Year Book 2008

ORGANIZATION

The Scientific Committee and the Steering Committee are the two principal committees of the Hang Lung Mathematics Awards. The Scientific Committee, comprising world-renowned mathematicians, is the academic and adjudicating body of the Awards. The Steering Committee, comprising mathematicians and representatives from different sectors of society, serves as the advisory body.

Scientific Committee 2008

The Scientific Committee upholds the academic standard and integrity of Hang Lung Mathematics Awards. Its members actively participate in the evaluation of all project reports, determination of the teams that will be invited to the oral defense, and adjudication at the oral defense.

The Screening Panel under the Scientific Committee handles the initial review of each report, supervises the second and final round of the review process, and liaises with all referees and members of the Scientific Committee regarding the project reports.

The Scientific Committee for the 2008 Hang Lung Mathematics Awards comprises of the following members:

Chair: Professor Shing-Tung Yau Harvard University
Professor Tony F. Chan University of California, Los Angeles
Professor David C. Chang Polytechnic Institute of New York University
Professor Chong-Qing Cheng Nanjing University
Professor John H. Coates University of Cambridge
Professor Benedict H. Gross Harvard University
Professor Ka-Sing Lau The Chinese University of Hong Kong
Professor Jian-Shu Li The Hong Kong University of Science and Technology
Professor Chang-Shou Lin National University of Taiwan
Professor Jill P. Mesirov Broad Institute of MIT and Harvard
Professor Kenneth C. Millett University of California, Santa Barbara
Professor Ngai-Ming Mok The University of Hong Kong
Professor Stanley J. Osher University of California, Los Angeles
Professor Duong H. Phong Columbia University
Professor Wilfried Schmid Harvard University
Professor Tom Yau-Heng Wan The Chinese University of Hong Kong
Professor Hung-Hsi Wu University of California, Berkeley

Screening Panel 2008

The members of the Screening Panel of the 2008 Hang Lung Mathematics Awards are:

Chair: Professor Tom Yau-Heng Wan The Chinese University of Hong Kong
Professor Wing Sum Cheung The University of Hong Kong
Professor Conan Nai Chung Leung The Chinese University of Hong Kong

Steering Committee 2008

The Steering Committee serves as an advisory body to Hang Lung Mathematics Awards, and comprises of mathematicians and representatives from different sectors of society, including leading educator and heads of mathematics departments in major Hong Kong universities. It also enlists some members from other Hang Lung Mathematics Awards committees to provide an overall oversight.

The Executive Committee, which reports to the Steering Committee, is responsible for the operation and administration of the competition, as well as managing the Resource Center and acting as the Secretariat for the Awards.

The Steering Committee for the 2008 Hang Lung Mathematics Awards comprises of the following members:

Chair: Professor Sir James A. Mirrlees 1996 Nobel Laureate in Economics
Professor Thomas Kwok-Keung Au The Chinese University of Hong Kong
Professor Wing-Sum Cheung The University of Hong Kong
Professor Ka-Sing Lau Chairman, Mathematics Department, CUHK
Professor Jian-Shu Li The Hong Kong University of Science and Technology
Professor Lo Yang Chinese Academy of Sciences
Mr. Siu-Leung Ma CEO, Fung Kai Public Schools
Mr. Chun-Kau Poon Principal, The Hong Kong Federation of Youth Group Lee Shau Kee College
St. Paul Co-educational College (retired)
Ms Susan Wong Hang Lung Properties Limited
Mr. Chee-Tim Yip Principal, Pui Ching Middle School

Executive Committee 2008

The members of the Executive Committee of the 2008 Hang Lung Mathematics Awards are:

Chair: Professor Thomas Kwok-Keung Au The Chinese University of Hong Kong
Dr. Ka-Luen Cheung The Hong Kong Institute of Education
Dr. Leung-Fu Cheung The Chinese University of Hong Kong
Dr. Charles Chun-Che Li The Chinese University of Hong Kong
Secretariat: Ms. Serena Wing-Hang Yip The Chinese University of Hong Kong

WINNERS of the 2008 Hang Lung Mathematics Awards

GOLD 

Topic: Isoareal and Isoperimetric Deformation of Curves
Team Members: Kwok Chung Li, Chi Fai Ng
Teacher: Mr. Wing Kay Chang
School: Shatin Tsung Tsin Secondary School
Abstract: In the report, we want to answer the following question: how to deform a curve such that the rate of change of perimeter is maximum while the area and the total kinetic energy are fixed? First we work on isosceles triangle as a trial. Then we study smooth simple closed curve and obtain information about the velocity of each point of the curve and its relation to the curvature. We also consider the applications of the results and the velocity for the dual isoperimetric problem.

