Dr LEUNG, King Shun   梁景信
Adjunct Assistant Professor
Department of Mathematics and Information Technology
Phone No: (852) 2948 7823
Email: ksleung@eduhk.hk
Contact
ORCiD
0000-0003-1056-5665
Phone
(852) 2948 7823
Email
ksleung@eduhk.hk
Scopus ID
35795429500
Research Interest
Tilings, fractals, mathematics of paper-folding, Recreational mathematics, Number theory, Problem-solving, Affective domain of mathematics education.
External Appointment
Dr Leung King Shun was invited by the Education Bureau to run a series of workshops titlted "Unfolding Mathematics through Paper-folding" for secondary school mathematics teachers in Dec 07. The same workshops were re-run in Jun 08. Dr Leung was invited again by the Education Bureau to give a series of seminars titled "Paper-folding Activities to Enhance the Learning of Mathematics" for secondary school mathematics teachers in Dec 08. On 3 May 08, Dr Leung gave an invited talk on "The Disklikeness of Self-affine Tiles" in the Dynamics and Fractals May Meet coorganised by Sun Yat Sen University and South China University of Technology in Guangzhou. Dr Leung was invited by the College of Mathematics and Computer Science of Hunan Normal University to visit them for academic exchange from 5 Oct 08 to 9 Oct 08. He gave two talks during the visits, one on "Disklike Self-affines " and the other "The Boundaries of Self-affine Tiles".
Professional Profile

Dr Leung King Shun is an Assistant Professor of the Department of Mathematics and Information Technology. He earned from The Chinese University of Hong Kong a BSc(Hons), an MSc and a PhD, all in mathematics. His doctoral dissertation won him the CUHK Young Scholars Dissertation Awards. Dr Leung studied mathematics education at The University of Hong Kong, from which he gained a Cert Ed and an MEd. Before joining the teacher education profession, he had been teaching mathematics at a government secondary school for seven years. He also held part-time teaching posts at The Open Learning Institute of Hong Kong (currently The Open University of Hong Kong) and The Baptist University. In 1995, he received the Fifth Anniversary Tutor Awards from the former. He also has rich experience in serving mathematics subject committees in the Education Bureau and the Hong Kong Examinations and Assessment Authority.
Research Interest

Tilings, fractals, mathematics of paper-folding, Recreational mathematics, Number theory, Problem-solving, Affective domain of mathematics education.
External Appointment

Dr Leung King Shun was invited by the Education Bureau to run a series of workshops titlted "Unfolding Mathematics through Paper-folding" for secondary school mathematics teachers in Dec 07. The same workshops were re-run in Jun 08. Dr Leung was invited again by the Education Bureau to give a series of seminars titled "Paper-folding Activities to Enhance the Learning of Mathematics" for secondary school mathematics teachers in Dec 08. On 3 May 08, Dr Leung gave an invited talk on "The Disklikeness of Self-affine Tiles" in the Dynamics and Fractals May Meet coorganised by Sun Yat Sen University and South China University of Technology in Guangzhou. Dr Leung was invited by the College of Mathematics and Computer Science of Hunan Normal University to visit them for academic exchange from 5 Oct 08 to 9 Oct 08. He gave two talks during the visits, one on "Disklike Self-affines " and the other "The Boundaries of Self-affine Tiles".
Selected Output

Scholarly Books, Monographs and Chapters
梁景信(2010):心中有數,江紹祥、梁志强,數學教育的探究學習,(頁65-72),香港,教育局數學教育組。
Leung, C. K., Lai, M. Y., Poon, K. K., & Leung, K. S. (Eds.) (2007). Proceedings of the Hong Kong Mathematics Education Conference 2007. 223 pp., Hong Kong: The Hong Kong Association for Mathematics Education.
Man, Y.K., Ng, Y.K., & Leung, K.S. (1999). Learning Elementary Number Theory with the World Wide Web: A Design of a Homepage on the Internet. In Bradbeer & Ng (Eds.), Current Practice in Multimedia Education (133-139). Hong Kong: The City University of Hong Kong.

