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Glite Dictionary
automorphic

automorphic

1 9.9
Stays the same after a particular change, for example a shape or function that matches itself
  • adjective
  • /ˌɔːtəˈmɔrfɪk/
  • Specialized
: automórfico
  • A shape is called automorphic if it maps onto itself under a specific operation.

Examples

  • In mathematics, an automorphic function remains the same after a certain transformation is applied.

  • The concept of automorphic numbers is important in number theory.

  • The number 1 is automorphic because it remains unchanged when squared.

  • Is the number 5 automorphic?

  • In mathematics, a function is called automorphic if it remains unchanged under a specific transformation.

  • The concept of an automorphic number is fascinating because it refers to numbers that appear in their own square.

  • An automorphic transformation allows the shape to map onto itself, highlighting its symmetrical properties.

Surface Forms

automorphic positive

Morphology

automorphic = morphic (opaque) = auto + morph + ic

Although the word is structurally built from 'auto-' + 'morphic', the specialized mathematical meaning is not directly predictable from the component parts for an average learner.

Etymology

The word automorphic comes from the parts auto- meaning 'self' and morph meaning 'shape' or 'form', like in automatic. So something automorphic is a 'self-shape' that looks the same after a certain change, which is why the word describes things that stay the same under a particular operation.