SILVER 

Topic: Sufficient Condition of Weight-Balance Tree
Team Members: Chi Yeung Lam, Yin Tat Lee
Teacher: Mr. Chun Kit Ho
School: The Methodist Church Hong Kong Wesley College
Abstract: Huffman’s coding provides a method to generate a weight-balance tree, but it is not generating progressively. In other words, we cannot have meaningful output if we terminate the algorithm halfway in order to save time. For this purpose, we want to design an alternative algorithm, therefore this paper aims at finding out a sufficient condition of being a weight-balance tree. In this paper, we have found out the sufficient condition. Besides, as the solution of building a weight-balance tree can be applied to solving other problems, we abstract the problem and discuss it in the manner of graph theory. The applications are also covered.

BRONZE 

Topic: Fermat Point Extension – Locus, Location, and Local Use
Team Members: Fung Ming Ng, Chi Chung Wan, Wai Kwun Kung, Ka Chun Hong
Teacher: Mr. Yiu Kwong Lau
School: Sheng Kung Hui Tsang Shiu Tim Secondary School
Abstract: Published in 1659, the solutions of Fermat Point problem help people find out the point at which the sum of distances to 3 fixed points in the plane is minimized. In this paper, we are going to further discuss when the number of fixed points is greater than 3, the relationship between the fixed points and the point minimizing the sum of distances to more than three given points. Also, we would like to find out if there exists a way such that the location of point minimizing the sum of distances to more than three given points can be determined just by compass and ruler, or approximated by mathematical methods.

4 HONORABLE MENTIONS

(ARRANGED IN ALPHABETICAL ORDER OF SCHOOL NAME)

Topic: A Cursory Disproof of Euler’s Conjecture Concerning Graeco-Latin Squares by means of Construction
Team Members: Jun Hou Fung
Teacher: Mr. Jonathan Hamilton
School: Canadian International School of Hong Kong
Abstract: In this report, our team has explored a mathematical structure commonly known as Graeco-Latin squares. Although we do give a broad scope of this field, we are particularly focused on one aspect: Euler’s Conjecture. According to this conjecture, there are certain types of Graeco-Latin squares that do not exist. In this report, we disprove this conjecture by demonstrating a means to construct an infinite number of these so-called non-existent squares. This branch of mathematics is highly related to group theory, combinatorics, and transversal design; therefore, we will also provide a brief overview of these topics throughout this report.
 
Topic: Equidecomposition Problem
Team Members: Cheuk Ting Li
Teacher: Miss Mee Lin Luk
School: La Salle College
Abstract: The equidecomposition problem is to divide a shape into pieces, and then use the pieces to form another shape. In this project, we are going to investigate the conditions under which a given shape can be broken down and combined into another specified shape. The classical problem on the equidecomposability of polygons has already been solved by mathematicians. We start by presenting the proof of the classical problem, which is the keystone of this research. Then the problem is generalized to weighted shapes, shape with curves, etc. Some interesting new results are obtained.
 
Topic: 3n+1 Conjecture
Team Members: Shun Yip
Teacher: Mr. Chi Keung Lai
School: Shatin Pui Ying College
Abstract: The aim of our project is to investigate the 3n + 1 conjecture. It is very hard to give a general path for each natural number to arrive at 1. So we investigate its negation i.e. there exists a natural number k with no path to 1. There are two possibilities: either ktakes a path which is a cycle to itself after n steps or its path is increasing indefinitely. These two possibilities lead us to study pre-numbers of any odd natural number and the number of peaks of paths. In the project, several interesting results were obtained by studying backward paths, number of peaks and cycles or forward paths.
 
