Was Pythagoras Chinese- Revisiting an Old Debate

(ProQuest: ... denotes formulae omitted.)IntroductionTwo of the great ancient civilizations were those of the Greeks and the Chinese. Many great works of art, architecture, philosophy and literature have been produced by both of these civilizations. When it comes to mathematics in the Western World, the Greeks have also been credited with many contributions to the field, especially geometry. Anyone who has completed a standard high school mathematical curriculum has been introduced to the names of Pythagoras, Euclid and Archimedes and their methods. Not as widely credited in the Western world are the mathematical contributions of the ancient Chinese civilization. An examination into Chinese mathematics reveals their deep understanding of mathematics, in some areas at a level greater than that of the Greeks. The Chinese civilization had their own mathematical greats, Liu Hui and Zu Chongzhi who were every bit as genius as their Greek counterparts. The purpose for mathematics and the techniques utilized by the two civilizations may differ, but the knowledge of the two civilizations is remarkably similar. This paper provides the reader a summary of the two civilizations works and mathematical philosophies and a comparison of the techniques used to determine π, proof of the right triangle theory, and the famous works of each civilization and the application of the civilizations mathematical knowledge in the science of land surveying.Chinese Mathematical HistoryThe origins of Chinese mathematics are steeped in legend. It is said that the Yellow Emperor, who ruled sometime around 2698-2598 BC charged one of his subjects named Li Shou to create arithmetic. (Li, 1987) The creation of a mathematical system cannot be credited to one individual, but the legend does give evidence of a mathematical system present in the 26th century BC in China. Evidence from the Shang Dynasty gives the first physical evidence of mathematical application in Chinese culture. The Shang Dynasty was a well developed agricultural society from the 16th to 11th century BC. Remains of large cylindrical grain bins have been discovered, along with bronze coins, evidence of a monetary system. Additional bone artifacts, known as plastrons, have the first known writing system of China. Including in the writing are numerals of a sexagesimal system (Li, 1987).The Zhoubi suanjing is the oldest known Chinese mathematical work. The Zhoubi suanjing is also known as Chou Pei Suan Ching or Chou Pi Suan Ching in some historical references (Dauben 2007). The author of the compilation is unknown, though it is believed to be composed sometime between 100 BC and 100 AD. However, the contents were likely from a much earlier period (Li 1987). The Zhoubi is a work focused on astronomy, but the mathematics and measuring methods discussed were also applicable to land surveying and construction. The Zhoubi was divided into two sections, the first dealing with mathematics and the second part with astronomy. The mathematics in section one is necessary for the explanations of astronomy in the second portion.Particularly of interest is its discussion of the right triangle theory in section one. While commonly referred to as the Pythagoras theorem in the Western World, it is known as the gou-gu theorem in ancient Chinese literature. The text concerning the gou-gu theorem is written as a dialogue between a teacher Chen Zi and a student Rong Fang, both of whom nothing is known historically(Dauben, 2007). After being asked be Rong Fang, Chen Zi explains how using the shadow cast by the sun at midday it is possible to determine the distance between the sun and the Earth. In this explanation first appears a statement of the gou-gu theorem. Commentary added to the work by subsequent authors has been argued to be proofs of the theorem, though again it is difficult to determine the exact time period the commentary was added (Dauben, 2007).The Zhoubi references the Emperor Yu being able to rule the country because of the Gougu theorem. …