什么是对称性？

Symmetry is the property of self-similarness of a geometric object (it can also be thought of as a rigid motion that maps a geometric object to itself). For example, let us look at the square:

Notice that if we flip the square along any of the marked axis, then it will retain the same shape. Therefore, the lines are called the axes of symmetry. These lines show the symmetry that this square has; specifically, it is its reflectional symmetry.

In addition, we can rotate the square along its center $90^{\circ}$, $180^{\circ}$, $270^{\circ}$, or $360^{\circ}$ with it still looking the same. This is another type of symmetry, known as rotational symmetry.

Symmetry can be found in other shapes too. Take the above regular pentagon for example. The colored lines are the Reflectional Axes of Symmetry for the pentagon.

However, some shapes do not have any axes of symmetry. Take a scalene triangle (No equal sides) for example:

There are no axes of symmetry for this triangle. Therefore, this shape is called Asymmetric.

Examples: Reflection and Rotation Symmetry $\\$

We talk about symmetry quite often in everyday life. Its mathematical difference is not that different. Here, we make a distinction between reflection and ** rotation** symmetry.

Reflection Symmetry$\\$ Reflection symmetry is closest to the meaning of symmetry when we talk about it in everyday life.

We see symmetry everywhere:

The mathematical definition of reflection symmetry is that the image is identical across a line of symmetry.

There is also a lot of symmetry in art! Kerry James Marshall is an American painter who explores race and being black in America. A couple of his work makes use of a line of symmetry.

Rotation Symmetry

Instead of a line of symmetry, rotation symmetry is when the image is identical through rotation by a partial turn. For example:

Some shapes or objects are symmetrical in both ways. For example, a slice of lemon.

Now, try the question below!