Concept of circle: A circle is a curved figure on a plane. 2. 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. 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. The radius is generally represented by the letter R. If the two feet of a compass are separated, the distance between the two feet is the radius of the circle. 4. The center of the circle determines the position of the circle and the radius determines the size of the circle. 5. Diameter: The line segment whose two ends pass through the center of the circle is called diameter. The diameter is usually indicated by the letter d.6. In the same circle, all radii are equal and all diameters are equal. 7. The same circle has countless radii and countless diameters. 8. The diameter of the same circle is twice the radius, and the radius is half the diameter. Represented by letters: D = 2RR = D9. Circumference: The length of the curve surrounding a circle is called circumference. 10. The circumference of a circle is always greater than 3 times the diameter, and this ratio is a fixed number. We call the ratio of the circumference to the diameter of a circle pi, which is expressed by letters. Pi is an infinite cyclic decimal. In the calculation, take 3. 14. Zu Chongzhi, a mathematician in China, is the first person in the world to calculate the value of pi to seven decimal places. 1 1. Circumference formula of a circle: C=d or C=2r 12. Area of the circle: The size of the plane occupied by the circle is called the area of the circle. 13. Cut a circle into an approximate rectangle. The length of the cut rectangle is equivalent to half the circumference (r) of the circle, and the width is equivalent to the radius (r) of the circle. Because the area of a rectangle = length× width, and the area of a circle = r×r. 14. Formula of circular area: S = R2 or S=(d2)2 or S = (C2) 2 15. Draw the largest circle in a square. The diameter of the circle is equal to the side length of the square. 16. Draw the largest circle in the rectangle, and the diameter of the circle is equal to the width of the rectangle. 17. A ring, the radius of the outer circle is R, the radius of the inner circle is R, and its area is S = R2-R2 or S = (R2-R2). (where r = the width of the ring. ) 18. The circumference of the ring = the circumference of the outer circle+the circumference of the inner circle 19. The circumference of a semicircle is equal to half the circumference plus the diameter. The formula of the circumference of a semicircle is c = D2+D or c = R+2R20. The formula of semicircle area = circle area 2 is s = R22 2 1. How many times the radius of the same circle is enlarged or reduced, the diameter and circumference are also enlarged or reduced by the same times. And the area is expanded or reduced by the square of the multiple. For example, the radius, diameter and circumference of the same circle are enlarged by 4 times, and the area is enlarged by 16 times. 22. The radius ratio of two circles is equal to the diameter ratio and the circumference ratio, and the area ratio is equal to the square of the above ratio. For example, if the radius ratio of two circles is 2: 3, then the diameter ratio and perimeter ratio of these two circles are both 2: 3, and the area ratio is 4: 9 (22: 32). 23. If the radius of a circle increases by one centimeter, the circumference will increase by one centimeter; When the diameter of a circle increases by one centimeter, its circumference increases by one centimeter. 24. In the same circle, the central angle accounts for a fraction of the central angle, and its sector area accounts for a fraction of the circular area; When the perimeters of rectangle, square and circle are equal, the area of circle is the largest and the area of rectangle is the smallest. 26. Arc length formula of the sector: l = area formula of the sector: s = R2 (n is the degree of the central angle of the sector, and r is the radius of the circle where the sector is located) 27. 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 an axisymmetric figure. The straight line where the crease lies is called the symmetry axis. 28. The figures with the symmetry axis of 1 include: angle, isosceles triangle, isosceles trapezoid, sector and semicircle. The figure with two symmetrical axes is: a rectangle with three symmetrical axes is: an equilateral triangle with four symmetrical axes is: a square with countless symmetrical axes is: a circle and a ring. 29. A straight line with a diameter is the symmetry axis of a circle. Unit 4: Understanding of cycle 1 Linear figure: a figure surrounded by line segments; Curved graph: a graph surrounded by curves. 2. Circle: A circle is a curved figure on a plane. 3, the center of the circle: a point of the center of the circle is called the center of the circle. Represented by the letter "o". 4. Radius: The line segment connecting the center of the circle and any point on the circle is called radius. Represented by the letter "r". 5. Diameter: The line segment whose two ends pass through the center of the circle is called diameter. All the line segments in the circle represented by the letter "D" have the longest diameter. 6. Basis for compasses to draw a circle: The distance (i.e. radius) from the center of the circle to any point on the circle is equal. 7. Two determinations: the center of the circle determines the position of the circle; The radius determines the size of the circle. 8. The distance between two feet of a compass is the radius of a circle. 9. In the same circle or equal circle, there are countless radii and countless diameters; All radii are equal and all diameters are equal. 10, the ratio of the circumference to the diameter of a circle is called pi, which is expressed by the letter "π". In other words: "π" is the ratio of the circumference to the diameter of a circle 1 1, and the circumference of a circle: the length of the curve surrounding a circle is called the circumference of a circle. 12, area: the size of the plane occupied by the graph. Area of the circle: the size of the plane occupied by the circle. 13. Divide the circle into several equal parts along the radius and cut it into an approximate rectangle. The length of this approximate rectangle is half the circumference of a circle, which is represented by the letter "πr"; The width of this approximate rectangle is the radius of the circle, which is represented by the letter "R"; Because the area of a rectangle is long times wide, the formula for the area of a circle is: s = π R2. 14. Relationship among radius, diameter and circumference of a circle: find diameter from known radius: ×2 find radius from known diameter: ÷2 find circumference from known diameter: ×3. 14 find diameter from known circumference: ÷ 3.5438+04 find circumference from known radius: × 2× 3. 15, common π values: 2π = 6.283π = 9.424π =12.565π =15.76π =18.847π = 21.9888π = = 50.2418π = 56.5225π = 78.536π =13.0449π =153.8664π = 200.9681π = 254. 17: Axisymmetric graph: If a graph is folded in half along a straight line, the graphs on both sides can completely overlap. This graph is an axisymmetric graph. The straight line where the crease lies is called the symmetry axis. Isosceles triangle, isosceles trapezoid, semicircle, sector and other figures have only one axis of symmetry; A rectangle has two symmetrical axes; An equilateral triangle has three axes of symmetry; A square has four axes of symmetry: a circle has countless axes of symmetry, and its axis of symmetry is the straight line where the diameter of the circle lies.