explain symmetrical figures with example in long 50 words
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Symmetry (from Greek συμμετρία symmetria "agreement in dimensions, due proportion, arrangement") in everyday language refers to a sense of harmonious and beautiful proportion and balance. In mathematics, "symmetry" has a more precise definition, that an object is invariant to any of various transformations; including reflection, rotation or scaling. Although these two meanings of "symmetry" can sometimes be told apart, they are related, so in this article they are discussed together.
Mathematical symmetry may be observed with respect to the passage of time; as a spatial relationship; through geometric transformations; through other kinds of functional transformations; and as an aspect of abstract objects, theoretic models, language, music and even knowledgeitself.
Types of symmetry
Reflective
In general usage, symmetry most often refers to mirror or reflective symmetry; that is, a line (in 2-D) or plane (in 3-D) can be drawn through an object such that the two halves are mirror images of each other. An isosceles triangle and a human face are examples. Mathematically, an object that exhibits mirror symmetry is said to be “invariant under reflection,” meaning reflecting the object in a certain way doesn’t change its appearance.
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, sea stars and jellyfish. Mathematically, such objects are described as exhibiting rotational symmetry, for being “invariant under rotation.” Such objects have a point (in 2-D) or an axis (in 3-D) about which an object can be rotated some amount and remain invariant.
Translational
If imagined to extend for infinity in all directions, a 2-D or 3-D pattern can exhibit translational symmetry, for being “invariant under translation.” All tessellations, many jungle gyms and most patterns found on rugs and wallpaper exhibit translational symmetry.
Mathematical symmetry may be observed with respect to the passage of time; as a spatial relationship; through geometric transformations; through other kinds of functional transformations; and as an aspect of abstract objects, theoretic models, language, music and even knowledgeitself.
Types of symmetry
Reflective
In general usage, symmetry most often refers to mirror or reflective symmetry; that is, a line (in 2-D) or plane (in 3-D) can be drawn through an object such that the two halves are mirror images of each other. An isosceles triangle and a human face are examples. Mathematically, an object that exhibits mirror symmetry is said to be “invariant under reflection,” meaning reflecting the object in a certain way doesn’t change its appearance.
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, sea stars and jellyfish. Mathematically, such objects are described as exhibiting rotational symmetry, for being “invariant under rotation.” Such objects have a point (in 2-D) or an axis (in 3-D) about which an object can be rotated some amount and remain invariant.
Translational
If imagined to extend for infinity in all directions, a 2-D or 3-D pattern can exhibit translational symmetry, for being “invariant under translation.” All tessellations, many jungle gyms and most patterns found on rugs and wallpaper exhibit translational symmetry.
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