Different Presentations Of Euclidean Algorithm In The History

Euclidean Algorithm,it is also known as photograph derogation in China.By interpretationof the original texts and the previous work.I undertake relatively comprehensive discussion andanalysis on the diferent origins and presentation of Euclidean Algorithm. The main results arebelow:Firstly,it elaborates Euclidean Algorithm in the original documents in the Euclidean Al-gorithm and Arithmetic in Nine Section.That this ancient algorithm can also appear in ancientGreece deductive system as the center of ancient Greek mathematics and algorithm system basedin ancient Chinese mathematics is not a coincidence. Tt explains that the Euclidean algorithmcan be used as a means of deductive reasoning and also can be used as the actual method ofcalculation.Secondly,it explores the usage of Euclidean Algorithm in the Chinese history of applicationmathematics in details,which points out the similarity between Through the Rate in the ThreeEC Calender and the calculated procedures and the meaning of a fraction in the Dayan method.Thirdly,it confers to the application of Euclidean Algorithm in the history of foreign math-ematics,which elaborates the calculating procedures in the continued fraction of Euclidean Al-gorithm and which also focuses on solving a congruence in Japan,and elaborates the IndianKuttaka Algorithm,and which also points out the diference between the Kuttaka and DayanMethod in China,but actually they both use Euclidean Algorithm.Fourthly,it uses various comparisons in answering the analyzable procedures for diferentregions,diferent time and diferent mathematicians.They think although,there are diferences intheir contributions of the ways of narration,yet they derive from diferent thoughts. Moreover,this thesis also figured out that the procedures of Euler’s solution is more complicated than thatof Jiushao Qin’s Dayan Method§and the solution of Zongxian Huang and Dunren Zhang justmade some improvements on Jiushao’s Qin.