The 'Malfatti Problem' in nineteenth-century China: An episode in the study of Western learning by the Chinese

Abstract

自第二次鴉片戰爭至中日甲午戰爭的三十余年間,中國展開了一場稱為'自強運動'的革新。這場革新帶動了學習西方科學技術的熱潮。1872年在《中西聞見錄》第五號刊登了一道問題:給定一個三角形,構作三個不重迭的圓,使得每個圓都與三角形的兩條邊及其余兩個圓相切。這道問題在西方世界是一道著名的數學問題,于1803年由意大利數學家馬爾法蒂(Malfatti)提出。這道題目在《中西聞見錄》提出后,引起熱切的公開學術交流。透過在該段時期對'馬爾法蒂問題'的討論歷程,可見中國學者在'自強運動'期間對學習西方科學技術的熱切追求。 The'Self-strengthening Movement'took place in China for more than thirty years between the second Opium War and the first Sino-Japanese War.This movement urged the Chinese to learn Western science and technology.Through the story of a discourse among Chinese scholars and students in solving a specific geometric problem,namely the Malfatti Problem,the enthusiasm of the Chinese in learning Western science and technology during the'Self-strengthening Movement'is illustrated.In 1872,a problem published in Issue Number 5 of the Peking Magazine asked for three non-overlapping circles placed inside a given triangle,each touching two sides of the triangle as well as the other two circles.This well-known problem in the Western world,proposed in 1803 by the Italian mathematician Gian Francesco Malfatti,led to a fervent exchange of academic discussion carried on in the public domain after its appearance in the Peking Magazine.