一些数学的新发现
一、一个变换
- One transformation
实际场景：一排小方块排成一排，然后对折，把不能对折的小方块取出来。重复这项操作，直到小方块两两排成一列，这个过程中取出来的小方块就是这个变换的结果。
Real condition: Some small squares are arranged in a row, and then folded in half. Take out the small squares that cannot be folded. Repeat this operation until the small squares are arranged in a row two by two. The small squares which are taken out in this process are the result of this transformation.
例如（这里拿1来表示小方块）：
For example(Take 1 here to represent the small square)
1111111111111111111111111（25）
对折1次(Fold once)：111111111111（12）
111111111111
总共取出1个小方块。
One square is taken out in total
对折2次(Fold twice)：111111（6）
111111
111111
111111
总共取出1个小方块。
One square is taken out in total.
对折3次(Fold three times)：111（3）
111
111
111
111
111
111
111
总共取出1个小方块。
One square is taken out
对折4次(Fold four times)：11（2）
11
11
11
11
11
11
11
总共取出9个小方块。
Nine squares are taken out in total.
因为小方块已经两两排成1列，所以变换结束。故25通过此变换后结果为9。
Because the small squares have been lined up two by two in a row, the transformation is over. So the result of 25 after this transformation is 9
二、此变换的应用
- Transformation application
我们可以通过程序查找像25和9这样，变换前的数是某数的平方，变换后的数是某数的平方的数对列。
We can use the program to find numbers like 25 and 9, which before transformation is the square of a certain number and after transformation is the row of square of a certain number.
这里列下程序查找结果（这里忽略了0的情况）：
The following is the program search result (0 is ignored)
25 9
36 4
100 36
144 16
400 144
576 64
1600 576
。。。。。。
603979776 67108864
1677721600 603979776
不难发现，从36和4开始，每个变换前的数，在下一列，都会变成变换后的数，而且把这些数每一位相加，如果得到的不是个位数，则继续每一位相加，直到得到个位数，会发现它们的结果都是9。而且有一个有趣的数就是576，这个数在手机九宫格里打，输出的结果有可能是“老婆”。
It is not difficult to find that starting from 36 and 4, each number before the transformation will become the number after the transformation in the next column. Add each of these numbers' digits, if it is not a single digit, continue to add, until you get the single digits, and you will find that their results are all 9. And there is an interesting number is 576. When this number is played in the mobile phone Jiugongge, the output result may be "wife"
三、规律解析
3.Law analysis
注:中间为数队列,左右两边为对应的规律。这里把所有的数字都对应到1-9中(方法就是把一个数所有数位相加,直到得到1-9的其中一个数字)。左右两边为数字的规律。
Note: There are several queues in the middle, and the corresponding rules are on the left and right sides. Here, all the numbers correspond to 1-9 (the method is to add all the digits of a number until one of the numbers in 1-9 is obtained). The left and right sides are the law of numbers.
