In geometry, symmetry is usually related to shape and space. A shape is said to be symmetrical if it remains unchanged after rotation, rotation or translation.
For example, a square has four equal sides and its diagonal divides it into two equal triangles. Therefore, a square is a symmetrical quadrilateral. In addition, the circle is also a symmetrical shape, because it is the same from any direction.
Besides geometry, algebra also has symmetry. For example, in group theory, a symmetric group is a set of all operations that can be performed on an object. The object remains unchanged under symmetric operation. Taking the rotation of a square as an example, the rotation of 90 degrees, 180 degrees and 270 degrees will get the same result, so these rotations form a symmetric group.
Symmetry is also used for analysis. For example, in function analysis, if a function satisfies a certain symmetry property, then the function can be expanded or restricted to adapt to different application scenarios. For example, if a function is even for all x values, the function can be extended to the negative range while maintaining its parity.
Besides in the field of mathematics, the concept of symmetry also exists widely in nature and daily life. For example, the human body itself is symmetrical, and so are our left and right sides. In addition, symmetry is also reflected in many works of art and buildings, such as the Eiffel Tower and the Temple of Heaven in China.
In a word, symmetry is a very important concept, which not only plays an important role in mathematics, but also widely exists in nature and daily life. Through the understanding and application of symmetry, we can better understand the world around us and solve problems in different fields.