2008恒隆數(shù)學獲獎論文集

內(nèi)容概要

本書集結(jié)了2008年“恒隆數(shù)學獎”的獲獎論文及數(shù)學家的精辟點評。每篇論文都是得獎者自定的數(shù)學專題之研習結(jié)果。參賽學生經(jīng)過一年多的努力，得以訓練多無智能和創(chuàng)意思考能力，并活學活用數(shù)學知識，擺脫傳統(tǒng)死讀書的學習模式，從中取得考試外的滿足感和喜悅感，借以領略數(shù)學的美。本書不僅可供中學生閱讀，亦可供數(shù)學教師和數(shù)學愛好者閱讀參考。
每兩年一屆的“陋隆數(shù)學獎”由恒隆地產(chǎn)和香港中文大學數(shù)學系主辦，乃為香港中學生而設的數(shù)學研究比賽。由恒隆地產(chǎn)有限公司董事長陳啟宗先生和世界杰出數(shù)學家、1982年費爾茲獎信2010年沃爾夫獎得主丘成桐教授于2004年創(chuàng)立，目的是鼓勵中學生盡量發(fā)揮數(shù)理創(chuàng)意，激發(fā)他們對數(shù)學及科學的求知熱情。

書籍目錄

Preface
　by Professor Shing-Tung Yau and Mr. Ronnie C. Chart
Acknowledgement
Hang Lung Mathematics Awards
Organization
　Scientific Committee, 2008
　Steering Committee, 2008
Gold, Silver, and Bronze
　ISOAREAL AND ISOPERIMETRIC DEFORMATION OF CURVES
　A SUFFICIENT CONDITION OF WEIGHT-BALANCED TREE
　FERMAT POINT EXTENSION-LOCUS, LOCATION, LOCAL USE
Photos
Honorable Mentions
　A CURSORY DISPROOF OF EULER'S CONJECTURE CONCERNING
GRAECO-LATIN
　SQUARES BY MEANS OF CONSTRUCTION
　EQUIDECOMPOSITION PROBLEM
　COLLATZ CONJECTURE 3n+l CONJECTURE
　GEOMETRIC CONSTRUCTION AREA TRISECTION OF A CIRCLE

章節(jié)摘錄

版權(quán)頁：   插圖：   5.Conclusions and Reflections In the previous chapter,we have followed the paths that mathematicianshas lain for us decades ago.Euler has provided the first constructionmethod,while Sade has given us the most recent(along with Parker,Bose,and Shrikhande and their transversal designs). To summarise their contributions:Euler has proven that Euler squares ofodd order or of an order that is a multiple of four exists(He also provedthe obvious nonexistence of Euler squares of order 2),while Parker,Bose,and Shrikhande constructed Graeco-Latin squares of all orders,includingthose of form4k+2,with the exception ofn = 2 and n = 6.On theother hand,Tarry has shown that Graeco Latin squares of order 6 are notpossible. Theorem 29.Euler squares exist for every order n except when n = 2or 6. But the research does not stop here.Recently,more elegant proofs havebrought forward by Stinson,Dougherty,and Zhu Lie.Also,research inthis area has taken on a greater scope.Mathematicians working in thisfield are now researching selforthogonal Latin squares -- squares thatare orthogonal to its transpose.Some error-correcting codes in algebraiccoding theory are also based on MOLS.Speaking of which,perhaps themost exciting developments come from finite projective planes,to whichthe following theorem will link MOLS. Theorem 30.A complete set of MOLS of order n implies a finite projective plane of order n. This had all started out as the simple riddle of 36 officers.After leadingto developments in combinatorics,group theory,field theory,transversaldesign,and work done by many mathematicians around the globe,wefinally begin to draw the close to this problem.Yet,the future of Latinsquares is still vast to explore. Where do we go from here? I list here a few open problems and conjecturesyet to be solved.

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《2008恒隆數(shù)學獲獎論文集》不僅可供中學生閱讀，亦可供數(shù)學教師和數(shù)學愛好者閱讀參考。

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