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In Euclidean space, such a dilation is a similarity of the space. [2] Dilations change the size but not the shape of an object or figure. Every dilation of a Euclidean space that is not a congruence has a unique fixed point [3] that is called the center of dilation. [4] Some congruences have fixed points and others do not. [5]
Google Translate is a multilingual neural machine translation service developed by Google to translate text, documents and websites from one language into another. It offers a website interface , a mobile app for Android and iOS , as well as an API that helps developers build browser extensions and software applications . [ 3 ]
Dilation (usually represented by ⊕) is one of the basic operations in mathematical morphology. Originally developed for binary images, it has been expanded first to grayscale images, and then to complete lattices. The dilation operation usually uses a structuring element for probing and expanding the shapes contained in the input image.
A mathematical symbol is a figure or a combination of figures that is used to represent a mathematical object, an action on mathematical objects, a relation between mathematical objects, or for structuring the other symbols that occur in a formula.
Together with the translations, all homotheties of an affine (or Euclidean) space form a group, the group of dilations or homothety-translations. These are precisely the affine transformations with the property that the image of every line g is a line parallel to g .
Rigor is a cornerstone quality of mathematics, and can play an important role in preventing mathematics from degenerating into fallacies. well-behaved An object is well-behaved (in contrast with being Pathological ) if it satisfies certain prevailing regularity properties, or if it conforms to mathematical intuition (even though intuition can ...
Google Dictionary is an online dictionary service of Google that can be accessed with the "define" operator and other similar phrases [note 1] in Google Search. [2] It is also available in Google Translate and as a Google Chrome extension. The dictionary content is licensed from Oxford University Press's Oxford Languages. [3]
In Euclidean geometry, a translation is a geometric transformation that moves every point of a figure, shape or space by the same distance in a given direction. A translation can also be interpreted as the addition of a constant vector to every point, or as shifting the origin of the coordinate system. In a Euclidean space, any translation is ...