塵封的經(jīng)典（第1卷）

內(nèi)容概要

　　《歐美初等數(shù)學(xué)經(jīng)典系列（第1輯）·塵封的經(jīng)典：初等數(shù)學(xué)經(jīng)典文獻(xiàn)選讀（第1卷）》搜集初等數(shù)學(xué)的經(jīng)典文獻(xiàn)，包括“拉格雷舊成果的新運用”“平面對成群的識別與標(biāo)記”“匈牙利的數(shù)學(xué)發(fā)展”“Bonnesen等周不等式”“準(zhǔn)割圓多項式”“n次冪差分的歐拉公式”“算數(shù)級數(shù)”“三角不等式”“調(diào)和級數(shù)的一些收斂子級數(shù)”等在內(nèi)，編輯成書，便于讀者進(jìn)行學(xué)習(xí)和查閱，《歐美初等數(shù)學(xué)經(jīng)典系列（第1輯）·塵封的經(jīng)典：初等數(shù)學(xué)經(jīng)典文獻(xiàn)選讀（第1卷）》適用于學(xué)生學(xué)習(xí)同時也可作為數(shù)學(xué)愛好者的興趣讀物。

書籍目錄

拉格雷老成果的新運用
平面對稱群的識別與標(biāo)記
關(guān)于三角形幾何學(xué)
匈牙利的數(shù)學(xué)發(fā)展
Bonnesen型等周不等式
準(zhǔn)割圓多項式
奇特的冪次和
n次冪差分的歐拉公式
算術(shù)級數(shù)
同余ar+s≡ar（MOD m）
三角不等式
調(diào)和級數(shù)的一些收斂子級數(shù)
單連通平面域的剖分
圖的剖分與纏結(jié)
再論柯匿泛函方程
m（m—1）
魏爾斯特拉斯不等式的統(tǒng)一處理
包含有理點的圓的特性
近似或等同練習(xí)
整數(shù)邊三角形
完全四邊形
契爾恩豪森轉(zhuǎn)換在初等方程論中的兩個運用
ax3+by3=ax3+bt3的整數(shù)解
xy=y2，x>0，y>0，x≠y的解法及圖示
一類互反方程的實數(shù)根
一個丟番圖方程的注解
論戴德金切線
方程（x+1 y）=（x y+1）的解法
三次方程的解法
三等分
代數(shù)圖
一個代數(shù)方程的根的新界限
某行列式的擴展
卡特蘭數(shù)的初步估值
編輯手記

章節(jié)摘錄

版權(quán)頁：   插圖：   All of these results were for convex curves only,and the extension to non-convex curves required essentially new methods. The first results are due to Erhard Schmidt in 1939.Using analytic rather than geometric methods,he derives several Bonnesen-type inequalities for plane domains bounded by an arbitrary rectifiable Jordan curve([68,p.690-694]).He does not,however,obtain the inequalities of Theorems 1 and 2 above.The first method to succeed here was integral geometry.The book of Blaschke(p. 26)gives a proof of (11)and(16)for convex curves,due to Santalo.Also using integral geometry,Hadwiger in 1941[41]obtained results equivalent to inequalities(15)and(20) for arbitrary rectifiable Jordan curves.He does not appear to notice the connections with Bonnesen inequalities, however,until a later paper[42],where he derives the inequalities(12),(13),(17),(18),(22)and(23),but only for convex domains. In the meanwhile,in the same volume of the journal that contains the first of Hadwiger's papers,there appeared a fundamental paper of Fiala.In it Fiala develops another method for proving Bonnesen inequalities for non-convex curves.That is the method of interior parallels,and,except for the proof of Theorem 3 above,it is the method used here.Fiala's principal focus is on obtaining isoperimetric inequalities on curved surfaces (see Section B below),but his paper applies in particular to the plane and is the first to give explicitly(on p.336)(11)and(14) for non-convex curves.His proof is for analytic Jordan curves.One could then obtain the result for more general curves by approximation.

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《塵封的經(jīng)典:初等數(shù)學(xué)經(jīng)典文獻(xiàn)選讀(第1卷)》適用于學(xué)生學(xué)習(xí)同時也可作為數(shù)學(xué)愛好者的興趣讀物。

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