古希腊数学家毕达哥拉斯毕达哥拉斯

古希腊数学家毕达哥拉斯毕达哥拉斯 守望灵魂——毕达哥拉斯的使命 2009级教育理工班魏荣 200901102256 一、简介 二、早年游学 三、勾股定理 四、万物皆数 五、几何的其他贡献 六、毕达哥拉斯的伦理观 七、毕氏定理 八、毕达哥拉斯教派的一些规矩 ,一,古希腊数学家毕达哥拉斯毕达哥拉斯(Pythagoras～约公元前580年一前500年)是古希腊著名的数学家～同时也是一位天文学家和哲学家～是毕达哥拉斯学派的创始人。他的名字和毕达哥拉斯定理共刻于世界数学史的里程碑上。 ,二,毕达哥拉斯于公元前580年左右出生在希腊萨摩斯岛的一个富裕家庭～他的父亲谟涅萨尔库是一个精细的指环雕刻师～非常精明且善于理财。早在青少年时代～毕达哥拉斯就热衷should be planted immediately after watering. Plant engineering can regulate the function of human life and the natural environment, which is the main part in Garden engineering, plays a beautiful and pleasant role. The object of the project is a plant, and construction of our professional and technical staff should be carefully studied, first planting season about plant materials, the different characteristics of the plant, the relationship between plants and soil, as well as the corresponding technical measures to prevent plant tree wilt and die. Plant engineering integrated construction project of a closeout nature, in the management of the entire project, including quality management, doing well at the same time, make sure the completion. The primary considerations in the construction are as follows: (1) be familiar with the design intent and design drawings, confirmed the construction site. (2) based on various conditions, preparation of project schedule planting project master plan. (3) the trees and use materials for quality management. (4) check the distribution plant operation results of construction technology management. In the actual construction, which operate according to the following specifications: ? point, line a, fixed line use tools: tools, portable tape, flowers, small stakes, stakes and ropes. Position b, the pegged after clear signs, trees draw the range of Lime Wire, stakes on the nails in a coil, clearly state the species, quantity, pit (point), and then use Visual methods to fix individual dots, dots indicate. C, the number of species and site and must conform to the design requirements of the drawing. D, tree location and configuration attention levels, avoid stiff, wish to edge away from the Center or from low high tilt canopy line, nearby trees not into mechanical geometry drawings or a straight line. E, Lone Tree point and line planting trees 于从事学术活动。他曾经到离萨摩斯岛不远的米利都～就学于伊奥尼亚学派创始人、著名的唯物主义哲学家泰勒斯。后来泰勒斯感到年事已高～无法亲自教导毕达哥拉斯～便把他介绍给自己的学生阿那克西曼德。 在泰勒斯师徒的影响下～毕达哥拉斯开始探讨万物的本原～把整个宇宙看做是有生命的～从对立中寻找世界演变的动力。可是不久～毕达哥拉斯转而从师于著名的唯心主义哲学家斐瑞库德。在斐瑞库德的影响下～毕达哥拉斯很快转向了宗教神秘主义和唯心主义。公元前7世纪以来～整个希腊世界处在新兴工商业奴隶主民主派和代表土地贵族奴隶主的保守势力之间剧烈的斗争过程中～总的趋势是～僭主政体正在逐步取代贵族奴隶主的寡头政体。毕达哥拉斯的家乡萨摩斯岛上的工商业奴隶主势力异常强大～公元前538--前522年～波利克拉底建立了僭主政体。毕达哥拉斯不满波利克拉底的统治～毅然离开家乡～远游埃及等东方国家。 公元前540年左右～毕达哥拉斯渡海来到埃及。 毕达哥拉斯在埃及期间～系统地学习了古埃及的象形文字。 他在那里居住了5年～和当地僧侣们有过频繁交往。毕达哥拉斯在埃及、巴比伦等地停留达15年之久～除了非常熟悉当地的宗教思想之外～他还吸收了当地的算术、几何学和天文学等方面的优秀成果。这些东西构成了毕达哥拉斯的哲学、科学和宗教思想的重要。 ,三,毕达哥拉斯本人以发现勾股定理(西方称毕达哥拉斯定should be planted immediately after watering. Plant engineering can regulate the function of human life and the natural environment, which is the main part in Garden engineering, plays a beautiful and pleasant role. The object of the project is a plant, and construction of our professional and technical staff should be carefully studied, first planting season about plant materials, the different characteristics of the plant, the relationship between plants and soil, as well as the corresponding technical measures to prevent plant tree wilt and die. Plant engineering integrated construction project of a closeout nature, in the management of the entire project, including quality management, doing well at the same time, make sure the completion. The