<p>Oh. Thanks for the reply :)</p>
<p>As I’ve stated earlier, my dismal performance in the olympiads when compared with national standards was mainly because I had no freaking idea what to expect. This was my first experience at any olympiad. However, I do understand that that offers very little in way of justification.</p>
<p>I don’t think I’ll be competing with the Singaporean cohort though because I’m an Indian national studying in Singapore on scholarship.</p>
<p>My research in Math is simple: we all know that when we graph functions, we plot the y-value vertically, and the x-value horizontally, which gives us a coordinate.
Now let’s take a coordinate plane, and divide the x-axis in tiny bits. Now construct isoceles triangles on these lines- take the two ends of the small lines on the x-axis, and connect these two ends to any point in the graph. These lines connecting the line to the points should be equal in length. These lines will make an angle at any point on the graph One should notice that the higher the graph [i.e. the larger the y-value], the smaller the angle that will be made.
Hence, instead of constructing a graph by graphing the value of the range against the value of the domain, one can plot the same graph by considering various value on the x-axis, and then the angles that these value will make with the graph.
This turns the whole of analysis [as far as my knowledge goes] on its head.</p>
<p>Moreover, I’ve also developed a sort of calculus for this [differentiation, not integration].
Some of the patterns displayed in such functions are quite neat…</p>