“In mathematics, ‘symmetry’… is usually used to refer to an object[1] that is invariant[2] under some transformations…
“Mathematical symmetry may be observed with respect to the passage of time; as a spatial relationship; through geometric transformations; through other kinds of functional transformations; and as an aspect of abstract objects, including theoretic models, language, and music…
“The opposite of symmetry is asymmetry, which refers to the absence or a violation of symmetry.”
This section of Wikipedia summarizes geometric symmetry quite well: https://en.wikipedia.org/wiki/Symmetry#In_geometry
“Generalizing from geometrical symmetry…, one can say that a mathematical object is symmetric with respect to a given mathematical operation, if, when applied to the object, this operation preserves some property of the object.”
Source of information: “Symmetry,” Wikipedia, retrieved 11/7/2020, emphasis added.
- [1] What is the Gist of a “Mathematical Object”?
- [2] What is the Gist of an “Invariant” (Mathematics)?
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Disclaimer:
I am not a professional in this field, nor do I claim to know all of the jargon that is typically used in this field. I am not summarizing my sources; I simply read from a variety of websites until I feel like I understand enough about a topic to move on to what I actually wanted to learn. If I am inaccurate in what I say or you know a better, simpler way to explain a concept, I would be happy to hear from you :).
