Year Book 2014

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 2014

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 2014 Hang Lung Mathematics Awards comprises of the following members:

Chair: Professor Shing-Tung Yau Harvard University and The Chinese University of Hong Kong
Professor Lars Andersson Albert Einstein Institute, Germany
Professor Raymond Hon-Fu Chan* The Chinese University of Hong Kong
Professor Tony F. Chan The Hong Kong University of Science and Technology
Professor Shiu-Yuen Cheng Mathematical Sciences Center, Tsinghua University
Professor Jaigyoung Choe Korea Institute for Advanced Study
Professor Ingrid Daubechies Duke University
Professor Ka-Sing Lau The Chinese University of Hong Kong
Professor John M. Lee University of Washington
Professor Ngai-Ming Mok The University of Hong Kong
Professor Duong H. Phong Columbia University
Professor Mark A. Stern Duke University
Professor Ye Tian Chinese Academy of Sciences
Professor Tom Yau-Heng Wan The Chinese University of Hong Kong
Professor Michael Wolf Rice University

*Note: Professor Chan was unable to join the Oral Defense and will be represented by Professor Jun Zou.

Screening Panel 2014

The members of the Screening Panel of the 2014 Hang Lung Mathematics Awards are:

Chair: Professor Tom Yau-Heng Wan The Chinese University of Hong Kong
Professor Conan Nai Chung Leung The Chinese University of Hong Kong
Dr. Charles Chun-Che Li The Chinese University of Hong Kong
Dr. Chi-Hin Lau The Chinese University of Hong Kong

Steering Committee 2014

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 educators 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 2014 Hang Lung Mathematics Awards comprises of the following members:

Chair: Professor Sir James A. Mirrlees 1996 Nobel Laureate in Economics
Master, Morningside College, CUHK
Professor Thomas Kwok-Keung Au EPYMT and Mathematics, The Chinese University of Hong Kong
Professor Tony F. Chan Vice-Chancellor, The Hong Kong University of Science and Technology
Professor Shiu-yuen Cheng Professor, Tsinghua University
Professor Wing-Sum Cheung Professor, Mathematics, The University of Hong Kong
Professor Ka-Sing Lau Professor, Mathematics, The Chinese University of Hong Kong
Mr. Siu-Leung Ma CEO, Fung Kai Public School
Ms. Michelle Sau-Man Mak Chairman’s Office, Hang Lung Properties Limited
Professor Tai-Kai Ng Associate Dean of Science, The Hong Kong University of Science and Technology
Professor Zhouping Xin Professor, Mathematics, The Chinese University of Hong Kong
Dr. Chee-Tim Yip Principal, Pui Ching Middle School

Executive Committee 2014

The members of the Executive Committee of the 2014 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
Secretariat: Ms. Mandy Ka-Man Leung
Ms. Konnie Wan Yu Pak
Ms. Serena Wing-Hang Yip
The Chinese University of Hong Kong
The Chinese University of Hong Kong
The Chinese University of Hong Kong

Winners of the 2014 Hang Lung Mathematics Awards

GOLD 

Topic Investigation of the Erdös-Straus Conjecture
Team Members Yuk Lun Fong
Teacher Mr. Kwok Kei Chang
School Buddhist Sin Tak College
Abstract

In this paper, we are going to investigate the ${\bf{\textit{Erdős-Straus Conjecture }}}$: For any positive $n \geq 2$, there exists positive integers $k,k_1,k_2$ such that
$$ \dfrac{4}{n} = \dfrac{1}{k}+\dfrac{1}{k_1}+\dfrac{1}{k_2}$$

Firstly, we will solve a simpler form $ \dfrac{3}{n} = \dfrac{1}{x} + \dfrac{1}{y}$ as a starting point. Next we will investigate the Erdos-Straus Conjecture in the following dimensions: the related geometric representation of the Erdos-Straus Conjecture, the properties of solutions of the Erdos-Straus Conjecture, further investigation of some paper of the Erdos-Straus Conjecture, existence of special forms of solutions of the Erdos-Straus Conjecture, and the investigation of the Erdos-Straus Conjecture in algebraic dimension. The aim of this report is to find evidence that shows the ${\bf{\textit{Erdős-Straus Conjecture}}}$ is true. If evidence is not strong enough, we still hope that this report can make an improvement to the researched result at present.

