Characteristics of circle: A circle is a closed figure composed of a curve, and the distance from any point on the circle to the center of the circle is equal.

The function of center and radius: the center determines the position of the circle, and the radius determines the size of the circle.

A circle is an axisymmetric figure, and a straight line centered on the diameter is the symmetry axis of the circle. A circle has countless axes of symmetry.

The diameter of the same circle is twice the radius.

The circumference of a circle refers to the length of the curve surrounding the circle. The circle with large diameter grows up, and the circle with small diameter has small circumference.

The quotient of the circumference divided by the diameter of the circle is a fixed number. We call it pi, which is usually 3. 14 in calculation.

Circumference: C=2πr or c = π d.

Find the radius: r=C/2π

Find the diameter: d=C/π

The area meaning of a circle: the plane size or the surface size of a circular object or figure is the area of a circle.

Area calculation formula: the square of π * R.

Calculation method of circular area: S=πR square -πr square or S=π(R square -r square).

(r is the radius of the big circle and r is the radius of the small circle.

2. Knowledge points of the first volume of the sixth grade mathematics circle in primary school

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1. Know the circle 1, circle 2 in daily life, draw and perceive the basic features of the circle (1). (2) Draw 3 with a tether. Compare and perceive the characteristics of a circle: rectangle, square, parallelogram, trapezoid, triangle, etc. What we have learned before are all plane figures surrounded by curved segments, and circles are surrounded by curves. Induction: A circle is a closed figure surrounded by curves. Second, the name of each part of the circle is 1. Center: After the compass draws a circle, the point where the needle tip is fixed is the center, usually represented by the letter O, and the center determines the position of the circle. Second, radius: the line segment connecting the center of the circle to any point on the circle is called radius. Generally, it is 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. 3. Diameter: The line segment whose two ends pass through the center of the circle is called diameter. Generally represented by the letter D, the diameter is the longest line segment in a circle. The main feature of a circle is 1. In the same circle or in the same circle, there are countless radii and countless diameters. All radii are equal and all diameters are equal. 2. In the same or equal circle, the length of the diameter is twice that of the radius, and the length of the radius is 1/2 of the diameter. Expressed in letters: d=2r or r=d/23. If a graph is folded in half along a straight line, the graphs on both sides can completely overlap, and this graph is axisymmetric. A circle is an axisymmetric figure with many axes of symmetry. 1. Understanding of the circumference 1. The length of the curve surrounding a circle is called the circumference of the circle. 2. The circumference is related to the diameter of the circle. The longer the diameter of a circle, the larger the circumference. The meaning of pi and the formula of pi are 1. Pi experiment: make a mark on the circular paper, aim at the scale of ruler 0, and roll on the ruler for one week. It is found that the general rule is that the ratio of the circumference to the diameter of a circle is a fixed number (π). 3. Pi: The ratio of the circumference to the diameter of any circle is a fixed number, which we call Pi.

3. Questions and answers about the application of circle knowledge in grade six.

1. Cut a circular piece of paper into several small sectors with equal areas along the radius and put them together to form an approximate rectangle. The circumference of the new pattern is longer than that of the circular paper 16 cm. What is the area of this round paper?

The newly added 16 cm is two widths of a rectangle, that is, two radii of a circle.

Then the radius is: 16÷2=8.

The area of the circle is 3. 14*8*8=200.96.

The difference between the areas of two circles is 209 square centimeters. Given that the circumference of a big circle is 10/9 times that of a small circle, how many square centimeters is the area of the small circle?

The circumference of a big circle is 10/9 times that of a small circle, the radius is 10/9 times, and the area is (10/9) 2 =100/81times. Here is the problem of difference times, and the small number = difference/(multiple -0 times).

3. There is a 40-meter-long copper wire, which is wound around a circular tube 12 times, leaving 2.32 meters. What is the diameter of the circular tube?

40-2.32 = 37.68m.

37.68÷ 12=3. 14 (m)

3.14 ÷ 3.14 =1(m)

Answer: diameter1m.

