Basic understanding of circle

1. Definition of a circle: A circle is a plane figure surrounded by a curve. In a plane, a closed curve formed by a moving point rotating around a certain length is called a circle.

2. Center of the circle: Fold a circular piece of paper twice, and the point where the crease intersects the center of the circle is called the center of the circle. As shown in figure 1, the center of the circle is generally represented by the letter o, and its distance to any point on the circle is equal.

3. Radius: The line segment connecting the center of the circle and any point on the circle is called radius. It is generally represented by the letter R, as shown by the purple line in 1. Separate the two feet of the compass, and the distance between the two feet is the radius of the circle.

4. Diameter: The line segment whose two ends pass through the center of the circle is called diameter. Generally, it is represented by the letter D, as shown by the red line in 1. The diameter is the longest line segment in a circle. The diameter is twice as long as the radius.

5. The center of the circle determines the position of the circle, and the radius determines the size of the circle. If the diameter is known, we have to divide the diameter by 2, change it into radius, determine the center of the circle, and then start drawing a circle. Comparing the sizes of two circles is to compare the diameters or radii of two circles.

6. In the same circle or equal circle, there are countless radii and countless diameters. All radii and diameters in the same circle are equal.

7. In the same or equal circle, the diameter is twice as long as the radius, and the radius is half as long as the diameter.

8. Axisymmetric figure: If a figure is folded in half along a straight line, the figures on both sides can completely overlap, and this figure is axisymmetric. The straight line where the crease lies is called the symmetry axis.

9. Rectangles, squares and circles are symmetrical figures, and they all have axes of symmetry. These figures are all axisymmetric figures.

10, symmetry axis of common figures:

Only the figures with 1 symmetry axis are: angle, isosceles triangle, isosceles trapezoid, sector and semicircle.

A figure with only two axes of symmetry is a rectangle.

A figure with only three axes of symmetry is an equilateral triangle.

Figures with only four axes of symmetry are: squares;

Figures with countless axes of symmetry are: circles and rings.

A circle is an axisymmetric figure with countless symmetry axes, and the symmetry axis is the straight line where the diameter lies.

1 1, the largest circle in a square. The two are related: side length = diameter;

Drawing: (1) Draw two diagonal lines of a square; (2) Draw a circle with the diagonal intersection as the center and the side length as the diameter.

12, the largest circle in a rectangle. The two are related: width = diameter.

Drawing: (1) Draw two diagonal lines of a rectangle; (2) Draw a circle with the diagonal intersection as the center and the width as the diameter.

13. Among all the line segments of the same circle, the diameter of the circle is the longest.

14, the distance the wheel rolls forward once is the circumference of the wheel.

Assuming that the speed of the wheel per minute is known, the distance traveled by the wheel per minute = wheel circumference × speed.

15, the quotient of the circumference of an arbitrary circle divided by its diameter is a fixed number, which we call pi. Represented by the letter π. π is an infinite acyclic decimal. π = 3. 14 1592653 ... When we calculate, we usually keep two decimal places and take its approximate value of 3. 14. The actual value of π is greater than 3. 14.

16, if the circumference of a circle is represented by c, then c = π d or c = 2 π r.

17. The method of finding the radius or diameter of a circle: d = c÷πr = c÷π2 = c÷π2.

18, the circumference of a half circle is equal to the circumference of a half circle plus a diameter. C semicircle = πr+2r+2r

19, the circumference of a circle with several diameters, N = the circumference of a circle with a diameter of n.

Prove: Suppose there are several circles with diameters d 1, d2, d3, …, dn, and the sum of their diameters is n, that is to say, d 1+d2+d3+…+dn=n, and the sum of the perimeters of these circles is =

πd 1+πD2+πD3+…+πdn =π(d 1+D2+D3+…+dn)=πn