Also how such inventions are created or discovered? how can someone come with these ideas?
In: Mathematics
A Fourier series is a certain *sum of sinusoids*. Sinusoids are shifted and scaled sine waves. So a particular fourier series might look like:
F(x) = 0.82sin(3x) + 0.13sin(16x+1) + 0.02sin(43x+2)
or it might be an infinite sum of a·sin(bx + c) terms.
Fourier’s famous trick was to show how *any* periodic function, as long as it follows a few rules, can be expressed as a sum like this. This means we can analyze all kinds of data to find periodic components – the ‘frequencies’ in something – which has applications in astronomy, seismology, music, data compression, mechanical engineering, and a zillion other things.
Was it a discovery or an invention? In math, it’s kind of both, you’re kind of discovering stuff *about* what you invent, and inventing stuff based on what you discover. I can’t tell you what gave Fourier this specific idea, but he might have been inspired by Taylor series, which does a similar trick using the terms of a polynomial instead of sinusoids.
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