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A detailed tutorial on symmetry and symmetric images. Step by step tutorial including several examples of symmetry for reference.

Symmetry is a very basic concept in geometry. It is similar to invariance. It is when something is equal to itself through both of its sides. If you compare the two sides of something and they match, then the object is said to be symmetric. When testing an image for symmetry, the easiest test is to draw an imaginary line down the middle. Then pretend to fold the image over. If the two sides are perfect matches of each other, then the image is symmetric.

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A detailed tutorial on invariants and the property of invariance. Step by step tutorial including several examples of invariants for reference.

Invariants are any function or number that displays the property of invariance. Invariance is when a function or number can go through several transformations without changing, or without going outside of its set parameters. The set parameters differ depending on the function or number. Some examples of invariant functions and numbers are the absolute value of a complex number, the degree of a polynomial, and certain parts of a square matrix