Extreme thinking, graphic test and chess test, square root, chip calculus theory.

1, limit thought: When Liu Hui proved various formulas in "Nine Chapters Arithmetic", he put forward the requirement of "analyzing with words and decomposing with diagrams", and established effective drawing test and chess score test methods for many problems. Some problems can't be solved by just using the chess chart, so we need to have a fairly clear limit thought. It is extremely important for Liu Hui to apply limit ideas and concepts to solve practical mathematical problems.

2. Look-up method and game method: Liu Hui used the look-up method and game method when solving mathematical problems. Both methods help to solve mathematical problems through figures or models on the chessboard.

3. Rooting: In Rooting, Liu Hui discussed the existence of irrational roots from the infinite meaning of rooting, introduced new numbers, and created a method of infinitely approaching irrational roots with decimals.

4. Fundraising calculus theory: Liu Hui first gave a clear definition of rate, and based on the three basic operations of multiplication, consistency and consistency, established a unified theoretical basis for the operation of numbers and formulas. He also used "rate" to define the "equation" in China's ancient mathematics, that is, the augmented matrix of linear equations in modern mathematics.