and equilibrium stations within other machines allowed for a more effective or accurate result. The watches he perfected through his work in hydraulics allowed for an extremely accurate reading of the time. For irrigation, he provided hydraulics systems which distributed water equally and swiftly, which allowed communities to trade more effectively, and therefore prosper. His most memorable engineering feat is the man-made Kunming Lake in Beijing, which provided water for all of the surrounding area of Beijing and allowed for the best grain transport system in the country. His work with other such reservoirs allowed people in inner China access to water for planting, drinking, and trading. Guo's work in mathematics was regarded as the most highly knowledgeable in China for 400 years. Guo worked on spherical trigonometry, using a system of approximation to find arc lengths and angles. He stated that pi was equal to 3, leading to a complex sequence of equations which came up with an answer more accurate than the answer that would have resulted if he did the same sequence of equations, but instead having pi equal to 3.1415. As people began to add onto his work, the authenticity of his work was questioned. Some believe that he took Middle Eastern mathematical and theoretical ideas and used them as his own, taking all the credit. However, he never left China which would have made it more difficult for him to access others' ideas. Otherwise, Guo was highly regarded throughout history, by many cultures, as a precursor of the Gregorian calendar as well as the man who perfected irrigation techniques in the new millennium. Many historians regard him as the most prominent Chinese astronomer, engineer, and mathematician of all time. His calendar would be used for the next 363 years, the longest period during which a calendar would be used in Chinese history. He also used mathematical functions in his work relating to spherical trigonometry, building upon the knowledge of Shen Kuo's (1031–1095) earlier work in trigonometry. It is debated amongst scholars whether or not his work in trigonometry was based entirely on the work of Shen, or whether it was partially influenced by Islamic mathematics which was largely accepted at Kublai's court. Sal Restivo asserts that Guo Shoujing's work in trigonometry was directly influenced by Shen's work. An important work in trigonometry in China would not be printed again until the collaborative efforts of Xu