Cao Chongsheng was five or six years old, and his intellect was as good as an adult. When Sun Quan tasted the giant elephant, Taizu wanted to know its weight, and when he visited the group, Xian Mo could not be reasoned. Chong Yue: "If the image is placed on the ship, and the water mark is carved, and the object is carried, the school can know it." Repeating the title of other thing, it is like a heavy can also be known as "Taizu Yue, that is, to carry out yan."
Do you feel familiar with the above text?
What did you learn after you learned this class at that time?
Whether I was like me only knew that Cao Chong at that time was relatively smart. Without studying the deeper implications of this method of weighing images. I've been busy with some things lately and I've been idle. One day I suddenly remembered this story, and I thought about the process of weighing an elephant and it felt quite interesting, so let's call it an elephant together.
How many steps does it take to weigh an elephant?
According to the original steps, the first step, placed on the boat, and carved its water marks. The elephant is herded to the boat and then the hull is marked along the water surface at the depth of the hull sinking when the elephant is on the boat.
In the second step, weigh the object to carry it, then the school can know. After catching the elephant ashore, load the ship with stones so that the hull sinks to the marked position.
The third step, to repeat the name of other things, is like a heavy can know also. Use weighing stones to know the total number of elephants.
Why weigh a stone can be known the weight of an elephant.
The answer is because there is a ship as a balance, and the depth of the elephant's sinking while on the boat is equal to the depth at which the stone sinks, so the weight of the elephant = the weight of the stone. At this point, the weight of the elephant is weighed.
If Sun Quan gave Cao Cao not one elephant but many elephants, how do you think you should weigh a group of elephants to know the weight of each elephant? How many times do you have to move a stone?
Mark the hull along the water as mark one (this can be called zeroing) before catching the elephant on the water. Marking the elephant along the water and on the hull after catching the boat is set to mark two. After driving the elephant down, you get the hull marking line in the picture below.
Suppose that the total weight of the stone is 1000kg after weighing the stone, and the vertical height of markers 1 to 2 is 30cm with a ruler. Assuming that the hull is relatively vertical, the sinking depth of the hull is linear with the weight on the ship, and the sinking depth of the hull from the mark is 30cm The weight on the ship is 1000kg. At an ideal sinking depth of 15cm, the weight on board is 500kg. There are table data as follows:
Graph with the actual weight as the y-axis and the hull sinking depth as the x-axis. Set the trend line and display the linear formula, the resulting linear formula is: y=33.333x.
The remaining elephants were herded to the boat to mark the depth of the sinking of the hull. The actual weight of the remaining elephants can be calculated by substituting the hull sinking depth into the linear relationship based on the linear relationship obtained by the previous calculation (y = 33.33x, x hull sinking depth). In this case, the stone needs only be moved once to calculate the total number of other elephants.
There is a large deviation in the actual weighing image, and there is no ideal linear sinking relationship. Because the hull is generally curved, the sinking relationship is not a linear linear relationship, perhaps a curve. The hull shape may be like this.
Then the hull sinks the relational data, hypothetically.
From the chart data, it can be seen that the trend line fit calculated using a simple linear relationship formula is relatively poor. In the end, if the relationship is used to weigh the elephant, it is inevitable that there will be a shortage of two pounds.
So how do you increase accuracy?
Change linearity to polynomial relation.
According to the graph shows that the known trend line almost coincides with the actual, the r-squared value rises from 0.9675 to 0.9998, which is very close to the actual data.
If you use this method to record the relationship between hull sinking and weight by first adding a stone of known weight to the ship to mark the sinking depth of the hull in proportion to the ship. Then calculate the relational formula, drive the elephant to the boat to record the sinking depth of the hull, and substitute the sinking depth of the hull into the relation to calculate the weight of the elephant.
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