they discover that that's not the case, they find it interesting, and that's what made the glide reflection special. Though a reflection does preserve distance and therefore can be classified as an isometry, a reflection changes the orientation of the shape and is therefore classified as an opposite isometry. Birational geometry of Calabi-Yau pairs and 3-dimensional Cremona transformations. I don't know why people consider a glide reflection special so I will make a guess. In this answer, I define a rigid motion to be noninverting when it can be gotten by applying a rotation about the origin then a translation and inverting when it can be gotten by applying an inversion about the x-axis then a rotation about the origin then a translation. 11 12 Transformations Activities that will ignite learning in your classroom. $\mathbb^2$ is a rigid motion if and only if it can be gotten either by applying a rotation about the origin then a translation or by applying an inversion about the x-axis then a rotation about the origin then a translation.
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