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Published byAshlyn Bennett Modified over 9 years ago
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Wheel Symmetry What you need to know to understand this type of symmetry
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Basis of these symmetry groups Circles –How many degrees in a circle? –Importance of the radii and the diameters? –The role of the center of the circle
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Basic Properties of Circles All circles comprise 360 degrees A radius is a line segment with one endpoint on the circle and the other endpoint at the center of the circle A diameter is a line segment whose endpoints are on the circle and intersects the center of the circle
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One type of symmetry that occurs Rotational Symmetry –There must be an angle that the shape is rotated through and a point about which the angle is centered The angle of rotation is the angle between two radii of a circle The center of rotation is ALWAYS the center of the circle
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A possible type of symmetry Reflective Symmetry –A line that acts as a mirror may be present –This line must be a diameter of the circle
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Classifying the Symmetry Groups Only rotational symmetries are present –These groups are called CYCLIC –Each of the rotations are by the same number of degrees
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Classifying the Symmetry Groups Rotational and reflective symmetries are present –These groups are called DIHEDRAL –All rotations are by the same degree measurement –There is a mirror along each rotational radius and halfway between each radius –There are the same number of mirror lines as rotations
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Notation to represent the groups Cyclic groups –Named by the number of rotations Four 90 degree rotations: C4 Ten 36 degree rotations: C10 Dihedral groups –Named by the number of rotations (Note: there are the same number of reflection mirrors) Three 120 degree rotations and three lines of reflection: D3 Six 60 degree rotations and six lines of reflection: D6
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Examples of Wheel Symmetry The picture to the right is of an automobile hubcap. It represents a wheel symmetry called D5. There are five rotational symmetries and five lines of reflection.
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Examples of Wheel Symmetry This hubcap is an example of a C7 symmetry There are seven rotations each measuring 360/7 degrees (or 51 3/7 degrees)
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Examples of Wheel Symmetry This hubcap is an example of a D8 symmetry Do you see the eight 45 degree rotations and the eight lines of reflection?
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Which symmetry groups are seen below?
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