Prime Numbers Brief description: Most people consider integers to be the most fundamental numbers, and all other numbers are built up upon them. However, there is another view from mathematicians. Every integer greater than 1 is either a prime or a product of primes. Therefore they regard prime numbers to be the most fundamental composition of numbers. Some ancient Chinese mathematicians called prime numbers 'math root', meaning the fundamental basis of mathematics.	Logarithms Brief description: Many mathematics textbooks have a logarithm table in the appendix. This is used for calculations involving logarithms. Do you know that the concept of logarithm actually developed after the logarithm table was invented?
Pi Brief description: In ancient times, people already discovered that the circumference of a circle increases as its diameter in a fixed proportion. Roughly, the circumference is a bit more than three times the diameter. In ancient China, there was the saying that "a diamater of 1 corresponds to a circumference of 3". Even in the Bible, this proportion was taken to be 3.	Pythagoras' Theorem Brief description: The Pythagoras' theorem is a famous theorem. As we all know, it says that in a right triangle, the square of the hypotenuse is equal to the sum of squares of the other two sides. But who discovered this great theorem which has more than 300 proofs?
The Development of Calculus Brief description: The earliest ideas involving differentiation were the concepts of infinity and limit. Long ago, many mathematicians had raised similar ideas about these concepts.	Abel Brief description: In the Royal Garden of Oslo, the capital of Norway, there is a cenotaph memorizing Abel, a mathematician who had developed the theory of elliptic functions and higher degree equations.
Playing Guess Game using Recurrence Relation Brief description: In 2002 there was a game of guessing numbers on a TV programme. In the game the computer first chooses an integers from 1 to 100. Players take turn to guess the number. If a player gets the number, he loses. Otherwise, the number being guessed splits the interval [1,100] into two, and the computer will announce the subinterval in which the chosen number lies. The game continues until someone loses. Suppose the game is played between two people. Is there a strategy that maximises the probability of winning the game? Is it more advantageous to be the first one or last one to guess numbers?	The Definitions and Axioms in Book I of Elements Brief description: Elements by Euclid was an important work in the history of mathematics. Before the book was written, people's mathematical knowledge was disorganised. The importance of Elements lies in the fact that it organised and arranged the various known mathematical knowledge in a logical matter, making it into a rigorous system. Of course, from modern view, Elements has its imperfections. However, its way of doing mathematics has been in use till now. The purpose of this paper is to analyse and discuss in detail the method adopted by Euclid and to investigate in depth the definitions and axioms in Book I of Elements. More importantly, we learn to understand and appreciate the work of ancient mathematicians.
The Mathematical Achievements and Methodologies of Archimedes Brief description: Archimedes is one of the 'Big Three' mathematicians in ancient Greece and even in history. He had many different contributions to mathematics thoughout his life. He had studied the problems of finding the lengths of curves, as well as finding areas and volumes. His special way of thinking paved the way for the development of many areas in mathematics, including integration, solution of cubic equations and the use of mechanics in mathematical proofs.	The History of Pi Brief description: This article discusses the history of p. This account is divided into four parts here to facilitate the discussion. Through this discussion, the readers should gain a better understanding of the mysterious value of p and witness the wisdom and persistence of man.
Charlie's IMO 2003 Travel Brief description: Charlie Yu Hok-pun, a member of Mathematical Database, have been Japan on 11-19 July 2003 to represent Hong Kong in the International Mathematics Olympiad (IMO) 2003. Are you interested in what happened in these 9 days? Come and have a look!	What is proportional representation? Brief description: In the Legislative Council Elections in Hong Kong, the geographical constituencies are elected using the "largest remainder method" in "proportional representation". Do you know how this works? We also frequently come across terms like "splitting lists" and "vote coordination". Do you know what they are? Let's have some discussions before the coming Legislative Council Elections.
From Human Knot to DNA Brief description: Have you ever played a game called "human knot" before? In the game, a group of about 10 people face each other to form a circle. Each player places both hands in the middle of the circle and each hand grasps another hand randomly. After ensuring only one circle is formed, the players need to untangle themselves, without letting go of hands, into an untangled circle. Here comes the problem: is it always possible to form an untangled circle?	More on Proportional Representation — Implications of the Results of the Legislative Council Election 2004 Brief description: In the article “What is Proportional Representation?”, we mentioned that proportional representation with the largest remainder method was used in the election of geographical constituencies in the Legislative Council (LegCo) in Hong Kong since 1998. The shortcomings of the method were discussed and supported by examples. Further analysis of the proportional representation will be made in this article based on the results of the geographical constituencies in the LegCo Election 2004.