One is that the distance from a (geometric) plane to a fixed point is equal to a fixed length. A figure composed of all points is called a circle.
Second, the trajectory of a moving point on a plane with a certain length as the center is called a circle.
Third, the set of points whose distance to a fixed point is equal to a fixed length is called a circle. In addition, in analytic geometry, circle is also regarded as a special conic curve, which can be expressed by equation. It can be seen that a circle is a curve, and primary school students will say "a circle is a circle" in a popular way, but obviously a circle is not a mathematical language, just like a square cannot be said to be a square, so students should be guided to express it in a standardized way in teaching.
In Chinese, a circle also refers to the plane surrounded by a circle, which we call "round surface" for the time being. Many controversies about circles are actually caused by using the word "circle" to express the concepts of "circumference" and "round surface".
Usually, people used to say "circle" refers to "circular surface", which is a plane figure, representing a circle and its enclosed plane parts, and the circle has an area.
When we say "circle" in primary school mathematics teaching, we often switch between "circle" and "circular surface", which also leads to a lot of controversy.
Therefore, some experts suggest that the plane surrounded by "circle" (that is, the temporarily named circular surface) be called "circle", so as to clearly distinguish the two concepts and avoid ambiguity. But as teachers, we should pay more attention to the growth of knowledge, the cultivation of spatial concept and the formation of ability in the process of students' understanding of the circle, rather than just giving some judgments.
Extended data
"Circle" is a common geometric figure in life, but in life, "circle" is often not truly displayed to people. For junior students, they are told that the sun is round and the earth is round from an early age, and then they gradually confuse "circle" with "ball". Later, someone told me that coins are round and buttons are round. I confused "slightly flat cylindrical objects" with "circles".
For senior students, teachers often hold a round piece of paper and say, "Divide this circle into ……" when teaching "Understanding fractions". At this time, they confuse "round surface" with "circumference".
Instead of directly defining the concept of a circle, students are told that a figure like this is a circle through an intuitive description. Because geometric figures come directly from common objects in life, the abstract process from physical objects to figures is essential.
Especially the coin in this case, students may think that the whole coin is a circle before, but after hiding the physical figure and leaving the geometric figure, students can further realize that the contour line of the coin is a circle, so as to have a more scientific understanding of the figure of the circle.