Journal Publications
Wang, L. & Leung, K. S. (2020). Radix expansion and connectedness of planar self-affine fractals. Monatschefte fur Mathematik (DOI: https://doi.org/10.1007/s00605-020-01461-0), 193 (3), pp. 705-724.
Leung, K. S., Luo, J. J. & Wang, L. (2020). Connectedness of a class of self-affine carpets. Fractals-Complex Geometry Patterns and Scaling in Nature and Society, 28, 1-10.
Leung, K. S. (2018). Paper-folding and cutting activities to demonstrate five-fold symmetry. The Mathematical Gazette, 102(555), 413-421.
Leung, K. S. & Luo, J. J. (2017). A characterization of connected self-affine fractals arising from collinear digits. Journal of Mathematical Analysis and Applications, 456(1), 429-443.
Leung, K. S. (2017). Approaching quadratic equations from a right angle. The Mathematical Gazette, 101(552), 424-438.
Leung, K. S. & Luo, J. J. (2015). Connectedness of planar self-affine sets associated with non-collinear digit sets. Geometriae Dedicata, 175(1), 145-157.
梁景信(2013):相似三角形與畢氏定理,《《數學教育期刊》》,第46期,頁77-81。
Leung, K. S., & Luo, J. J. (2013). Boundaries of disk-like self-affine tiles. Discrete and Computational Geometry, Volume 50, Issue 1, pp 194-218.
Leung, K. S. (2012). Converting a fraction into a decimal by hand calculation. Mathematical Spectrum, 45 (1), 34-37.
Leung, K. S. (2012). Dividing a right-angled trapezium into two similar quadrilaterals. The Mathematical Gazette, 96 (536), 304-309.
Leung, K. S., & Luo, J. J. (2012). Connectedness of planar self-affine sets associated with non-consecutive collinear digit sets. Journal of Mathematical Analysis and Applications, 395 (1), 208-217.
Leung, K. S. (2012). Similar triangles and the Cosine Rule. The Mathematical Gazette, 96 (535), 169-172.
梁景信(2011):解二次方程的規矩,《《數學教育期刊》》,第45期,頁95-99。
梁景信(2009):摺紙解方程,《《數學教育期刊》》,第44期,頁28-31。
Leung, K. S., & Lau, K. S. (2007). Disklikeness of planar self-affine tiles. Transactions of the American Mathematical Society, 359 (7), 3337-3355.
Leung, K. S., & Sze, C. L. (2007). Paper folding fractions. The Mathematical Gazette, 91 (520), 87-91.

Conference Papers
梁景信(2011,6):等分手工紙的一些簡單方法,發展21世紀能力的電子學習-運用評估促進數學的學習研討會,香港。
梁景信、張家麟(2011,6):數學歸納法的教與學,香港數學教育會議2011,香港。
Leung, K. S. (2011, May). The connectedness of planar self-affine sets associated with non-consecutive collinear digit sets. 2011 National Mathematics Conference on Fractals Theory and Dynamical Systems, Zhangjiajie, Hunan.
Leung, K. S. (2008, December). Dislike self-affine tiles. Paper presented at the Seminar on Fractal Geometry and Related Topics, Zhuhai, China.

All Other Outputs
(2007):《香港數學教育會議2007論文集》,香港教育學院,香港。

Project

The Connectedness of Planar Self-affine Sets Generated by Digit Sets with an Outlier
In this project, we study a class of planar self-affine sets generated by a 2×2 integral expanding matrix A with characteristic polynomial f(x)=x^2+px+q (|q|≥3) and a digit set D={d_0,d_1,…,d_(|q|-1)}⊆Z^2 with exactly one outlier. It is well-known that there exists a unique compact set T≔T(A,D) satisfying AT=T+D. We attempt to characterize the connectedness of T in terms of the position of the outlier.
Project Start Year: 2020, Principal Investigator(s): LEUNG, King Shun 梁景信
 
