As a freshman in college, I was wondering, is pi's connection with the very simple differential equation [tex]\frac{d^{2}y}{dx^{2}}[/tex] = -y with initial condition that (0,0) be included (or even if that is not the case a connection can be made) the reason it is so ubiquitous in mathematics. This of course implies that a circle is just a specific case that utilizes this differential equation. Pi can be defined in my head as the difference between x's of sequential zeros in the solution above.(adsbygoogle = window.adsbygoogle || []).push({});

So really what I am asking of people is to explain to me anything related to this in higher level mathematics perhaps that I would not have come by or thought of. And by the way this is just my own random thinking, nobody has taught me anything about pi in this manner.

The solution of the differential equation [tex]\frac{dy}{dx}[/tex] = y with initial condition that (0,1) be included, looks very similar to the equation above, and of course the solution to this equation is the exponential function, e[tex]^{x}[/tex].

Thank you in advanced, Matt.

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# Pi's connection to e, and its ubiquity in math

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