12/11/2023 0 Comments Myst book of squares![]() The first is a diagram of a closed tour, and the second is an open tour (numbers are included in the second diagram to further illustrate the knight’s movements): Many chess problems can be discussed quite nicely using techniques and terminology from ‘graph theory’ in mathematics. The following are two diagrams of knight’s tours. The famous mathematician Euler spent some time creating his own knight tours. If on visiting the last square the knight is able to hop to the square on which it first started it is known as a closed tour (and so the knight could resume the exact same sequence of moves to complete another tour) while if the knight is unable to hop to the original square, it is known as an open tour. For those of you who are not familiar with the knight’s tour, the goal is to place a knight on an empty chess board and then move the knight to each of the remaining 63 squares while only visiting each square once. In some more interesting cases (to me at least), you can apply certain math techniques to analyze some chess positions and decide the answer to the ultimate question: who, if anyone, is winning in a given position (although this might have to wait until a future article)? Hopefully, some of you will also be introduced to some new concepts, will find them interesting, and will go on to explore some new and beautiful ideas! To begin, let’s look at the famous knight’s tour in chess. In many cases, some familiar chess problems are really just math problems in disguise. In this article, I would like to introduce some of the connections between mathematics and chess. Many other great chess players were also in fields related to mathematics Botvinnik, for example, was an electrical engineer and computer scientist. I would suggest it is no coincidence that some of the best chess players ever were also accomplished mathematicians: Euwe, Lasker and Nunn to name a few. Certainly, many traits of a successful mathematician or chess player overlap: strong analytical ability, spatial awareness, a high level of creativity, intuition, pattern recognition and on and on. People often talk about the connections between math and chess, assuming that being good at one means that you are (or would be with a bit of effort) also good at the other.
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