How to get students to understand the formula for calculating the area of a circle

Use circular paper to guide students to deduce the formula by themselves: divide the circle into equal parts and put them together into an approximate parallelogram or rectangle.

You have to let your classmates know how they came about.

The circular area formula is a theorem law. is the square of pi * radius, which can be expressed by letters as: s= r or s= ·d 2). Indicates pi (radius, d represents diameter).

Radius of the circle: r

Diameter: dPi: (the value is an infinite non-cyclic decimal between to), which is usually taken as the value of .

Circle area: s = d 4

Circle Area = Pi Radius Radius.

Area of the semicircle: s semicircle = (r2) 2

Area of a semicircle = pi radius radius 2

Ring area: s large circle s small circle = (r2-r2) (r is the radius of the great circle, r is the radius of the small circle).

Ring area = outer major circle area Inner minor circle area.

Circumference of a circle: or.

Circumference of the circle = diameter of pi.

Circumference of the semicircle:

Or. The circumference of the semi-circle is like a bend, and the length = pi radius + diameter.

**Tale. Broadcast.

Kepler. Johannes Kepler was a German astronomer who discovered the three laws of planetary motion, which can be described as follows: all planets orbit in elliptical orbits of different sizes; In the same time, the area swept by the planetary radius in the orbital plane is equal; The square of the planet's orbital period is proportional to the cube of its distance from the Sun.

These three laws eventually earned him the nickname "Legislator of the Sky". He provided the most reliable evidence for Copernicus's heliocentric theory, and at the same time he also made important contributions to optics and mathematics, and he was the founder of modern experimental optics.

Kepler was a mathematics teacher, and he was very interested in finding the problem of area, and he did in-depth research. He thought that ancient mathematicians used the method of partition to find the area of a circle, and the results obtained were all approximations. To improve the degree of approximation, they constantly increase the number of splits.

However, no matter how many times it is divided, tens of thousands of times, as long as it is a finite number of times, the approximate value of the circle area is always obtained. In order to find the exact value of the area of the circle, it is necessary to divide the circle an infinite number of times, and divide the circle into equal parts.

Kepler also imitated the method of cutting watermelons, dividing the circle into many small fans; The difference is that he begins by dividing the circle into infinitely many small fan-shapes. The area of the circle is equal to the sum of the areas of an infinite number of small sectors, so in the last formula, the sum of the small arcs of the segments is the circumference of the circle 2 r, so there is This is the formula for the area of the circle that we are familiar with.

Kepler used the method of infinite division to find the area of many figures. In 1615, he published this new method of finding the area of a circle in his book The Solid Geometry of Wine Barrels.

Kepler boldly divided the circle into infinitesimal small sectors, and boldly asserted that the area of the infinitesimal sector is equal to the area of the corresponding infinitesimal triangle. He took an important step forward on the basis of his predecessors' search for the area of the circle.

The book "Stereo Geometry of Wine Barrels" quickly spread in Europe. Mathematicians spoke highly of Kepler's work, praising the book as a source of inspiration for new ways to find the area and volume of a circle.

Because the area of the circle is seven-ninths of the area of its inscribed square, Li Yu said that "the area of the circle s is equal to seven times the square of one-third of the square of its direct disturbance diameter d". The formula for calculating the area of a circle is: Heng Row S=7(d 3).

The area of the circle Radius Radius.

The area formula of the circle is known in the wild state

f Elimination.

In a plane, a moving point is centered on a certain point, and a closed curve formed by a certain length from the rotation of the hand is called a circle. A circle has an infinite number of axes of symmetry.

The area formula for a circle.

A circle is cut along the diameter, divided into several parts, and put together into an approximate rectangle, the length of the rectangle is equivalent to half of the circumference of the circle (half of the c) and the width is equivalent to the radius of the circle (r).

Because: the area of the rectangle = length x width = the area of the circle.

So: the area of the circle = length x width = 2 c = the square of the vultures.

The formula is: the square of the vultures.

The circle is calculated by the diameter of the area formula:

s=πd²/4

Where: s is the area of the circle, d is the diameter of the circle;

The concept of a circle. 1.The set of points whose distance to a fixed point is equal to a fixed length is called a circle. This fixed point is called the center of the circle and is usually denoted by the letter "o".

2.The line connecting the center of the circle to any point on the circumference of the circle is called the radius, usually represented by the letter "r".

3.The segment of the line that passes through the center of the circle and both ends are on the circumference of the circle is called the dashed sail diameter, which is usually denoted by the letter "d".

4.A line segment that connects any two points on a circle is called a string. In the same circle or equal circle, the longest chord is the diameter.

5.The part between any two points on a circle is called a rental arc, or arc for short. An arc larger than a semicircle is called an excellent arc, and an excellent arc is represented by three letters. Arcs that are smaller than a semicircle are called inferior arcs, and inferior arcs are represented by two letters difference bridge hail. A semicircle is neither an excellent nor an inferior arc.

Area of the circle: s = r = d 4

Sector arc length: l = central angle (radian system) *r = n° r 180° (n is the central angle).

Sector area: s=n r 360=lr 2 (l is the arc length of the fan).

Diameter of the circle: d=2r

Conical side area: s= rl (l is the length of the busbar).

Cone bottom radius: r=n° 360°L (l is the length of the busbar) (r is the bottom radius).

1. Circle area = pi radius radius, which can be expressed in letters as: s= r or s= *d 2). Represents pi (represents the radius of the locust and d represents the diameter).

2. Divide the circle into several parts, which can be put together into an approximate rectangle. The width of the rectangle is equal to the radius of the circle (r), and the length of the rectangle is half the circumference of the circle (c). The area of the rectangle is ab, and the area of the circle is:

The radius of the circle is rub rent (r) multiplied by lead such as half of the circumference of a potato c, s=r*c 2=r*r.

Elementary school students can understand that the bending scum of a circular surface is an exact formula by following these steps:

Define the area of a circle: The area of a circle refers to the area of the plane covered by the circle.

Illustrate the calculation of the area of a circle: You can derive the formula for calculating the area of a circle by cutting a circle into many sectors and then putting these sectors together into a shape that approximates a rectangle.

Guide students to the accuracy of the formula: By calculating the area of a circle with different radii, students can find that the area value calculated using the formula is very close to the actual circle area value, so as to understand the accuracy of the circle area formula.

Take practical measurements: You can verify the accuracy of the circle area formula by having your students quietly measure the radii of different circles using tools such as a tape measure and compass and then calculate their areas.

Through the guidance of the above steps, students can gradually understand that the area of a circle is an accurate formula, and be able to master the calculation method of the area of a circle.

1.Start with a concrete object, such as showing elementary school students a round card with a diameter of 10 centimeters and asking them to measure the circumference of the circle with a ruler. If the measurement is in centimeters, tell the child that this is the ratio of the circumference and diameter of the circle, which is about the same value