I don't know when the nine-ring chain was invented. Because of its long history and lack of historical materials, many people think it is likely to come from the people. /kloc-cardano, a great mathematician in the 6th century, made outstanding contributions to the popularization of cubic equation solution, and mentioned the Nine Chains in 1550 (equivalent to the middle of Ming Dynasty in China). Later, the great mathematician Wallis also made an incisive analysis of the nine-ring chain. In the Ming and Qing Dynasties, everyone liked everything from the so-called "scholar-officials" to peddlers and pawns.
Nine-ring chain is usually made of thick lead wire. Few folk artists are engaged in this work now, so we must make one ourselves. It has nine rings, each ring is connected with a thin straight lead rod, and each rod passes through the latter ring and is inserted into a row of small holes on the tin plate. The lower end of the rod is bent by a small circle, so that they can only move up and down in the small hole, but they can't get out. In addition, make a double-stranded hairpin with thick lead wire.
The purpose of playing this game is to put nine rings on the hairpin one by one, or to take all nine rings off the hairpin. It is not easy to put it on or take it off. There are hundreds of procedures and certain rules to follow. In mathematical terms, there is a set of "algorithms".
First, introduce two basic actions. If you want to put the ring on the hairpin, you should first put the ring on the head of the hairpin from bottom to top. This action can be done at any time except the first ring, and other rings can't be worn because there are other rings. However, it should be noted that if an adjacent ring in front has put on the hairpin, and the other rings in front are not on the hairpin, then just move the ring on the hairpin to the front of the hairpin head temporarily to make way for the hairpin head, the ring behind can be put on, and then the ring in front can be restored to its original position.
As for the basic action of taking off the ring from the hairpin, just reverse the action of "putting on the ring" above.
After understanding these two basic movements, we need to practice more, so that we can use them freely whether we put them on or take them off. Now it can be seen that if you just put on the first ring, you only need one step. To wear the first ring and the second ring, you can wear the first ring first and then the second ring. Therefore, a * * * takes two steps. What if I want to wear three rings? The procedure is more troublesome. You must connect the first ring and the second ring first, then take off the first ring before you can connect the third ring and finally connect the first ring. In this way, a * * * needs five steps. For the sake of unity, each link counts as a step. The more rings there are, the more complicated the procedure will be. If you make a mistake, it's broken. Fortunately, ancient researchers in China have long considered it. According to the characteristics of ancient calculation, they created three formulas: "1213121, the head of the hairpin is followed by two, and the single ring is on the back ring of the hairpin." (The last five steps are12131; The first five steps are 13 12 1. )
In other words, every eight steps can be regarded as a unit, and the first seven steps must be "1213121". Whether it is "up" or "down" depends on the natural trend. That is, what is not on the hairpin should be "up" and what is on the hairpin should be "down". As for the eighth step, it depends on the situation of issuing cards at that time: if there are two rings connected together, the ring at the back must be taken off; If there is only one ring on the hair stick, you must wear the latter ring. The above is the meaning of the formula, and all the secrets of the algorithm are here. According to these three formulas, it is not difficult to untie or put on nine rings, although there are as many as 34 1 step. According to the records of China's ancient novels, it only takes about five minutes for old folk artists to untie all the Nine Rings.
1975 An album was published abroad, focusing on various series. Due to the rapid development of electronic computers, there is a tendency of "discretization" in mathematics. Therefore, the publication of this book is considered unprecedented and has been well received in all aspects. In this book, the following series are also included:
1、2、5、 10、2 1、42、85、 170、34 1、……
At first, everyone wondered what it was for, because it was neither a arithmetic progression nor a geometric series, nor a famous series. However, once pointed out, it suddenly dawned that it was originally a "nine-chain" series. 1 in the first item means that it takes only one step to untie one ring, and 2 in the second item means that it takes two steps to untie two rings, and so on. Therefore, it takes 34 1 step to untie the nine-ring one * * *.