Shen Kuo, a great scientist in the Northern Song Dynasty, initiated the "gap product technique" in Mengqian Bitan, and began to study whether some items (such as jars, balls, chess pieces, etc.) were defective. ) According to certain rules, pile up to find the total, that is, the sum of high-order arithmetic progression, and calculate the formula of rectangular platform stacking. Yang Hui, a mathematician in the Southern Song Dynasty, enriched and developed the achievements of Shen Kuo's gap product method in Nine Chapters' Detailed Explanation of Algorithms and Origin and Variation of Algorithms, and put forward some new superposition formulas. The sequence discussed by Shen Kuo and Yang Hui is different from the general arithmetic progression. The difference between the two terms is not equal, but the difference of item by item or the difference of higher order is equal. This kind of high-order arithmetic progression's research is generally called "piling up" after Yang Hui.