4. Cut a circle along the radius and make it into an approximate rectangle. Given that the circumference of a rectangle is 4 1.4 cm, what is the circumference and area of this circle?

Solution: Let the radius be x cm. (Because the width of a rectangle is the radius of a circle, the two lengths of a rectangle are the circumference of a circle. The formula of the circumference is: radius *2*3. 14).

(3. 14*2x)+2x=4 1.4

6.28x+2x=4 1.4

8.28x=4 1.4

x=5

Circumference of a circle: radius *2*3. 14.

5*2*3. 14=3 1.4 cm2

Area of circle: radius * radius *3. 14.

5*5*3. 14=78.5 square centimeters

Namely: 20% x+6+(20% x+6)-2+x/3 = X.

X=37.5 tons

4. The sixth grade mathematics circle knowledge induction.

1, circle: A circle is a plane figure surrounded by curves.

(Rectangular, trapezoidal, etc. Are all plane figures surrounded by several line segments?)

2. Radius: The line segment with one end in the center and one end on the circle is called radius. In the same circle, there are countless radii, all equal.

3, diameter: through the center of the circle, the line segment with both ends on the circle is called diameter. The same circle has countless diameters, all of which are equal.

The diameter of the same circle is twice the radius. (d=2r，r=d÷2)

4. A circle is an axisymmetric figure with numerous symmetry axes, and the symmetry axis is the diameter.

5. The center of the circle determines the position of the circle, and the radius determines the size of the circle.

6. The largest circle in a square. The two are related: side length = diameter.

7. The largest circle in a rectangle. The two are related: width = diameter.

8. The diameter is the longest line segment in a circle.

1 1, the circumference of a semicircle is equal to half the circumference plus a diameter.

14, the area of a semicircle is half of a circle. Half = the square of π x r÷2

15. Compare two circles, the multiple of radius = the multiple of diameter = the multiple of perimeter, and the multiple of area = the multiple of radius = 2 times.

16, the area of the circle is the largest in the plane graphics with equal perimeters; In a plane figure with equal area, the circumference of a circle is the shortest.

17. A triangle with three vertices on a circle and a diameter on one side must be a right triangle.

By applying this rule, the diameter and center of a circle can be found.

(1) Draw a right angle with a point on the circle as the vertex.

(2) Connect two sides of an angle with two intersections of a circle, and this line is the diameter.

5. The knowledge points of the perimeter and area of the sixth grade mathematical circle in Zhejiang Education Edition are knowledge points, similar to the outline.

Summary of circle knowledge points 1. The formula of the circumference of a circle: C= πd or C=2π r 2. Area of the circle: The area occupied by the circle is called the area of the circle. 3. Cut a circle into an approximate rectangle. The length of the cut rectangle is equivalent to half of the circumference, and the width is equivalent to the radius of the circle. Because the area of a rectangle is equal to length * width, the area of a circle is equal to π. Or S= π( d\2)? Or S= π(C÷π÷2)? Draw the largest circle in a square, and the diameter of the circle is equal to the side length of the square. 6. Draw the largest circle in the rectangle, and the diameter of the circle is equal to the width of the rectangle. 7. A circle, the radius of the outer circle is r, the radius of the inner circle is r, and its area is S=πR? -πr？ Or S=π(R? -r？ (where R=r+ the width of the ring. ) 8. The circumference of the ring = the circumference of the outer circle+the circumference of the inner circle 9. The circumference of a semicircle is equal to half the circumference plus the diameter. The formula of the circumference of a semicircle is C=πd ÷2+d or C=πr+2r 10. The area of a semicircle = the area of a circle. ÷ 2 1 1. In the same circle, the diameter and circumference will be expanded or reduced by the same multiple, while the area will be expanded or reduced by the square of the above multiple. For example, in the same circle, the radius is enlarged by four times, the diameter and circumference are enlarged by four times, and the area ratio of area enlargement 16 times 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 the two circles are both 2:3, and the area ratio is 4:9. 13. The radius of the circle is increased by one centimeter, and the circumference is increased by 2π one centimeter; When the diameter of a circle increases by one centimeter, the circumference increases by one centimeter. 14. 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.