Chance me?

[frankchn]

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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.

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<p>If you divide the x-axis into tiny but finite bits, you will end up with a series of points and not a continuous function. If you divide the x-axis into infinitely tiny bits, then I think you will lose the concept of “triangle”. </p>

<p>Anyway, to turn a standard one-one y=f(x) function into your concept, I think it is just “angle of triangle with base at location x-dx to x+dx” = tan^-1(f(x)/dx) where dx is of course the “tiny bit”.</p>