What other graphics did math diary miss in the last article? Yes, it is round. It's not yuan, it's not original, it's round, it's cylinder, it's cone, it's ellipse, it's round table, it's round.

Let's review the knowledge and terminology of circles first. A plane figure with a center, curved edges, no straight edges and no corners. The center of the circle is called the center. Through the center of the circle, the line segment with two ends on the edge of the circle is called the diameter of the circle, and half of the diameter is called the radius. A line segment with two endpoints on the edge of a circle is called the diameter of the circle, and half of the diameter is called the radius. A line segment whose two endpoints are two points on the edge of a circle is called a chord. The ratio of the circumference of a circle to the radius of a circle is called pi, which is about 3. 14 16. If the circle is divided into 360 parts according to the center, the angle in each part is 1.

Our life is full of circles. Tires, clocks, basketball, football, electric fans, hula hoops ... Almost all the planets and stars are round. The reason why the tire is round is because the distance between any point on the edge of the circle and the center of the circle is equal-which is why only the circle has a radius in many plane drawings-so the car runs stably. The same is true of clocks and watches. The iron frame of the electric fan can be made into a disc shape, saving materials.

The strings on the ring don't mean a few on the guitar-they are a bit like them. The diameter of a circle is the longest chord. And the same two points on two equal-length chords are also the same from the center of the circle. Speaking of the center of the circle, I'm going to teach you a way to make the center of the circle: fold the circle in half to form two semicircles, and then fold it in half to form four 1/4 circles. After opening, the junction of two creases is the center of the circle.

The circle is indeed the strangest and most unique figure in graphics. In the huge project of studying pi, we can see people's hard work under pi, and now the figure of pi has reached more than 200 billion decimal places. I hope everyone can go further in the study of the circle!

Math diary (cylinder)

Unconsciously, two weeks have passed, and as a graduating student, I can't help but feel deeply. Everyone is persistent in doing one thing-keep writing a weekly diary! This is good for everyone. It can not only help you consolidate what you have learned, but also exercise your writing ability.

Looking back on my study and life a few days ago, I can't help but benefit a lot.

After a week's study, we learned the knowledge of finding the lateral area, surface area, volume and volume of a cylinder. Let's recall what we have learned again! First think about the name of the cylinder: the upper and lower surfaces of the cylinder are called the bottom surface of the cylinder, and the surface surrounded by the cylinder has a curved surface called the side surface of the cylinder. The distance between the two bottom surfaces of a cylinder is called the height of the cylinder.

By expanding the side of the cylinder, a rectangle can be obtained. The length of the rectangle is equal to the circumference of the bottom of the cylinder, and the width of the rectangle is equal to the height of the cylinder. In this way, we can easily see that the lateral area of a cylinder is equal to the perimeter of the bottom multiplied by the height.

How to find the surface area of a cylinder? Spread all the surface of the cylinder, then we can see that it is like a division symbol, and the surface area of the cylinder is equal to the lateral area of the cylinder plus two bottom areas. Next, I have to do the problem again, and I need a very troublesome cylindrical area. Alas, it is not easy to find the surface area. We need to find the bottom area and the side area, and then add them up. If we are not careful, we will make mistakes. Is there any good way to put it all together? I was thinking. Look at the bottom area and lateral area's formula!

S-bottom =πr2, which has two bottoms, namely 2πr2. Let's look at lateral area's formula: S-side =2πrh, add them together, extract the similar term: 2πr, and form a new formula: S-table =2πr(r+h) by using the law of multiplicative association. A new formula was born. With this formula, just multiply it once and everything will be fine!

I used a formula to find the area of a ring: s ring =π(R2-r2). Come to think of it, this is actually a combination of formulas! Subtract two circles, extract π and * * *, and get a new formula.

The birth of these new formulas is attributed to flexibility and laziness! If it was not too much trouble, there would be no such formula. In fact, it is also important to use the formula flexibly. Sometimes, the questioner steals a lazy person and misses a condition, so we can ask for more. However, we need to be lazy in some places, and we can't be lazy.

There is a problem: there is an inscribed circle in a big square, and the area of the big square is 20 square centimeters. Find the area of a circle.

According to common sense, we should first find the side length of a big square, which is D, then R, and finally the area. However, in this problem, how can we find R&D? Unless a prescription is prescribed, it will be troublesome and will certainly be inexhaustible. What should I do? At this time, it is necessary to use the formula flexibly. Since the area formula of a circle is πr2, it is ok to find r2 instead of R! At this time, we can regard it as a whole a, that is, we only need to find aπ. How to ask? The area of a square should be (2r)2, which is 4r2 after simplification, that is, 4a. So we can use 20÷4=5(cm2) to find a, and then use 5×π≈ 15.7(cm2). The area of the circle is about 15.7cm2, so the area of the circle aπ can be solved without roots.

Many formulas can be combined with each other to form a simple and practical new formula.

As long as we innovate, we are actually kneading the steamed bread eaten by the giants into a ball and making new rolls. Is this not good?

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