primary considerations in the construction are as follows: (1) be familiar with the design intent and design drawings, confirmed the construction site. (2) based on various conditions, preparation of project schedule planting project master plan. (3) the trees and use materials for quality management. (4) check the distribution plant operation results of construction technology management. In the actual construction, which operate according to the following specifications: ? point, line a, fixed line use tools: tools, portable tape, flowers, small stakes, stakes and ropes. Position b, the pegged after clear signs, trees draw the range of Lime Wire, stakes on the nails in a coil, clearly state the species, quantity, pit (point), and then use Visual methods to fix individual dots, dots indicate. C, the number of species and site and must conform to the design requirements of the drawing. D, tree location and configuration attention levels, avoid stiff, wish to edge away from the Center or from low high tilt canopy line, nearby trees not into mechanical geometry drawings or a straight line. E, Lone Tree point and line planting trees 理)著称于世。这定理早已为巴比伦人和中国人所知(在中国古代大约是战国时期西汉的数学著作 《周髀 算经》中记录着商高同周公的一段对话。商高说:“…故折矩～勾广三～股修四～经隅五。”商高那段话的意思就是说:当直角三角形的两条直角边分别为3,短边,和4,长边,时～径隅,就是弦,则为5。以后人们就简单地把这个事实说成“勾三股四弦五”。这就是中国著名的勾股定理.)～不过最早的证明大概可归功于毕达哥拉斯。他是用演绎法证明了直角三角形斜边平方等于两直角边平方之和～即毕达哥拉斯定理(勾股定理)。 (四)毕达哥拉斯继承了希腊古老传统～非常重视音乐的教育作用～并把它看做是净化灵魂的方法。毕达哥拉斯认为万物皆数～数是万物的原型。万物都是模仿数的～是数的摹本。数的特征是内在于音阶～内在于天体～内在于许多其他事物,数的原则统治着宇宙中的一切现象。 毕达哥拉斯学派认为～数既是万物的质料～又是万物存在的形式。 毕达哥拉斯和他的学派不把物质的东西而把数看做独立存在的万物的始基或根源～赋予数以产生万物的神秘力量～这使他们不可避免地陷入了唯心主义的泥潭。但是～他们首次提出数的概念～把数作为他们哲学思想的基础～这在人类认识发展史上却又是一个很大的进步。由于毕达哥拉斯赋予数以巨大意义～所以他的学派非常注意研究数和数的比例关系～并取得了很多辉煌的成果～其中以毕达哥拉斯定理的证明最should be planted immediately after watering. Plant engineering can regulate the function of human life and the natural environment, which is the main part in Garden engineering, plays a beautiful and pleasant role. The object of the project is a plant, and construction of our professional and technical staff should be carefully studied, first planting season about plant materials, the different characteristics of the plant, the relationship between plants and soil, as well as the corresponding technical measures to prevent plant tree wilt and die. Plant engineering integrated construction project of a closeout nature, in the management of the entire project, including quality management, doing well at the same time, make sure the completion. The primary considerations in the construction are as follows: (1) be familiar with the design intent and design drawings, confirmed the construction site. (2) based on various conditions, preparation of project schedule planting project master plan. (3) the trees and use materials for quality management. (4) check the distribution plant operation results of construction technology management. In the actual construction, which operate according to the following specifications: ? point, line a, fixed line use tools: tools, portable tape, flowers, small stakes, stakes and ropes. Position b, the pegged after clear signs, trees draw the range of Lime Wire, stakes on the nails in a coil, clearly state the species, quantity, pit (point), and then use Visual methods to fix individual dots, dots indicate. C, the number of species and site and must conform to the design requirements of the drawing. D, tree location and configuration attention levels, avoid stiff, wish to edge away from the Center or from low high tilt canopy line, nearby trees not into mechanical geometry drawings or a straight line. E, Lone Tree point and line planting trees 为著名。 ,五,在几何学方面～毕达哥拉斯学派证明了“三角形内角之和等于两个直角”的论断,研究了黄金分割,发现了正五角形和相似多边形的作法,还证明了正多面体只有五种——正四面体、正六面体、正八面体、正十二面体和正二十面体。 ,六,在早年的治学时期～毕达哥拉斯经常到各地演讲～以向人们阐明经过他深思熟虑的见解～除了“数是万物之原”的主题外～他还常常谈起有关道德伦理的问题。 他认为对儿女的爱是不能指望有回报的～但做父亲的应当努力用自己的言行去获得子女由衷的敬爱。父母的爱是神圣的～作子女的应当珍惜。子女应是父母的朋友～兄弟姐妹之间也应该彼此互敬互爱。当提到夫妻关系时～他说彼此尊重是最重要的～双方都应忠实于配偶。 他谈到过自律的问题。他说～自律是对人个性的一种考验～对儿童、少年、老人、妇女来说～能自律是一种美德～但对年轻人来说～则是必要。自律使你身体健康～心灵洁净～意志坚强。毕达哥拉斯从如何培养自律讲到教育的重要性～他认为人的自律只能在理性和知识的指导下才能培养起来～而知识只能通过教育才能获得～所以教育的重要性是不容忽视的。 ,七,初等几何中最精彩、最有用的定理之一～就是著名的should be planted immediately after watering. Plant engineering can regulate the function of human life and the natural environment, which is the main part in Garden engineering, plays a beautiful and pleasant role. The object of the project is a plant, and construction of our professional and technical staff should be carefully studied, first planting season about plant materials, the different characteristics of the plant, the relationship between plants and soil, as well as the corresponding technical measures to prevent plant tree wilt and die. Plant engineering integrated construction project of a closeout nature, in the management of the entire project, including quality management, doing well at the same time, make sure the completion. The primary considerations in the construction are as follows: (1) be familiar with the design intent and design drawings, confirmed the construction site. (2) based on various conditions, preparation of project schedule planting project master plan. (3) the trees and use materials for quality management. (4) check the distribution plant operation results of construction technology management. In the actual construction, which operate according to the following specifications: ? point, line a, fixed line use tools: tools, portable tape, flowers, small stakes, stakes and ropes. Position b, the pegged after clear signs, trees draw the range of Lime Wire, stakes on the nails in a coil, clearly state the species, quantity, pit (point), and then use Visual methods to fix individual dots, dots indicate. C, the number of species and site and must conform to the design requirements of the drawing. D, tree location and configuration attention levels, avoid stiff, wish to edge away from the Center or from low high tilt canopy line, nearby trees not into mechanical geometry drawings or a straight line. E, Lone Tree point and line planting trees 毕达哥拉斯定理(中国称之为勾股定理)。这个定理说:“在任何直角三角形中～斜边的平方等于两直边的平方和。”一般认为～这个定理是由毕达哥拉斯首先提出来的～并且也是由他组织门徒们首先证明的。 毕达哥拉斯有一个学生名叫希伯斯～他勤奋好学～富有钻研精神。有一次～他在用毕达哥拉斯定理求正方形的对角线时发现了无理数。希伯斯的这一重大发现～实际上推翻了毕达哥拉斯“世界上只有整数和分数”的论断～因而也就动摇了毕达哥拉斯学派关于数的神秘主义的哲学基础。希伯斯的发现～对于毕达哥拉斯来说是一个很大的“触犯”。〃 当毕达哥拉斯了解到这方面的突破性研究后～十分紧张～马上下令封锁希伯斯的发现～并且声称～如果有人胆敢把这一机密泄露给局外人～那就要处以极刑。后来～希伯斯泄露了秘密～畏“罪”潜逃～最终葬身大海～数学也因希伯斯的发现而出现了第一次危机。在数学史上～毕达哥拉斯被誉为“使几何学完备的人”。他在几何学方面作出了卓越的贡献～提出了几何学上的点、线、面和空间的概念。毕达哥拉斯也是第一个提出面积贴合理论的数学家。面积贴合理论～能够说明一个直线围成的图形大于、等于或小于另一个图形。毕达哥拉斯在比较图形时而命名的椭圆、双曲线、抛物线等圆锥曲线的名称～直到现在人们还在使用。毕达哥拉斯通过长期的实践～认真研究和观察周围事物～证明了三角形的三个内角之和等于180。。他还提出内接于半圆所对的圆周角都是直角的定理～因为圆周角的度数等于它所对的弧的度数的一半。