Math diary's 300-word article on circles.
We explored the circle before, and now we continue our exploration journey. If a circle has a perimeter, it will naturally have an area. Now let's explore the perimeter of our circle and the area of the "brother" circle.
The circumference of the previous circle is about the diameter, and the "brother" area is about the "brother" radius of the diameter. We read the inquiry activities in the book, and we took out the math tools. There are two circles in it, one is to divide a circle into 12 parts, and the other is to divide a circle into 24 parts. I cut out 12 copies, and according to the book, we made a figure similar to a parallelogram. I was surprised. I continued to make 24 copies and made a rectangular figure. I gradually understand that the height of a parallelogram is equivalent to the radius of a circle, and its base is equivalent to half the circumference of a circle. The length of a rectangle is equivalent to half the circumference, and the width is equivalent to the radius of the circle. From my understanding, I derived a formula for calculating the area of a circle:? Multiply by the square of r to get the area of the circle. On the original basis, I generalized and listed three methods to find the area of a circle in the exam: 1. Which is the simplest and most direct way to find the area with known radius? Multiply it by the square of R2. To find the area of a known diameter, this method first needs the radius (diameter divided by 2= radius) and then multiplies it by the square of the radius? Do it. It's a bit difficult to know the perimeter as an area, but you can do it well as long as you are careful. Find the diameter first: perimeter divided by? , and then find the radius: diameter divided by 2, and then? Just multiply it by the square of R.
In mathematics, we should learn to draw inferences from others and work out formulas by ourselves, so that mathematics will become your bosom friend.
Math diary's 300 words, the second chapter is about the circle.
The teacher will teach us how to calculate the circumference this morning.
The teacher first took out the disc and said, let's draw a circle or take out a round thing and try to measure its circumference. ? So, we began to discuss. Let's find a way first, and then start the operation. A classmate immediately came up with an idea and said, I have an idea. Make a mark on the disc first, and then roll from that mark to the right on the ruler to make a mark. The measured length is the circumference of the disc. ? I immediately thought of a way, and I said, I have an idea, too. Let's wrap a piece of paper around the disc, make a mark, and then measure the length of the paper, that is, the circumference of the circle. ?
After a while, after listening to our respective methods, the teacher said that some methods will inevitably have some mistakes. I'll teach you how to calculate the circumference!
? The circumference of a circle needs a diameter. The circumference of a circle is always greater than three times its diameter. In fact, the circumference divided by the diameter of a circle is a fixed number. Let's call it pi It is said that the calculation usually takes 3. 14, so the circumference of a circle = diameter? Pi (3. 14), that is, c=? D or c=2? R. The teacher gave another example.
Math diary's 300 words, the third chapter is about the circle.
Learning mathematics is a difficult but enjoyable thing. Whenever I encounter difficulties, I want to give up, but I am curious about mathematics and always want to do the problem well. Difficulties came to me step by step, but I overcame them again and again. Is it true?/You don't say. Where there is a will, there is a way.
What impressed me the most was the area of the circle at that time. At that time, I only knew how to find the area of a circle, but now the two circles are together. I don't know how to find it. I gave up without serious thinking and didn't do my homework well. I thought: I can't go on like this, I have to work hard. In class, I listened carefully to the teacher's explanation and immediately understood that I knew how to do this problem.
So, math is like life. Many things are experimented by ourselves, so that we can make progress slowly and make achievements slowly.
Diary of Mathematical Circle Part IV
The teacher asked us to fold the circle in the study tool and see what we can find from it. I wonder in my heart: a circle is a circle. What is there to fold? So let's fold the circle and understand the symmetry of the circle!
We took out scissors and cut a circle, and then cut it into eight parts on average. The teacher asked us to think about how to make the ball out of a circle. Some students say it is very useful? Take it, some say that everyone is fighting for radius, and the class is very lively. Finally, the teacher asked us to try to put eight pieces of fan-shaped paper together. I spelled a figure similar to a parallelogram.
Then, we divide the circle into 16 and 32 respectively, and then put the cut small sectors together to form a polygon. At this time, I found that the more the average score, the closer the graph is to a rectangle.
Because: rectangular area = length? extensive
So: the area of the circle =C/2? r=2？ r/2？ r=？ r2
After the decomposition and reorganization of the graph, I know how to find the area of the circle! Math is amazing ~
Diary of Mathematical Circle Chapter 5
We explored the circle before, and now we continue our exploration journey. Does a circle have a circumference? Sure, okay? There will be area. Now we explore the circumference of our circle? Brother? The area of a circle.
The circumference of the previous circle was probably the diameter, so? Brother? Is the area about the diameter? Brother? Radius. We read the inquiry activities in the book, and we took out the math tools. There are two circles in it, one is to divide a circle into 12 parts, and the other is to divide a circle into 24 parts. I cut out 12 copies, and according to the book, we made a figure similar to a parallelogram. I was surprised. I continued to make 24 copies and made a rectangular figure. I gradually understand that the height of a parallelogram is equivalent to the radius of a circle, and its base is equivalent to half the circumference of a circle. The length of a rectangle is equivalent to half the circumference, and the width is equivalent to the radius of the circle. From my understanding, I derived a formula for calculating the area of a circle:? Multiply by the square of r to get the area of the circle. On the original basis, I generalized and listed three methods to find the area of a circle in the exam: 1. Which is the simplest and most direct way to find the area with known radius? Multiply it by the square of R2. To find the area of a known diameter, this method first needs the radius (diameter divided by 2= radius) and then multiplies it by the square of the radius? Do it. It's a bit difficult to know the perimeter as an area, but you can do it well as long as you are careful. Find the diameter first: perimeter divided by? , and then find the radius: diameter divided by 2, and then? Just multiply it by the square of R.
In mathematics, we should learn to draw inferences from others and work out formulas by ourselves, so that mathematics will become your bosom friend.
Diary of Mathematical Circle (6)
Mathematics is everywhere. There are many kinds of mathematics around us. Mathematics is essential, otherwise it will bring all kinds of inconvenience to life. Let's look for mathematics and explore mathematics together.
? Round? We can see everywhere, aren't the bottoms of moon cake boxes, tea cans and medicine boxes all round? But they are called cylinders as a whole. Pick up these cylinders and you may think, why do you want to make the bottom round? Why not make it rectangular or square? I have questioned it before, and now I can help you solve it!
When you make a cuboid, a cube and a cylinder from the same material, you can calculate the volume. This is what we will find: the volume of a cylinder is the largest, the volume of a cube is the second, and the volume of a cuboid is the smallest. At this time, I realized that in order to save materials, I made these boxes round, which also expanded the volume.