Who Is Fourier? · Part 4
Summation, Radians, and a Sneak Peek at Fourier Coefficients
Today I'm going to understand two handy math tricks: radians and summation, plus a sneak peek into our next leg of the series, the Fourier coefficient.
The idea, in my own words.
Summation is basically when you want to shorten addition. You use a sign called sigma, which is basically a mutated Z.
Fig. 1 — Z, post-experiment.
Radians, on the other hand, are a different way of expressing 360 degrees, or omega. A radian is about 57.2958°, and you can fit exactly 6.28 of them in a full circle. So instead of using ω = 360° × 1/T, we can use ω = 2π × 1/T.
Fig. 2 — One radian: when the arc length equals the radius.
Worked example.
Let's see how we can use summation in an example. Let's say you wanted to calculate B = (x + 1) + (x + 2) + (x + 3).
Fig. 3 — Compact form on the left, expanded on the right, total below.
We can see that the sigma symbol is in the middle and everything else is surrounding it.
Carried question.
Now that we've wrapped up everything to talk about in the Fourier series, what is the difference between our new chapter, the Fourier coefficient, and the old chapter, the Fourier series?