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Wheel Symmetry What you need to know to understand this type of symmetry.

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Presentation on theme: "Wheel Symmetry What you need to know to understand this type of symmetry."— Presentation transcript:

1 Wheel Symmetry What you need to know to understand this type of symmetry

2 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

3 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

4 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

5 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

6 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

7 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

8 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

9 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.

10 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)

11 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?

12 Which symmetry groups are seen below?


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