Overview: What is Symmetry?
Symmetry in mathematics, especially in geometry, has a formal meaning that can be demonstrated by relationships between parts of a design. For example, a figure is symmetrical along an axis of reflection if both halves of the figure are exactly the same. In fact, if the edge of a mirror is placed along an axis of reflection, so that only half the figure is visible, it will look exactly the same as the whole figure did.
Lines and Planes of Symmetry
While some polygons have only one axis of symmetry, others, such as equilateral triangles, have three. Two-dimensional figures have lines of symmetry, but three dimensional symmetrical objects have planes of symmetry. Circles and spheres have many. Lines of symmetry are useful because exact duplicates of figures can be constructed using them.
Rotational and Helical Symmetry
Rotational symmetry is a special property that allows figures to be turned around a central point, called the “center of rotation.” Helical symmetry is a special type of symmetry that accounts for the movement of springs, Slinky toys, and drill bits. Windmills are also common objects that show rotational symmetry as the points spin.
Symmetry in Nature
Snowflakes are among many objects in nature that are symmetrical, even though no two snowflakes are alike. Butterflies, bipedal animals, and even insects are bilaterally symmetrical. If a line of reflection is drawn, both halves will be roughly the same. Flower petals are symmetrical around the flower center. Starfish and sea anemones are among the many sea creatures that are symmetrical.
Symmetry and the Concept of Beauty
In addition, many of the most beautiful objects are symmetrical. The Taj Mahal is one of the seven wonders of the ancient world, and it is often used as an example of symmetry. Classical designs in pottery are symmetrical, and so are patterns in tiles and mosaics. Every culture uses symmetry in art forms, from Celtic knots to African friezes.
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