This is the final paper written for my first independent research. As usual, I only post the introduction and the conclusion here. Please feel free to contact me via email (refer to the Home page) if you would like to read some of my arguments in detail or offer any critic. Introduction This paper explores… Continue reading The Myth of Infinity: Does Platonism Pave the Stairs to God?

# Category: Mathematics

## Proof by Contradiction: An Accessible Introduction with Simple Applications

Proof by contradiction is a fundamental proof method in undergraduate Mathematics, and in fact, it may even be relevant for pre-U students. Yet, how to make use of the method has been much overlooked in A'Level H2 Mathematics. Perhaps it is used by some students in certain elite schools or Olympiad programmes, but the method… Continue reading Proof by Contradiction: An Accessible Introduction with Simple Applications

## The Geometrical Meaning of the Tangent of an Eclipse

Original Question: Let $Latex (x_{0},y_{0})$, where $latex y_{0} \neq 0 $, be a point on the ellipse $latex \frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1 $. Show that the tangent line to the ellipse passing through $Latex (x_{0},y_{0})$ is $Latex \frac{x_{0}x}{a^{2}}+\frac{y_{0}y}{b^2}=1 &s=1$. Suggested Solution: This is not a difficult question to tackle considering the fact that $Latex (x_{0},y_{0})$ is on the… Continue reading The Geometrical Meaning of the Tangent of an Eclipse