Hello DSP community,

Today, something I haven't figured out hit me differently, and I want to discuss it. I was thinking about the perimeter of the circle, which is quite easy to say straightforwardly:

Perimeter=2(\pi)r, and this is also an arc length. Now, assume you take a compass with a unit radius. You start to draw just one circle. You get 2(\pi), which is a perimeter, and it is no longer in radians. It can be seen as radians because the value is exactly (2\pi), but it is not a angle anymore; it's a length. See the trick.

Then I started asking myself why we need degrees, because degrees mess with the whole logic. If I think in radians, I don't need to memorize equations for perimeter and arc length, and I can see the angle/length transformations clearly; instead, I can see the whole logical path.

I thought this is important and shapes the definition of period, and, what’s more, it's a kind of fundamental for signal analysis. How do you learn such formula? Is there anything wrong with my thinking?

Happy day!

Edit: Typo