Rigel Kent

\(\pi\) is a fundamental constant in mathematics. It is also an important constant in science for it appears naturally in so many applications: in the period of a simple pendulum in mechanics , Maxwell-Boltzmann distribution for gas molecules in thermodynamics, Coulomb's law for electrostatic force in electromagnetic theory, Heisenberg's uncertainty principle in quantum mechanics, Einstein's field equation in general relativity theory. Since \(\pi\) is such an important constant, it should be properly introduced to students, both historically and mathematically. In Malaysian secondary schools, this constant is first taught to a typical 14-year-old when he/she is learning the geometric properties of the circle. In a recent book titled "Essential Mathematics Form 2", published by Longman, the authors wrote, in page 163, the value of \(\pi\) is an estimated value, which is \(\frac{22}{7}\) or 3.142 This remark is technically incorrect. I guess the authors p...

In most of the secondary school level mathematics reference books found in local bookstores, the mathematical object "circle" is introduced as follows: A circle is a set of points that are equidistant from a fixed point. There is something wrong with this description. It is rather vague because a set of points could mean the following set of 8 points {P1, P2, P3, P4, P5, P6, P7, P8}: Although these points are equidistant from a fixed point, this particular set does not form or look like a circle. This problematic description of "circle" is not entirely the fault of the reference book authors, because it actually originates from page 45 of the Curriculum Specifications for Form 2 Mathematics, compiled in 2002, by the Curriculum Development Centre, Ministry of Education Malaysia. I must say that it is rather difficult to describe "circle" or any other mathematical objects with words. A better version (but still imprecise) would be: A circle is a c...