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Symmetries

Symmetry is seen when a line dividing an object leaves each half an exact reflection of the other. In truth, this is reflectional symmetry and is only one type of symmetry. When an object can be rotated by degrees without changing the image, this is known as rotational symmetry. There are also translation and glide translation symmetries. These four represent the Four Plane Symmetries.

Symmetry can be taught using web quests which aide in guiding students to understand the concepts through visual means. There are simple worksheets and lesson plans which can be printed out for younger kids and complex worksheets and lesson plans for high school students. Games which teach about symmetry can be created in Shockwave. A group of advanced geometry students created other games which deal with shapes and translational symmetry.

The 17 Planes or wallpaper group gives a demonstration of patterns in mathematics and how lines of symmetry are used.

Even in literature and poetry there exist certain symmetries. Sir Gawain and the Green Knight gives older students an in-depth look at the symmetry in how a story is structured and in its themes.

Origami, the Japanese art of paper-folding, is a valuable tool for all ages in learning about lines of symmetry. Even abstract forms of art hold some amount of symmetry and they are shown in this KinderArt lesson plan. A very complex origami instructional document is designed to help students see the planes and lines used in creating an entire chess set from paper squares.

While symmetry can be seen all around in nature, in humans and animals, art, and other visual perceptions, its use in mathematics and applied sciences continue to grow. The DNA structure is an example of helical symmetry, the pattern seen in springs, drill bits, augers, and slinky toys. This cylindrical shape has distinctive symmetry. Hub caps or wheel bases show circle symmetry. Fractals, patterns, or shapes which are repeated in smaller and finer detail inside the same pattern, are all non-Euclidian symmetries.

The terms Euclidian and non-Euclidian are so named for the third century mathematician, Euclid of Alexandria. His findings were true and relevant on symmetrical patterns as he applied them, but were later disputed as his geometry only worked on two-dimensional flat surfaces and some three-dimensional areas having lines. In 1839, Janos Bolyai, a German mathematician, discovered non-Euclidiangeometry.