Topic: Geometric Construction – Area Trisection of a Circle
Team Members: Shun On Hui, Kin Ho Lo, Kai Ming To, Maureen Tsz Yan Ho , Wai Hang Ng
Teacher: Mr. Wai Hung Ho
School: Tsuen Wan Public Ho Chuen Yiu Memorial College
Abstract: When dividing a cake of circle shape into equal parts, it is quite easy to divide it from the centre. However, if we need to divide it from its edge, how can we accomplish this task accurately? This report aims to find a method to divide the area of a circle into 3 equal parts with two straight lines by Euclidean construction, i.e. the construction with compass and straightedge only. However, we were aware that it is difficult, if not impossible, to find the exact method of construction. Therefore, we try to find some methods to divide the area of circle approximately into three equal parts. In this report, we have three analytic approaches: by Lagrange Interpolating Polynomial, by infinite series of sine function and by method of bisection. Then, we will discuss three methods of construction, which are: inscribing a regular polygon with a large number of sides, inscribing a regular polygon with a small number of sides and bisecting the slope. At last, we will give a comparison of these three methods

 

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2008 Awards Ceremony Video

The 2008 Hang Lung Mathematics Awards winners were announced and recognized on December 21, 2008. Seven awards were announced: a Gold Award, a Silver Award, a Bronze Award, and four Honorable Mentions.

Winning Students, teachers, and schools were recognize on stage, and received crystal trophies and certificates from world renowed scholars.

Welcome Remarks

Prof. Shing-Tung Yau
Chairman, 2008 Hang Lung Mathematics Awards Scientific Committee

Mr. Ronnie Chi-Chung Chan
Chairman, Hang Lung Group

Opening Remarks

Mr. Michael Ming-Yeung Suen
Secretary for Education, HKSAR

Prof. Sir James A. Mirrlees
Chairman, 2008 Hang Lung Mathematics Awards Steering Committee

Announcement Presentation

Gold Award
Shatin Tsung Tsin Secondary School
Silver Award
The Methodist Church Hong Kong Wesley College
Bronze Award
Sheng Kung Hui Tsang Shiu Tim Secondary School
Honorable Mention
Canadian International School of Hong Kong
La Salle College
Shatin Pui Ying College
Tsuen Wan Public Ho Chuen Yiu Memorial College

Special Remarks

Prof. Shing-Tung Yau
Chairman, 2008 Hang Lung Mathematics Awards Scientific Committee
Mr. Ronnie Chi-Chung Chan
Chairman, Hang Lung Group

Closing Remarks

Dr. Gerald L. Chan
Non-Executive Director, Hang Lung Group

2008 DEFENSE MEETING VIDEO

Please click on the “Playlist” menu below to select the video to watch:

Finalist Teams Selected for the Oral Defense at the 2008 Hang Lung Mathematics Awards

(arranged by school name in alphabetical order)

Sufficient Condition of Weight-Balance Tree
The Methodist Church Hong Kong Wesley College
Interesting Findings in Rational Triangles and its relation to an Elliptic Curve
Buddhist Sin Tak College
3n + 1 Conjecture
Shatin Pui Ying College
Least Wet Under Rain
Kwok Tak Seng Catholic Secondary School
The tactics of winning “RISK”
S.D.B. NG SIU MUI SECONDARY SCHOOL
“Fermat Point” – Locus, Location, and Local Use
Sheng Kung Hui Tsang Shiu Tim Secondary School
Analysis of Mastermind
Immanuel Lutheran College
Geometric Construction – Area Trisection of A Circle
Tsuen Wan Public Ho Chuen Yiu Memorial College
Wire In Magnetic Field
SKH Lam Woo Memorial Secondary School
Equidecomposition Problem
La Salle College
Isoareal and Isoperimetric Deformation of Curves
Shatin Tsung Tsin Secondary School
A Cursory Disproof of Euler’s Conjecture Concerning Graeco-Latin Squares By Means of Construction
Canadian International School of Hong Kong
Be a Smart Banker A research on 1 vs 1 gambling
Shatin Tsung Tsin Secondary School
Capture King – a Mathematics game
Munsang College (HK Island)
Is there a function for the absolute percentage error in the period of a pendulum when using the standard formula
Sha Tin College