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Dihedral Groups

This document provides an insightful overview of symmetry in mathematics, focusing on dihedral groups as presented by Diana Mary George, Assistant Professor at St. Mary’s College, Thrissur. It discusses various types of symmetry, including line symmetry, rotational symmetry, and reflectional symmetry, illustrating how these concepts are applicable in everyday life and mathematics. Readers will gain an understanding of how symmetry contributes to harmony and beauty in objects, particularly through the lens of geometric figures like squares.

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Dihedral Groups

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  1. Dihedral Groups Diana Mary George Assistant Professor Department of Mathematics St. Mary’s College Thrissur-680020 Kerala

  2. Symmetry in everyday language refers to a sense of harmonious and beautiful proportion and balance. Dihedral Groups,Diana Mary George,St.Mary’sCollege

  3. Types Of Symmetry • Line Symmetry • Rotational Symmetry Dihedral Groups,Diana Mary George,St.Mary’s College

  4. Line Symmetry An object has line symmetry or reflective symmetry when it is the same on both sides of a line drawn down the middle. Dihedral Groups,Diana Mary George,St.Mary’s College

  5. Dihedral Groups,Diana Mary George,St.Mary’s College

  6. Plane Or Reflectional Symmetry A figure which does not change upon undergoing a reflection has reflectional symmetry. Dihedral Groups,Diana Mary George,St.Mary’s College

  7. Dihedral Groups,Diana Mary George,St.Mary’s College

  8. Rotational Symmetry An object is said to have rotational symmetry if it remains the same after being rotated around a central point. Dihedral Groups,Diana Mary George,St.Mary’s College

  9. Dihedral Groups,Diana Mary George,St.Mary’s College

  10. Order Of Rotational Symmetry The number of positions a figure can be rotated to, without bringing in any changes to the way it looks originally, is called its order of rotational symmetry. Dihedral Groups,Diana Mary George,St.Mary’s College

  11. SYMMETRIES OF A SQUARE Dihedral Groups,Diana Mary George,St.Mary’s College

  12. Composition Of Motions = * = * Dihedral Groups,Diana Mary George,St.Mary’s College

  13. Dihedral Groups,Diana Mary George,St.Mary’s College

  14. Observations Dihedral Groups,Diana Mary George,St.Mary’s College

  15. Applications Dihedral Groups,Diana Mary George,St.Mary’s College

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