这些数学上的should be planted immediately after watering. Plant engineering can regulate the function of human life and the natural environment, which is the main part in Garden engineering, plays a beautiful and pleasant role. The object of the project is a plant, and construction of our professional and technical staff should be carefully studied, first planting season about plant materials, the different characteristics of the plant, the relationship between plants and soil, as well as the corresponding technical measures to prevent plant tree wilt and die. Plant engineering integrated construction project of a closeout nature, in the management of the entire project, including quality management, doing well at the same time, make sure the completion. The primary considerations in the construction are as follows: (1) be familiar with the design intent and design drawings, confirmed the construction site. (2) based on various conditions, preparation of project schedule planting project master plan. (3) the trees and use materials for quality management. (4) check the distribution plant operation results of construction technology management. In the actual construction, which operate according to the following specifications: ? point, line a, fixed line use tools: tools, portable tape, flowers, small stakes, stakes and ropes. Position b, the pegged after clear signs, trees draw the range of Lime Wire, stakes on the nails in a coil, clearly state the species, quantity, pit (point), and then use Visual methods to fix individual dots, dots indicate. C, the number of species and site and must conform to the design requirements of the drawing. D, tree location and configuration attention levels, avoid stiff, wish to edge away from the Center or from low high tilt canopy line, nearby trees not into mechanical geometry drawings or a straight line. E, Lone Tree point and line planting trees 成就～对后来的数学发展产生了巨大的影响。 ,八,禁食豆子 。东西落下了～不要拣起来。 不要去碰白公鸡。 不要擘开面包。 不要迈过门闩。 不要用铁拨火。 不要吃整个的面包 。不要招花环。 不要坐在斗上。 不要吃心。 不要在大路上行走。 房里不许有燕子。 锅从火上拿下来的时候～不要把锅的印迹留在灰上～而要把它抹掉。 不要在光亮的旁边照镜子。 普洛克鲁斯描述过毕达哥拉斯——此人永远是个颇为蒙胧的人物——乃是第一个把几何学当作一种学艺的人。尽管他的哲学思想有历史的局限性～然而毕达哥拉斯学说深刻地影响了希腊古典哲学的发展和中世纪欧洲思想的发展。 should be planted immediately after watering. Plant engineering can regulate the function of human life and the natural environment, which is the main part in Garden engineering, plays a beautiful and pleasant role. The object of the project is a plant, and construction of our professional and technical staff should be carefully studied, first planting season about plant materials, the different characteristics of the plant, the relationship between plants and soil, as well as the corresponding technical measures to prevent plant tree wilt and die. Plant engineering integrated construction project of a closeout nature, in the management of the entire project, including quality management, doing well at the same time, make sure the completion. The primary considerations in the construction are as follows: (1) be familiar with the design intent and design drawings, confirmed the construction site. (2) based on various conditions, preparation of project schedule planting project master plan. (3) the trees and use materials for quality management. (4) check the distribution plant operation results of construction technology management. In the actual construction, which operate according to the following specifications: ? point, line a, fixed line use tools: tools, portable tape, flowers, small stakes, stakes and ropes. Position b, the pegged after clear signs, trees draw the range of Lime Wire, stakes on the nails in a coil, clearly state the species, quantity, pit (point), and then use Visual methods to fix individual dots, dots indicate. C, the number of species and site and must conform to the design requirements of the drawing. D, tree location and configuration attention levels, avoid stiff, wish to edge away from the Center or from low high tilt canopy line, nearby trees not into mechanical geometry drawings or a straight line. E, Lone Tree point and line planting trees