Mathematician Christian Taful Santos from the University of Montreal has conducted a study comparing the speed of movement of the chess knight and the king on the board. According to his calculations, the knight reaches its target approximately 1.85 times faster than the king does. This means that if the king requires 24 moves to reach a certain square, the knight can do it in just 13 moves.
Aside from determining this speed difference, Taful Santos also explored a method of summarizing the movements of the knight by linking them to Fibonacci numbers. He introduced the concept of a “super-knight,” which can move a cells in one direction and b cells in the other, where a and b are coprime numbers with an odd sum. This concept expands the potential movements of the knight and enables the exploration of their mathematical properties.
For instance, when a = 2 and b = 3, a super-knight is, on average, 2.9 times faster than the king. When the numbers a and b correspond to the Fibonacci sequence, the speed of movement is related to the golden ratio, approximately 1.618.
The study also reveals that while the knight has local advantages, the king can sometimes nearly catch up on specific diagonal paths, reducing the speed difference to 1.5 times.
Taful Santos’ research extends beyond the realm of chess. By intertwining number theory, geometry, and combinatorics, it opens up possibilities for the exploration of objects and movements in higher-dimensional spaces. Even after 1500 years, chess continues to serve as a source of inspiration for mathematical discoveries.