The Beauty of Mathematics
Tags
Summary
Editor's review
Who it's for
A good fit for
- Junior and senior high school mathematics teachers who need materials to broaden teaching horizons and competency-oriented content
- Upper-level secondary students interested in the history of mathematics and famous mathematical problems
- Science enthusiasts who want to understand mathematical structure and culture beyond problem drills
- Teaching-research and teacher-training readers concerned with how core mathematical competencies can be implemented
Not a good fit for
- Readers who only want to drill problems and improve scores, seeking short-term exam techniques
- Readers without junior or senior high school mathematics foundations who want a zero-start introduction
- Readers expecting a systematic university mathematics textbook or rigorous proof training
Reading tips
- Read chapter by chapter according to the problems; in each chapter, close the book and think for a moment first, then compare with the author's explanation and historical context.
- When reaching the mathematical games and paradoxes, work them out by hand or discuss with peers to deepen understanding of the concepts.
- Teacher readers can excerpt the historical materials and competency connection points and turn them into classroom introductions or extension materials.
- Do not feel compelled to finish in one sitting; it works well as a desk reference to read in multiple sessions, jumping by interest.
About the publisher
Peking University Press is a comprehensive university press whose publishing areas cover classical literature, popular science, social culture, world history, Western philosophy, and culture. Its catalogue contains 6,031 titles, with representative books including A Dream of Red Mansions, Relativity: The Special and General Theory (15th Edition) (with Einstein's classic papers on unified field theory and other topics), Elements, Conics, The Aristocratic Families of the Eastern Jin, The Philosophy of Mythology (Volume I), The Philosophy of Mythology (Volume II), and The Origin of Continents and Oceans. Representative authors include Cao Xueqin, Zhou Ruchang, Albert Einstein, Euclid, Apollonius, Tian Yuqing, Schelling, and Xian Gang. The press has developed distinctive strengths in classical Chinese literature and in the translation of Western philosophical classics, while also covering scientific classics and social and cultural studies. As public information is limited, this description is based only on the books in the catalogue and offers no further extrapolation.
Contents
- 版权信息
- 内容提要
- 序言
- 前言
- 第1章 无处不在的杨辉三角
- 一、杨辉三角简史
- 二、杨辉三角、二项式定理、组合数
- 三、三角形数和四面体数
- 四、杨辉三角之高尔夫球杆定理
- 五、杨辉三角与概率
- 六、杨辉三角中的斐波那契数列
- 七、分离系数法构造杨辉三角
