Yang Hui, one of the four great mathematicians in Song and Yuan Dynasties, was the first mathematician in the world to draw a wealth of vertical and horizontal maps and discuss their composition rules.

Speaking of this achievement of Yang Hui, we have to start with an accidental event.

Later, Yang Hui sorted out this kind of problems scattered in predecessors' works and circulated among the people, and got many similar pictures, such as Five-Five, Six-Six, Evolution, Yi Tu, Nine-Nine and Hundred-Child.

Yang Hui has always called these graphs vertical and horizontal graphs, and wrote them into his own mathematical book "Algorithm for Continuation of the Ancient" at 1275, and passed them on to future generations. But for a long time, people used to treat it as a pure mathematical game and didn't pay due attention to it.

With the development of modern combinatorial mathematics, vertical and horizontal graphs show more and more vitality, and find a place in graph theory, combinatorial analysis, game theory, computer science and other fields.

Yang Hui can be said to be the first mathematician in the world to give such a rich vertical and horizontal diagram and discuss its composition law.

? ? In addition to this achievement, Yang Hui also made a major contribution, that is, the "Yang Hui Triangle".

On one occasion, Yang Hui got a book "Nine Chapters of Yellow Emperor's Arithmetic Fine Grass", which was written by several Jia Xian in the Northern Song Dynasty. There are many great achievements, for example, Jia Xian drew a picture called "Source Map of Prescription Science". In the west, it was not until16th century that someone drew a similar figure on the cover of a book. Pascal, a French mathematician, discussed the properties of this figure in detail in his paper 1654, so it is also called "Pascal triangle" in the west.

In addition to the above achievements, Yang Hui also wrote books such as Daily Algorithm, Multiplication and Division, Changing Background, and Field Method of Multiplication and Division, which provided extremely important information for future generations to understand the mathematical outlook at that time.

? Yang Hui's works have greatly enriched the treasure house of ancient mathematics in China and made outstanding contributions to the development of mathematical science. He deserves to be one of the "four great masters in Song and Yuan Dynasties".