? As we all know, there are some differences between circles and other figures. The edges of other figures are straight lines, while the edges of circles are curves. Other three-dimensional graphics can't move there, but the sphere can scroll in one position. This shows that the circle is really different from our other geometric figures, but it is also very common in daily life.
? For example: Why is the manhole cover round? Why are tires round? First of all, let's look at the manhole cover: the longest line segment in the middle of the circle-its diameter is always the same, so the diameter can always be supported on it, so that the manhole cover will not fall off. If it is rectangular, put the rectangular manhole cover vertically, and as soon as you let go, the manhole cover will fall off. Look at the tire again: the tire is round, so that the car can go straight ahead, because the distance from the center of the tire to the ground is always the same-this distance is called the radius, which is half the diameter-if it is replaced by other graphics with straight lines as the edges, it will affect the driving of the car. So circles are also very common.
perimeter of a circle
Ok, we have named the radius and diameter, and now we are going to study the circumference of the circle. First of all, how can we measure the circumference of a circle? Can you measure with a rope: after measuring the length of a rope, make a circle with this rope, and the length of the rope is the circumference of the circle-is that ok?
This is certainly possible, but if you want to measure the circumference of several circles of different sizes, you can't all use the rope measurement method, or is there a formula to calculate the circumference of the circle?
Actually, there is. First of all, what might the circumference be related to? Could it have something to do with the diameter? I will. The circumference of a circle is actually related to its diameter. The teacher asked us to measure the circumference of several circles of different sizes. We find that the ratio of the circumference to the diameter of a circle has been floating around the number three. We guess it is a fixed value. Of course, there will be errors when we measure, which will cause the numbers to change all the time. Later, the teacher told us: In fact, this number is the "Wu" we knew a long time ago (3. 145438+05926). Since their ratio is Uyghur, that is to say, diameter × Uyghur = circumference. So the formula comes out: Wu d = C. But Wu is an infinite acyclic decimal. For the convenience of calculation, we take Wu's approximate value as 3. 14. If 3. 14× diameter is used, it is roughly equal to the circumference.
? Area of a circle
Now that we know the circumference of the circle, we need the area of the circle. To find the area of some figures, we can divide them into triangles by division, such as dividing a rectangle into two triangles, dividing a parallelogram into two triangles, dividing a trapezoid into two triangles, and so on. So can you divide a circle into triangles and then calculate the area of the circle?
But there is a problem here-the circle is a curve figure and the triangle is a straight line figure. No matter how the circle is divided, it can't be a triangle, because the curve can't be a straight line. But if we divide the circle infinitely with the idea of limit, the triangle will eventually be divided.
? Then we combine these triangles into a rectangle. But is this picture really square? Actually, it's not, because the triangles we split are all similar. Therefore, the area of this figure can only be similar to the area of a circle, but not completely equal.
We put these approximate triangles together to form an approximate rectangle, and the area of the rectangle is equal to the area of the circle.
? Because we need a rectangular area, we must use the length x width. So what is the relationship between the length and width of this rectangle and the circle? We did the manual operation again, and then magically found that the length of this rectangle is half of the circumference of the circle, and the width is the radius of the circle. Then it is half the circumference, and the x radius is about equal to the area of the circle. This formula is simplified as Uyghur rx (square of Uyghur R)-radius x square of Uyghur (take 3. 14).
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? Course summary
This is the circumference and area of a circle. Any suggestions can be made. After all, there are still some incomplete places in the paper that need to be revised. So let's call it a day.