勾股定理的起源，證明和教育價值
The origin of the Pythagorean theorem, proof and the value of Education

12400字 25頁

目 錄
引 言 1
第一章 勾股定理的起源 2
1.1 從西方看勾股定理的起源 2
1.2 從東方看勾股定理的起源 3
1.3 勾股定理的發(fā)展 4
第二章 勾股定理的證明 7
2.1 西方著名證明 7
2.2 東方著名證明 10
2.3 其他證明 11
2.4 說明 14
第三章 勾股定理的教育價值 15
3.1 引發(fā)學(xué)生的探索、創(chuàng)新思維 16
3.2 強(qiáng)化學(xué)生對于幾何圖形的數(shù)學(xué)感覺以及對幾何的興趣 16
3.3 有助于教育現(xiàn)代化的實(shí)現(xiàn) 17
結(jié) 論 19
致 謝 20
參考文獻(xiàn) 21


摘要：勾股定理是幾何平面中非常重要的一個定理，勾股定理又叫做畢達(dá)哥拉斯定理， 本文將從其起源，證明和教育價值三個方面來進(jìn)行說明。在古印度，古巴比倫，古代中國，希臘，埃及等等這些地方，很早已經(jīng)有了勾股數(shù)的記載和研究，古巴比倫石板，中國西漢時期的《周髀算經(jīng)》，印度的“繩子規(guī)則”這些都是最好的說明。據(jù)說最早是西方的畢達(dá)哥拉斯證明了這個定理，然后歐幾里德在他的幾何原本里面記錄了證明方法，中國的劉徽與趙爽他們幾乎同時證明了勾股定理。勾股定理對中西方，古代現(xiàn)代的教育都有著深刻的影響。在本文中，作者通過運(yùn)用陳述法，舉例法，分析討論法，給讀者展現(xiàn)一個真實(shí)的，清晰的勾股定理。通過勾股定理的起源以及證明表現(xiàn)東西方在數(shù)學(xué)文化上的異同點(diǎn)，同時勾股定理是全人類共同的文化遺產(chǎn)，世界各國都非常重視勾股定理的社會文化價值，借助計算機(jī)，我們可以在傳統(tǒng)數(shù)學(xué)教育和現(xiàn)代數(shù)學(xué)教育之間搭建一個教學(xué)平臺，為實(shí)現(xiàn)數(shù)學(xué)教育現(xiàn)代化提供一條有效的措施。


關(guān)鍵詞： 畢達(dá)哥拉斯 畢達(dá)哥拉斯定理 證明 教育價值
The origin of the Pythagorean theorem, proof and the value of Education
Abstract The Pythagorean theorem is a very important theorem in geometric plane. This paper will explain from three aspects about its origin, prove and educational value. In ancient India, ancient Babylon, ancient Greece, Egypt China, these places and so on, has been recorded and the Pythagorean number very early. Old Babylonian tablets, Chinese Western Han period, "Zhou Bi Suan Jing", India's "rope rules" which is the best explanation. It is said that Pythagoras proved the theorem first, and then the Euclidean geometry records the proof method in his original. Chinese Liu Hui and Zhao Shuang they almost at the same time proved the Pythagorean theorem. The Pythagorean theorem has a profound effect to the west, the ancient and modern education. In this paper, the authors use the representation, example method, analysis method, to show readers a true, clear the Pythagorean theorem. The origin and proof of the Pythagorean theorem perform the similarities and differences of the of East and West in mathematics cultural, at the same time the Pythagorean theorem is the common heritage of all mankind, the world has attached great importance to the Pythagorean theorem of social and cultural value. With the help of computer, we can build a teaching platform between traditional education and modern mathematics education , provides an effective measure for the realization of modernization of mathematics education.


Key words Pythagorean Pythagorean theorem prove The educational value