What is glide reflection? - Mathematics Stack Exchange
2013年10月3日 · Glide reflection is the composition of a reflection and a translation parallel to the plane of reflection. If you compose the glide reflection operation with itself, you get a pure translation by twice the original translation vector; this is one way to single out what that vector is.
geometry - Why are glide reflections one of four isometries ...
2018年12月28日 · A glide reflection, or ; The identity map. In particular: an (ordinary) reflection is not a glide reflection, and a glide reflection is not a reflection, despite the overlap of terminology. Now, there are a lot of interesting descriptions of what happens when you combine two of them. Here's some examples:
Finding the glide reflection using a compass or straightedge
2017年4月13日 · This is the line of reflection for your glide transformation. Construct vector $\overrightarrow{BB'_1}$, the translation vector for your glide transformation. To show this is correct, I have shown the translation of $\triangle ABC$ under vector $\overrightarrow{BB'_1}$.
prove that a conjugate of a glide reflection is a glide reflection
2019年1月29日 · This question has an answer elsewhere, a conjugate of a glide reflection by any isometry of the plane is again a glide reflection, but they use results which were not mentioned in the book. The question comes from Artin's Algebra 6.3: "Prove that a conjugate of a glide reflection is a glide reflection, and that the glide vectors have the same ...
Axis of glide reflection - Mathematics Stack Exchange
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What is special about glide reflection? - Mathematics Stack …
2016年6月26日 · $\begingroup$ The composition of a reflection and a general translation will not be a glide reflection; it'll just be a reflection about a different line. But glide reflections are special because you're translating parallel to the line of reflection, and this is not again a …
geometry - How to show that f is a glide reflection? - Mathematics ...
How do I know that this is a glide reflection? I can tell that f is not a translation, because the two lines Af(A) and Bf(B) are not parallel. If I can also show that f is not a rotation, then f should be a glide reflection, but I don't know how.
What kind of isometry is a composition of a glide reflection with ...
2012年12月12日 · Try do proof this using only geometric arguments; if you have a glide reflection then it has a line in which it reflects; this line must divide the plane in two components, in such a way that when you apply the reflection again, the original geometric object which is being reflected is in the original "side" of the plane, but translated ...
What`s the algebraic difference between a reflection and a glide ...
2020年8月15日 · There, he defines four types of symmetry (orientation-preserving: rotation and translation; orientation-reversing: reflection and glide-reflection) and goes on to show that they can all be represented as the composition of a reflection on the x1-axis (if it's orientation-reversing), a rotation around the origin and a translation.
The composition of two different glide reflections is a rotation
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