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Combining two equal glide plane operations gives a pure translation with a translation vector that is twice that of the glide reflection, so the even powers of the glide reflection form a translation group. In the case of glide-reflection symmetry, the symmetry group of an object contains a glide reflection and the group generated by it. For ...
Likewise, (x, −y) are the coordinates of its reflection across the first coordinate axis (the x-axis). In more generality, reflection across a line through the origin making an angle with the x-axis, is equivalent to replacing every point with coordinates (x, y) by the point with coordinates (x′,y′), where
The translation was particularly difficult in that it required special attention to the numerical aspect of the book. He was also challenged by the necessity to use simple English words appropriate for the target audience of The Number Devil—that is, children aged eleven to fourteen. [6] The mathematics book was then published in English in ...
In mathematics, reflection symmetry, line symmetry, mirror symmetry, or mirror-image symmetry is symmetry with respect to a reflection. That is, a figure which does not change upon undergoing a reflection has reflectional symmetry. In 2-dimensional space, there is a line/axis of symmetry, in 3-dimensional space, there is a plane of symmetry.
A net translation can be composed of many small translations, so to obtain the translation operator for a finite increment, replace Δr by Δr/N and Δt by Δt/N, where N is a positive non-zero integer. Then as N increases, the magnitude of Δr and Δt become even smaller, while leaving the directions unchanged.
Transformation of coordinates (a,b) when shifting the reflection angle in increments of When the direction of a Euclidean vector is represented by an angle θ , {\displaystyle \theta ,} this is the angle determined by the free vector (starting at the origin) and the positive x {\displaystyle x} -unit vector.
The descriptive writer's task is one of translation: he wants to find words to capture the way his five senses have registered the item, so a reader of those words will have a mental picture of it. [10] Essays whose governing intent is descriptive or narrative are relatively uncommon in college writing. Exposition and argument tend to prevail. [11]
Memories, Dreams, Reflections (German: Erinnerungen, Träume, Gedanken) is a partially autobiographical book by Swiss psychologist Carl Jung and an associate, Aniela Jaffé. First published in German in 1961, an English translation appeared in 1963.