高考中的數(shù)學文化

第一章 數(shù)學文化總論 ··················································································· 1 第一節(jié) 什么是數(shù)學文化 ········································································ 1 第二節(jié) 數(shù)學文化的四個層面 ································································· 3 一、知識系統(tǒng) ······················································································· 4 二、工具系統(tǒng) ······················································································· 4 三、價值系統(tǒng) ······················································································· 5 四、史實系統(tǒng) ······················································································· 7 第三節(jié) 數(shù)學文化的人本特性 ································································· 7 一、精神特性 ······················································································· 8 二、物質特性 ······················································································· 8 三、行為特性 ······················································································· 9 四、審美特性 ······················································································· 9 第二章 數(shù)學歷史 ························································································ 11 第一節(jié) 數(shù)學名著 ················································································ 11 一、《九章算術》 ················································································ 12 二、《數(shù)書九章》 ················································································ 19 三、《算數(shù)書》 ··················································································· 24 第二節(jié) 數(shù)學故事 ················································································ 27 一、畢達哥拉斯的故事 ········································································· 27 二、高斯的故事 ·················································································· 36 三、哥德巴赫的故事 ············································································ 41 第三節(jié) 數(shù)學名題 ················································································ 44 一、米勒問題 ····················································································· 45 二、斐波那契數(shù)列 ··············································································· 57 三、阿基米德窮竭法 ············································································ 66 四、柯西不等式 ·················································································· 73 五、角谷猜想 ····················································································· 80 六、阿波羅尼奧斯圓 ············································································ 85 七、回文數(shù) ························································································ 93 八、勾股數(shù) ························································································ 98 九、平均數(shù) ······················································································· 101 十、皮克定理 ···················································································· 108 十一、數(shù)字黑洞 ················································································· 114 十二、伯努利不等式 ··········································································· 119 十三、正整數(shù)方冪和 ··········································································· 124 十四、切比雪夫多項式 ········································································ 130 十五、馬爾科夫定理 ··········································································· 135 十六、四色問題 ················································································· 143 十七、萊布尼茨三角形 ········································································ 146 十八、黃金分割比 ·············································································· 151 第三章 數(shù)學精神 ······················································································· 155 第一節(jié) 理性求真 ··············································································· 155 第二節(jié) 創(chuàng)新意識 ··············································································· 167 第四章 數(shù)學應用 ······················································································· 177 第一節(jié) 營銷決策類 ············································································ 178 第二節(jié) 金融經(jīng)濟類 ············································································ 183 第三節(jié) 環(huán)境保護類 ············································································ 188 第四節(jié) 建設工程類 ············································································ 195 第五節(jié) 交通運輸類 ············································································ 204 第六節(jié) 概率統(tǒng)計類 ············································································ 209 第七節(jié) 日常民生類 ············································································ 218 第五章 數(shù)學之美 ······················································································· 227 第一節(jié) 和諧美 ··················································································· 227 一、結構形式的和諧統(tǒng)一 ····································································· 228 二、項、項數(shù)、次數(shù)的和諧統(tǒng)一 ···························································· 235 三、轉換的和諧統(tǒng)一 ··········································································· 239 第二節(jié) 簡潔美 ··················································································· 242 第三節(jié) 對稱美 ··················································································· 248 第四節(jié) 奇異美 ··················································································· 253 一、解法多樣的奇異美 ········································································ 254 二、解法之巧的奇異美 ········································································ 259 第六章 數(shù)學語言 ······················································································· 264 第七章 交匯拓展 ······················································································· 272 第八章 數(shù)學游戲 ······················································································· 276 附錄一 本書習題參考答案 ········································································· 285 附錄二 高考數(shù)學文化最新動態(tài) ································································· 325 參考文獻 ···································································································· 344