Symmetry

Synopsis

David Wade introduces the main principles of symmetry, and shows how, despite opinions over exactly what it is, symmetry can be found in almost every corner of science, nature and human culture.

Summary

Chapter 1: Mirror Symmetry

Summary: Mirror symmetry is a type of symmetry where a figure can be divided into two identical halves by a mirror line.

Real example: A butterfly's wings are mirror-symmetrical, meaning that if you fold the butterfly down the middle, both sides will look identical.

Chapter 2: Rotational Symmetry

Summary: Rotational symmetry occurs when a figure looks the same after being rotated a certain number of degrees around a fixed point.

Real example: A wheel has rotational symmetry because it looks the same after it is rotated any number of degrees around its center.

Chapter 3: Translational Symmetry

Summary: Translational symmetry involves repeating a pattern along a straight line.

Real example: The bricks in a wall exhibit translational symmetry, as they are repeated in a straight line along the wall.

Chapter 4: Glide Reflection

Summary: Glide reflection is a combination of translation and reflection. It involves translating a figure along a line of symmetry and then reflecting it across that line.

Real example: A staircase has glide reflection symmetry, as each step is translated along the staircase and then reflected across the horizontal plane.

Chapter 5: Complex Symmetry

Summary: Complex symmetry refers to more intricate types of symmetry, such as point symmetry, helical symmetry, and fractal symmetry.

Real example: The snowflake exhibits six-fold point symmetry, meaning it looks the same after being rotated by 60 degrees around a central point.

Chapter 6: Symmetry in Nature

Summary: Symmetry is commonly found in nature in various forms, including mirror symmetry in animal bodies, rotational symmetry in flowers, and translational symmetry in crystals.

Real example: The human body exhibits both bilateral symmetry (mirror symmetry) and axial symmetry (rotational symmetry around a vertical axis).

Chapter 7: Symmetry in Art and Architecture

Summary: Symmetry has been used extensively in art and architecture for centuries to create pleasing and harmonious designs.

Real example: The Taj Mahal is an architectural masterpiece that showcases perfect bilateral symmetry, with its central dome flanked by two identical minarets.