Claire Xen  🏳️‍⚧️ 🏳️‍🌈 🧙🏻‍♀️ BLM  🏴 🚩

No, you only get y=x in (-pi,pi), as you’ve drawn, and then extended periodically from there (since every function in the series is 2pi periodic). The dual of the line is the line, so you’d need an integral to recover the actual line. Presumably you know this, so why fib?...

that's right, it converges to y=x in (-π,π) for the Fourier series (as opposed to the transform). Given that it does converge to a line on (-π,π), i wouldn't say i fibbed.. This is twitter,not an academic conference.The purpose of my tweets is to get across the basic idea in..

But ... isn't the "basic idea" that one can use a Fourier series to approximate any periodic signal? So why start with a "straight line", an inherently aperiodic object? Also, sorry for the nitpick, but it doesn't converge to y=x in (-π,π). The integral error converges to zero.

lines are precisely what sawtooth waves are..