What is Symmetry? In geometry, an object displays symmetrylooks the same after a transformation, such as reflection or rotation. Symmetry is the mathematical principle behind all patterns and is important in art, mathematics, biology, chemistry and physics.
The word "symmetry" is a 16th century Latin derivative from the Greek words for "together" (syn) and "measure" (metron).
Symmetry Types
- reflective
In general usage, symmetry usually refers to the reflective symmetry or the mirror; that is, a line can be drawn through an object in such a way that the two halves are mirror images of each other.
One isosceles triangle is an example of reflective symmetry. Mathematically, an object that exhibits mirror symmetry is considered “invariant under reflection,” meaning that reflecting the object in a certain way does not change its appearance.
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In biology, reflective symmetry is often referred to as bilateral symmetry, as found in mammals, reptiles, birds, and fish.
- rotational
Another form of symmetry commonly found in biology is radial symmetry. It is found in flowers and many sea creatures, such as sea anemones, starfish and jellyfish.
Mathematically, such objects are described as exhibiting rotational symmetry, as they are “invariant under rotation”. Such objects have a point or an axis about which an object can be rotated and remain invariant.
- translational
A 2D or 3D pattern can display translational symmetry for being “invariant under translation”. All mosaics and most patterns found in rugs and wallpapers exhibit translational symmetry.
Related Content:
- plane geometry
- Spatial Geometry
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