Connectedness of a Class of a Self-Affine Carpets
Study the connectedness of a class of self-affine set (called a self-affine carpet) generated by the matrix A=3I and a nine-digit set obtained by moving a digit from the 3x3 digit set to other positions. We classify the digit sets into two categories: those generate connected carpets and those do not.
Project Start Year: 2019, Principal Investigator(s): LEUNG, King Shun 梁景信
 
Radix Expansion of Rational Points and Disk-like Self-affine Tiles
In this project, we develop a method for finding the radix expansion of a rational point on the plane with respect to an expanding matrix A and a digit set D with |detA| elements. It is also required that the self-affine set T generated by A and D is disklike (homeomorphic to the closed unit disk). Our method will make use of the Cayley-Hamilton Theorem which states that f(A)=0 where f(x) is the characteristic polynomial of A.
Project Start Year: 2018, Principal Investigator(s): LEUNG, King Shun 梁景信
 
Topological structure of self-affine fractals
In this project we study the connectedness of a class of planar self-affines sets associated with an expanding
Project Start Year: 2017, Principal Investigator(s): LEUNG, King Shun 梁景信
 
Disklike Planar Self-Affine Tiles Associated with Non-Collinear Digit Sets
In this project, we study the condition for the class of planar self-affine tiles associated with non-collinear digit sets to be connected and disklike (being homeomorphic to the closed unit disk). The main tools used are the radix expansion method developed by the principal investigator and a result of C. Bandt and Y. Wang. on how to determine a self-affine set to be disklike by counting the number of its neighbours
Project Start Year: 2016, Principal Investigator(s): LEUNG, King Shun 梁景信
 
Developing Exploratory Pedagogy to Enhance Teaching and Learning of Mathematics
This project aims to: (a) develop exploratory pedagogy for enhancing teaching and learning of mathematics; (b) design and develop relevant exploratory teaching and learning materials for use by lecturers and students; (c) study the impact of the end-products via peer-reviews, try-outs, questionnaires and interviews.
Project Start Year: 2010, Principal Investigator(s): MAN, Yiu Kwong 文耀光 (LEUNG, King Shun 梁景信 as Co-Investigator)
 
The HKIEd Longman Mathematics Day 2007
It aims to promote our Institute and Department to senior secondary students and in-service teachers, and it is achieved through involving these students and teachers in interesting and meaningful mathematics activities at our campus. These activities are designed to stimulate students' interest in mathematics, and to encourage them to participate in mathematics learning in ways that are different from those normally adopted in their school studies. Besides, it also provides opportunity for in-s . . .
Project Start Year: 2007, Principal Investigator(s): WONG, Tak Wah 黃德華 (LEUNG, King Shun 梁景信 as Co-Investigator)
 
The HKIEd Longman Mathematics Day 2006
This project intends to promote HKIEd and the Mathematics Department to senior secondary students, and is achieved through involving these students in interesting and meaningful mathematics activities at our campus. These activities are designed to stimulate students' interest in mathematics, and to encourage them to participate in mathematics learning in ways that are different from the normally adopted in their school studies. The project involves a number of strands, which include talks, work . . .
Project Start Year: 2006, Principal Investigator(s): WONG, Tak Wah 黃德華 (LEUNG, King Shun 梁景信 as Co-Investigator)
 
Further Development of Complete Teaching and Learning Materials for Mathematics Modules
The Department of Mathematics has noted that students have frequently expressed their concern about the difficulty of learning mathematics, and about the shortage of appropriate learning materials. These concerns have validity because of the differences in focus, depth and orientation between the standard university mathematics curriculum and a curriculum that would be appropriate for the education of primary/junior secondary mathematics teachers. Because of these differences, and the much sma . . .
Project Start Year: 2005, Principal Investigator(s): LAM Suk Wah, Louisa (LEUNG King Shun as Co-Investigator)