Concept
Symmetry
Overview
In everyday life, Symmetry (from Ancient Greek συμμετρία (summetría) 'agreement in dimensions, due proportion, arrangement') refers to a sense of harmonious and beautiful proportion and balance. In mathematics, the term has a more precise definition and is usually used to refer to an object that is invariant under some transformations, such as translation, reflection, rotation, or scaling. Although these two meanings of the word can sometimes be told apart, they are intricately related, and hence are discussed together in this article.
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.
This article describes symmetry from three perspectives: in mathematics, including geometry, the most familiar type of symmetry for many people; in science and nature; and in the arts, covering architecture, art, and music.
The opposite of symmetry is asymmetry, which refers to the absence of symmetry.
Overview adapted from Wikipedia (CC BY-SA 4.0; see the article history for authors).
Possible passages
Found by search and not yet checked by a person; they may only mention the idea in passing.
The required axiom of kinetic symmetry is that rest in {sigma} will be represented in {alpha} by the same velocities along and perpendicular to the {beta}-direction in {alpha} as those velocities in {beta} along and perpendicular to the {alpha}-direction which represent rest in {pi}.
Alfred North Whitehead, The Concept of Nature The Tarner Lectures Delivered in Trinity College, November 1919
States what Symmetry is; names Symmetry several times.
Whence comes this notion of symmetry which we have, and which we attribute to him? Unless we fall back upon the old doctrine of innate ideas, we must admit that the idea of bilateral symmetry is derived from without; and to admit this is to admit that it is derived from the higher animals.
Herbert Spencer, Illustrations of Universal Progress
Names Symmetry several times; states what Symmetry is.
PROTARCHUS: Most true. SOCRATES: And now the power of the good has retired into the region of the beautiful; for measure and symmetry are beauty and virtue all the world over. PROTARCHUS: True. SOCRATES: Also we said that truth was to form an element in the mixture. PROTARCHUS: Certainly.
Plato, Philebus
States what Symmetry is; names Symmetry several times.
Related ideas
- Game theory
- World Scientific
- Princeton University Press
- Springer Science+Business Media
- If and only if
- Judgement
- Justice
- Dialogue
- Language
- Logical conjunction
- Logical connective
- Mathematics
- Music
- Literature
- Geometry
- Group (mathematics)
- Mathematical object
- Molecule
- Theoretical physics
- Architecture
- Nature
- Statistics
- Science
- Space
Opposing perspectives
Place in the tradition
Part of Classicism.