SILVER 

Topic Pseudo Pythagorean Triples Generator for Perpendicular Median Triangles
Team Members Yan Lam Fan, Wai Pan Yik
Teacher Mr. Ho Fung Lee
School Pui Ching Middle School
Abstract The problem of finding all integral sides and lengths of a right-angled triangle is famous and the solution set is called the Pythagorean Triple.
Now, instead of the sides of a triangle, we concern ourselves with the orthogonality of lines from vertices to their opposite sides. We want to generalize the problem to the arbitrary rational ratio on the sides.

BRONZE

Topic Probability, Matrices, Colouring and Hypergraphs
Team Members Hok Kan Yu, Dave Lei, Ka Chun Wong, Sin Cheung Tang
Teacher Mr. Yan Ching Chan
School P.L.K. Centenary Li Shiu Chung Memorial College
Abstract In this project, we achieved various results using Probabilistic Methods. By exploiting the concept of probability and expected value, we managed to achieve three results: distribution of entries on a cube, colouring of vertices of a hypergraph and a lower bound of a maximal independent set on a hypergraph.

HONORABLE MENTIONS

(ARRANGED IN ALPHABETICAL ORDER OF SCHOOL NAME)

Topic Classification of Prime Numbers by Prime Number Trees
Team Members Man Him Ho, Chun Lai Yip, Yat Wong, Yin Kei Tam
Teacher Mr. Alexander Kin Chit O
School G.T. (Ellen Yeung) College
Abstract The traditional sieve of Eratosthenes gives a simple algorithm for finding all prime numbers. However, prime numbers seem to appear unpredictably but with regular population ratio in the ranges of integers, as Gauss had found a density function of prime numbers within a range of x. On the other hand, there are few methods of classification of prime numbers. We developed a new classification of prime numbers by prime number trees. In the prime number trees, the following number is generated by attaching a digit either 1, 3, 7, or 9 to the right hand side of the preceding prime number. If the number generated remains a prime, then the process continues, otherwise it stops. The prime number trees group prime numbers with similar digits together and show the elegance of a shorthand of prime numbers. This method also shows a regular classification of prime numbers.
 
Topic Two Methods for Investigating the Generalized Tic-Tac-Toe
Team Members Kam Chuen Tung, Luke Lut Yin Lau
Teacher Ms. Mee Lin Luk
School La Salle College
Abstract In this paper, we look into the (m,n,k,p,q) game, one of the generalizations of the well-known Tic-Tac-Toe game. The objective of the game is to achieve ‘k-in-a-row’ with one’s pieces before one’s opponent does. We use two methods – exhaustion and pairing strategy – to investigate the results of the (m,n,k,p,q) game for several different values of the five parameters.
 
Topic A General Formula to Check the Divisibility by All Odd Divisors and its Extensions
Team Members Chun Kit Du, Tung Him Lam, Hok Leung Chan, Chi Ming Ng, Kai Yin Ng
Teacher Mr. Kwok Tai Wong
School S.K.H. Lam Woo Memorial Secondary School
Abstract The paper places much emphasis on the method of checking, without using division, the divisibility of an integer by an odd divisor. In part A, it mainly focuses on getting the general way to perform the divisibility test by an algorithm using the unit digit and the rest of the truncated digits of the dividend. Parts B and C are extensions of part A. In part B, it attaches importance to using the last two or more digits of the dividend and so the divisibility test is not just restricted to the ones digit. While parts A and B focus on the method of verifying the divisibility of a number, part C mainly concentrates on finding the quotient without performing division algorithm. This unique method of division is discovered in the process of investigation in part A.
 
