1, the formula for finding the area of a circle is an important knowledge point in mathematics, which helps us to calculate the area of a circle. We need to know the definition of a circle. A circle is a plane figure surrounded by a curve, in which the distance between any two points and the center of the circle is equal. This distance is called the radius.
2. We can deduce the formula of circle area by cutting and recombination. We can cut the circle into many small sectors. Each sector can be regarded as a triangle, the base of which is a part of the circumference and the height is the radius. We can rearrange these sectors into an approximate rectangle.
The length of this rectangle is half of the circumference and the width is the radius. We can calculate the area of this rectangle. The area of a rectangle is equal to the length times the width, that is, half the circumference times the radius. To simplify the calculation, we can use the formula of pi C=2πr, where c stands for circumference and r stands for radius.
4. Substituting this formula into the calculation formula of rectangular area, we get: area = 1/2× 2π r× r = π r 2. This is the formula of circular area. The area of a circle is equal to the square of the radius times π. π is an irrational number, which is approximately equal to 3. 14 159. As the radius increases, the area of the circle will increase accordingly; When the radius decreases, the area of the circle decreases accordingly.
The benefits of learning mathematics
1. Mathematics is a rigorous discipline, which requires students to make rigorous reasoning and logical thinking. By studying mathematics, we can cultivate our logical thinking ability and improve our problem-solving ability. Problems in mathematics often need us to analyze and solve. By studying mathematics, we can learn how to analyze problems, find out the key points of problems and adopt appropriate methods to solve problems.
2. Concepts and theories in mathematics are often abstract, which requires us to abstract laws and patterns from concrete things. By studying mathematics, we can cultivate our abstract thinking ability and improve our ability to understand and apply abstract concepts. Mathematics is a subject that needs calculation and operation.
3. By studying mathematics, you can improve your calculation and operation ability, and improve the speed and accuracy of mathematical calculation. Geometry is an important branch of mathematics, which involves the shape and structure of space. By studying geometry, we can cultivate our spatial imagination ability and improve our understanding and application ability of three-dimensional space.