Introduction to mathematician Yang Hui
Yang Hui was a famous Chinese mathematician who lived in the 13th century during the Song dynasty. He wrote several books on mathematics, which are among the few that survived from that time. He was interested in many topics, such as magic squares, magic circles, binomial theorem, and geometry.
One of his most famous contributions is Yang Hui's Triangle, which is a way of arranging numbers in a triangular shape. Each number in the triangle is the sum of the two numbers above it. For example, the first row has only one number, 1. The second row has two numbers, 1 and 1. The third row has three numbers, 1, 2, and 1. The fourth row has four numbers, 1, 3, 3, and 1. And so on.
Yang Hui's Triangle can help us find the coefficients of a binomial expansion. A binomial is an expression with two terms, such as (a+b). A binomial expansion is when we multiply a binomial by itself several times, such as (a+b)^2 or (a+b)^3. The coefficients are the numbers that appear before each term in the expansion. For example, in (a+b)^2 = a^2 + 2ab + b^2, the coefficients are 1, 2, and 1.
To find the coefficients using Yang Hui's Triangle, we just need to look at the row that corresponds to the power of the binomial. For example, if we want to find the coefficients of (a+b)^3, we look at the fourth row of the triangle: 1, 3, 3, and 1. These are the coefficients of (a+b)^3 = a^3 + 3a^2b + 3ab^2 + b^3.
Yang Hui's Triangle was actually discovered by another mathematician named Jia Xian about 500 years before Yang Hui. Yang Hui acknowledged Jia Xian's work and explained how to use the triangle in more detail. Yang Hui's Triangle is also known as Pascal's Triangle in Europe, because a French mathematician named Blaise Pascal wrote about it in the 17th century.
Yang Hui was also good at solving geometric problems and proving mathematical propositions. He criticized some of his predecessors for using methods without explaining their principles or origins. He said: "The men of old changed the name of their methods from problem to problem, so that as no specific explanation was given, there is no way of telling their theoretical origin or basis." He wanted to make mathematics more clear and logical.
Yang Hui was a brilliant and influential mathematician who advanced the knowledge of mathematics in China and beyond. His works were later studied and admired by mathematicians in Korea and Japan as well. He is one of the great figures in the history of mathematics.
词汇表
mathematician [ .mæθәmә'tiʃәn ] n. 数学家
origin [ 'ɒridʒin ] n. 起源, 起因, 出身, 开端 [计] 原点; 起始地址; 信件来源的相关数据
term [ tә:m ] n. 术语, 专有名词, 期限, 学期, 任期, 条件, 价钱, 关系, 地位, 项, 界石 vt. 称, 呼 [计] 检索词; 项
above [ ә'bʌv ] prep. 在上方, 超出 adv. 在上面 a. 上述的, 上面的
acknowledge [ әk'nɒlidʒ ] vt. 承认, 告知收悉, 答谢, 报偿 [经] 承认, 答谢, 收到的通知
admire [ әd'maiә ] vt. 赞美, 钦佩, 爱慕 vi. 称赞, 惊奇
advance [ әd'vɑ:ns ] n. 前进, 进展, 行过的路程 vi. 前进, 进展, 提高, 上涨 vt. 使前进, 促进, 提出, 提高, 使提前, 预付 a. 前面的, 预先的
arrange [ ә'reindʒ ] v. 安排, 排列, 达成协议 [计] 重排
basis [ 'beisis ] n. 基础, 主要成分 [化] 基底
beyond [ bi'jɒnd ] prep. 超过, 在那一边, 迟于 adv. 在远处 n. 更远处
binomial [ bai'nәumjәl ] a. 包含两个名词(或名称的), 二项式的, 双名的 n. 二项式, 双名
brilliant [ 'briljәnt ] a. 光辉的, 灿烂的, 有才气的 [机] 亮的
coefficient [ kәui'fiʃәnt ] n. 系数 [计] 系数
contribution [ .kɒntri'bju:ʃәn ] n. 捐助, 捐助之物, 贡献 [经] 贡献, 捐款, 补助品
correspond [ .kɒri'spɒnd ] vi. 符合, 通信, 相当 [法] 符合, 一致, 相当
criticize [ 'kritisaiz ] v. 批评, 吹毛求疵, 非难
detail [ 'di:teil ] n. 细节, 详情 vt. 详述, 选派 vi. 画详图 [计] 详细数据
dynasty [ 'daɪnæstɪ ] n. 朝代, 王朝
expansion [ ik'spænʃәn ] n. 扩充, 开展, 膨胀 [计] 扩展
explanation [ .eksplә'neiʃәn ] n. 解释, 说明, 辩解, 表明 [经] 解释, 注释, 说明
figure [ 'figә ] n. 数字, 价格, 图形, 形状 vt. 描绘, 表示, 演算, 认为 vi. 计算, 出现, 估计
geometric [ .dʒiәu'metrik ] a. 几何学的, 几何学上的, 几何学图形的
geometry [ dʒɪ'ɒmәtrɪ ] n. 几何学 [机] 几何学
history [ 'hɪstәrɪ ] n. 历史, 过去, 经历, 发展过程, 历史学, 过去的事, 历史记录 [计] 历史记录
influential [ .infu'enʃәl ] a. 有影响的, 有势力的
logical [ 'lɒdʒikәl ] a. 合乎逻辑的, 合理的 [法] 逻辑的, 符合逻辑的
mathematical [ .mæθә'mætikl ] a. 数学的, 精确的 [机] 数学上的
mathematics [ .mæθә'mætiks ] n. 数学 [机] 数学
multiply [ 'mʌltɪplaɪ ] v. 繁殖, 乘, 增加 [计] 乘
pascal [ 'pæskәl ] [计] PASCAL语言 [化] 帕斯卡
predecessor [ .predi'sesә ] n. 前任, 先辈, 前身 [医] 初牙, 前辈, 祖先
principle [ 'prinsipl ] n. 原则, 原理, 主义 [化] 原理
proposition [ .prɒpә'ziʃәn ] n. 建议, 命题, 主张 vt. 向...提议, 向...提出猥亵的要求
prove [ pru:v ] vt. 证明, 查验, 检验, 勘探, 显示 vi. 证明是
specific [ spi'sifik ] n. 特效药, 特性 a. 特殊的, 明确的, 具有特效的, 特定地, 具体地
sum [ sʌm ] n. 总数, 总和, 金额, 概要, 顶点 vt. 总计, 概括 vi. 合计 [计] 系统实用程序和维护
survive [ sә'vaiv ] vt. 比...活得长, 生存, 生还, 幸免于 vi. 活下来, 幸存
theorem [ 'θiәrәm ] n. 定理, 原理 [化] 定理
theoretical [ θiә'retikәl ] a. 理论的, 理论上的, 假设的, 推理的 [计] 理论的
triangular [ trai'æŋgjulә ] a. 三角形的, 三人间的 [医] 三角的, 三角形的