First of all, this question:
Traffic on the street, cars coming and going, the wheels of each car are round; When we move a heavy object, we will put the object on a cylinder or a circular tube. Seeing this, I am puzzled: why are they all round and not other shapes?
This problem has been bothering me for a long time. It was not until this semester when we were studying "circle" that the teacher showed us the ridiculous performance of triangle wheel and square wheel in the courseware that I realized that if the wheel was made into a circle, the distance between the axle and the ground would always be equal to the radius of the wheel. This makes it easy for the wheels to roll on the ground. If this wheel is square and triangular, and the distance from the rim to the center of the wheel is not equal, then this kind of car will definitely bump up and down and shake badly. Therefore, the wheels are round, and when moving things, you will also choose the circular tube pad below.
But I'm still thinking: Is there really only a circle? Is there any other shape that can replace the circle?
Second, thinking and exploration:
During the weekend, I found a toy car, a foam board, a knife and so on, and started my exploration journey.
1, the first exploration: increasing the number of edges.
I noticed that the square wheel in the courseware is much smoother than the triangular wheel, although it is bumpy, so I thought: if the wheel is made into a regular hexagon, will it be more stable?
So, I made four regular hexagonal wheels and tried them, which was much smoother. I can't help but get excited: as long as we do more edges, won't it be more stable? I began to fantasize in my mind that "the number of wheels is increasing, and the car is getting more and more stable", but when I think about it carefully, I feel that something is wrong: the number of sides is increasing, isn't it gradually becoming a circle? This is the same as what I learned from The Area of a Circle: "The more copies of a circle, the closer the figure is to a parallelogram", which should be what the teacher said.
I'm a little depressed at the thought: this method won't work.
2. The second exploration: the imitation show of the circle.
If a plan fails, a plan will be regenerated. I thought again: the reason why the wheel is round is because the distance from the center to the surrounding is the same. Triangular and square wheels will bump because the distance from the center to the edge is shorter than the distance from the vertex to the edge. Wouldn't it be ok if we increased the distance from the center to the edge to make them the same length?
With this in mind, I drew a regular triangle, found its center (the intersection of three midlines), and drew three arcs with it as the center and the length from the center to the vertex as the radius. Secretly proud in my heart, isn't this distance equal to? But when I saw it, I was dumbfounded: it's just a circle! I didn't give up, so I drew a square, found the center of the circle and drew four arcs. The result is still a circle.
This road seems to be blocked.
3. The third exploration: change the center of the circle.
The second failure made me realize that you can't take the original center as the center of the circle, because it will turn it into a circle. So where is the center of the circle? Looking at the figure in front of me, an idea arises spontaneously: how about using the vertex as the center of the circle?
At first, I drew a regular triangle, and then made three arcs with its three vertices as the center and the side length as the radius. So a strange guy was born.
I couldn't wait to make four such wheels, but the experimental results shattered all my hopes: these wheels are much smoother than triangles, squares, regular hexagons and so on. , but it still fluctuates up and down, failing to achieve the effect of a round wheel.
4. Dad's strange idea:
Continuous failures make me very depressed. I sat there disheartened, and I felt that I was at the end of my rope: maybe only a circle can make a wheel.
My father noticed my depressed expression and came over to ask me. I tried my best to tell him my doubts and several attempts, hoping that my father could give me a train of thought. Dad looked at my "masterpiece" with interest while listening. It was a long time before he said, "Your ideas are all very good. It doesn't matter if you fail, the work is very interesting. " He pointed to the strange guy I finally made and said, "Try putting a board on it. Note: put it directly on the wheel, not on the shaft. "
"What? Directly on the round? " I can't believe my ears. "This is a strange idea." Although I was puzzled, I believed that my father would not say this for no reason, so I did it. When I finished writing, I pushed it forward. Strange! The car is flat! The car is smooth! Smooth as a round wheel!
I jumped up and looked at my father in surprise, hoping he could give me an answer. Dad looked at my dumbfounded expression and smiled and said, "Your boy is not simple. This thing you "create" is called an isometric curve. If you are interested, you can go online to find relevant information. "
Iii. Answers and new doubts:
I can't wait to find information on the internet. I found the explanation of the equiwidth curve on the Internet: "Equiwidth curve refers to a non-circular equiwidth curve and a closed curve with a fixed distance from the" support line ". When the wheel with equal width curve rolls horizontally, the height of the highest point is displayed unchanged. " That's true. Only when it rolls, the highest point remains the same, and the car can remain as stable as before.
What surprises me even more is that curves with equal width can also be used as wheels! The following are the articles and pictures I saw on the Internet:
Operation: Press the start button to observe the running state of the car with equal width curve wheels.
Principle: The wheel doesn't have to be round, and its shape is similar to the "triangle" of the wheel with equal width curve, which can also make the car run smoothly. If two parallel lines are tangent to a curve with the same width, the distance between the two parallel lines is equal no matter where you aim. Therefore, when a wheel with an equal width curve rolls horizontally, it means that the height of the highest point remains unchanged.
Through the demonstration of this exhibit, we can vividly reveal the wonderful characteristics of equidistant curve and its internal relationship with circle, so that the audience can break through the conventional way of thinking.
After many twists and turns, I finally found a circle instead of a figure-"equal width curve", which made me very happy. In this journey of mathematical exploration, I not only realized the difficulty of exploring the mysteries of mathematics, but also felt the joy of successful exploration. This feeling is just like what grandpa Chen Shengsheng, a mathematician, said: Mathematics is really fun!
With joy, a new question slowly emerges: obviously, the axle of this car can't be in the center, so where is it?