Topic On the Geometric Construction of Triangles and the Algebraic Interpretation of the Notion
Team Members Chi Cheuk Tsang, Ho Lung Tsui, Justin Chi Ho Chan Tang, Ian Yu Young Kwan
Teacher Mr. Perrick King Bor Ching
School St. Joseph’s College
Abstract This study centers on the Euclidean construction of triangles under several given pre-conditions, and carries out several major objectives surrounding this aim:
1. to devise a scheme to primarily distinguish cases in which Euclidean construction is impossible;
2. to seek the simplest agenda in the construction of possible cases;
3. to give a strict definition of Euclidean constructability; and
4. to determine the methods and rigorous proofs of inconstructability.
 
Topic The Application of Graph Theory to Sudoku
Team Members Josephine Yik Chong Leung, Wai Shan Lui
Teacher Mr. Tad Ming Lee
School Ying Wa Girls’ School
Abstract In this project, we establish the Sudoku graph by studying the relationship between Sudoku and graphs with the help of NEPS (Non-complete Extended P-Sum). The approach is to look for the chromatic polynomial of the Sudoku graph, so that we can determine the total number of possible solved Sudoku puzzles. Although the chromatic polynomial of the Sudoku graph is not presented in this research, we have found some properties of the polynomial that may provide inspirations for further research.
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2014 Awards Ceremony Video

The 2014 Hang Lung Mathematics Awards winners were announced and recognized on December 11, 2014.  Eight awards were announced: a Gold Award, a Silver Award, a Bronze Award and five Honorable Mentions.

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

Welcome Remarks

Mr. Ronnie Chan
Chairman, Hang Lung Properties Limited

Prof. Shing-Tung Yau
Chairman, 2014 Hang Lung Mathematics Awards Scientific Committee

Opening Remarks

Mrs. Carrie Lam, GBS, JP Chief Secretary for Administration,
The Government of the Hong Kong Special Administrative Region

Professor Sir James A. Mirrlees
Chairman, 2014 Hang Lung Mathematics Awards Steering Committee

Announcement and Awards Presentation

Gold Award
Buddhist Sin Tak College

Silver Award
Pui Ching Middle School

Bronze Award
P.L.K. Centenary Li Shiu Chung Memorial College

Honorable Mention
G. T. (Ellen Yeung) College

Honorable Mention
La Salle College

Honorable Mention
S.K.H. Lam Woo Memorial Secondary School

Honorable Mention
St. Joseph’s College

Honorable Mention
Ying Wa Girls’ School

Presentation of Souvenirs

Mr. Ronnie C. Chan
Chairman, Hang Lung Properties Limited

2014 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 2014 HANG LUNG MATHEMATICS AWARDS

(arranged by school name in alphabetical order)

Probability Study using Matrix to Analyze Football Tournaments
Baptist Lui Ming Choi Secondary School
Investigation of the Erdös-Straus Conjecture
Buddhist Sin Tak College
Snake
Chiu Lut Sau Memorial Secondary School
Classification of Prime Numbers by Prime Number Trees
G.T. (Ellen Yeung) College
On the Investigation of Fundamental Solutions to the Pell Equation
G.T. (Ellen Yeung) College
Two Methods for Investigating the Generalized Tic-Tac-Toe
La Salle College
Probability, Matrices, Colouring and Hypergraphs
P.L.K. Centenary Li Shiu Chung Memorial College
Pseudo Pythagorean Triples Generator for Perpendicular Median Triangles
Pui Ching Middle School
A General Formula to Check the Divisibility by All Odd Divisors and its Extensions
S.K.H. Lam Woo Memorial Secondary School
Passing Through the Surface
Shatin Pui Ying College
More about a Finger-Counting Trick
Sir Ellis Kadoorie Secondary School (West Kowloon)
On the Geometric Construction of Triangles and the Algebraic Interpretation of the Notion of Constructability
St. Joseph’s College
How to Keep Water Cold II – A Study about the Wet Contact Surface Area in a Cube
St. Stephen’s Girls’ College
Rock-Paper-Scissors
Tsuen Wan Public Ho Chuen Yiu Memorial College
The Application of Graph Theory to Sudoku
Ying Wa Girls’ School