- 八、杨辉三角行列式
- 九、杨辉三角与素数判定
- 十、杨辉三角与费马小定理
- 十一、魔术般的数学公式
- 十二、杨辉三角与高阶等差数列
- 十三、数学探究活动（完全图）
- 十四、容斥原理与杨辉三角
- 十五、杨辉三角中的分形、杨辉三角中的完全数
- 十六、杨辉三角与卡塔兰数
- 第2章 当我们谈论正方体时，我们能够谈论些什么？
- 一、正方体与其他正多面体的关系
- 二、切割正方体所得截面是什么？
- 三、欧拉示性数
- 四、画正方体的截面图形及空间作图问题
- 五、空间解析几何解题很有效
- 六、如何作出球内接正方体？
- 七、在空间中解决平面问题
- 八、正方体可以从同样大小正方体上的洞中穿过
- 九、数学探究活动（共有多少种六色正方体）
- 十、蜂房结构与菱形十二面体
- 十一、从中国古代对正方体的切割想到完全数
- 十二、三个视图都一样的立体
- 十三、超立方体与完全幻方
- 十四、在正方体内构造正八面体
- 第3章 从√2说开来
- 一、√2矩形
- 二、神秘的对角线
- 三、任何小数形式的有理数都可以化为分数
- 四、√2的连分数表示及四年一闰是怎么回事？
- 五、√2的近似计算
- 六、从√2引出的几个趣味题
- 七、对称多项式、一元二次方程、二元一次方程组
- 八、趣味数学——神奇的数学餐桌
- 九、有趣的“幂塔”
- 十、超越数π的表达式的最内层是代数数√2
- 十一、数学表达式的严谨之美
- 十二、数学对称美与带饰
- 十三、用几何方法解决代数问题（花剌子米的成就）
- 十四、用几何方法研究代数问题（海亚姆的成就）
- 第4章 斐波那契数列与黄金分割
- 一、面积少了1个单位——这个数学谬误是怎么产生的？
- 二、兔子繁殖问题与斐波那契数列
- 三、斐波那契数列与蛙跳问题及多个有趣的生活实例
- 四、斐波那契数列的通项公式竟然是用无理数表示的！
- 五、连分数、斐波那契数列、黄金数
- 六、斐波那契点与斐波那契双曲线
- 七、正五边形中的黄金分割
- 八、数学探究活动（星状多边形）
- 九、游戏与黄金数与斐波那契数（两例）
- 十、有趣的斐波那契数列的数论性质
- 十一、斐波那契数列与几何图形和三角公式
- 十二、类角谷猜想
- 十三、√5的近似计算
- 十四、黄金分割的三种作图方法及黄金矩形
- 十五、菠萝中的斐波那契数
- 第5章 圆锥曲线面面观
- 一、圆锥曲线的定义和基本性质
- 二、丰富多彩的椭圆作图法及其背后的理论依据
- 三、用离心率的统一观点讲述椭圆、抛物线和双曲线
- 四、准圆、准线、动圆（椭圆、抛物线、双曲线）
- 五、圆锥曲线与圆锥的关系
- 六、与椭圆切线相关的丰富知识
- 七、与椭圆相关的平面几何证明题（逻辑思维训练）
- 八、圆柱、椭圆周长、正弦曲线
- 九、斜二测画法画圆，你画对了吗（椭圆的仿射几何学画法）
- 十、等轴双曲线内接三角形的垂心轨迹、九点圆相关知识
- 十一、借助圆锥曲线及其他特殊曲线解决三大作图不能问题
- 十二、阿基米德计算抛物线弓形区域面积与穷竭法
- 十三、安全抛物线（包络线）
- 十四、抛物线、反演、心脏线，太神奇了！
- 十五、抛物线与蔓叶线
- 十六、解题思路可以明确一些——每一步在做什么
- 第6章 感悟数学的魅力与威力
- 一、圆周率π竟然隐藏在不等式的变形中
- 二、圆周率π的无穷级数表示、无穷乘积表示及连分数表示
- 三、复利与欧拉数e
- 四、eπ与πe谁大？
- 五、两个重要极限与两个重要常数
- 六、求球体积的牟合方盖方法、阿基米德方法和微积分方法
- 七、数学让人精细——从正三角形到正方形的剖分
- 八、神奇的骰子
- 九、神奇的复数
- 十、费马数与正多边形的尺规作图
- 十一、正多边形的平面密铺问题与单位分数
- 参考文献（我的数学书单——100部）
FAQ
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About the author
Shao Yong is a Chinese author known for writing on mathematics. Publicly available information about him is limited, and his nationality, dates of birth and death, and educational background cannot be confirmed. Judging from the three works held in the collection, his writing focuses on two areas: popular mathematics and mathematical thinking training. On the one hand, books such as The Beauty of Mathematics introduce general readers to the interest and elegance of the subject; on the other, the junior-high and senior-high volumes of Mathematical Thinking: Training in Problem-Solving through the "Lafen" Method offer students preparing for examinations a systematic treatment of solution strategies and methods. His works combine the readability of popular science with the practicality of study materials, and are commonly classified under popular science and examinations, indicating that his readership spans both casual interest reading and exam preparation. Overall, he is an author who writes for the classroom while also reaching a broader public.
