Mathematics of Symmetry (Part 2)
Symmetric Patterns A plane figure has symmetry if there is a non-trivial transformation that maps the figure onto itself. A trivial transformation refers to the identity transformation which maps every point in the plane onto itself. Symmetry lines of a square (reflection)
Symmetric Patterns If a figure can be rotated less than 360 0 about a point so that the image and the pre-image are indistinguishable , then the figure has rotational symmetry . Rotational Symmetries of a square ( 0 0 /360 0 , 90 0 , 180 0 , and 270 0 ) The square has rotational symmetry of order 4 because there are four rotations of less than 360 0 that produce an image indistinguishable from the original. The rotational symmetry has a magnitude of 90 0 = 360 0 4 . Some mathematicians refer to 180 0 rotational symmetry about a point as a point symmetry .
Design and Pattern A design is a figure with at least one non-trivial symmetry. A pattern is a design that has a translation symmetry. A plane pattern has symmetry if there is an isometry of the plane that preserves it. Arts and mathematics intersect in the concept of symmetry. In art, symmetry is a basic design element, something that many people consider pleasing to look at. In mathematics, symmetry can be defined and verified by finding motions that leave a design unchanged. These motions can be combined and analyzed in much the same way numbers are.
Tessellations A tessellation is a repeating pattern of figures
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- Spring '14
- Rotational symmetry, tessellations, Mathematics of Symmetry