3 ms·
The more general formula (e^ix = cosx + i*sinx) looks better to me because it defines exponentiation of a complex number as a rotation around a unit circle. It
by jstx1 5y ago
The more general formula (e^ix = cosx + i*sinx) looks better to me because it defines exponentiation of a complex number as a rotation around a unit circle. It has a nice proof, some cool visualisations and a lot of implications to a bunch of other things in mathematics - I can get behind calling that beautiful.
The special case of x=pi... it's like being excited that sin(pi)=0 or cos(pi)=-1. It doesn't really say anything meaningful or consequential, people like it only because of the symbols it includes. It feels kind of like a math meme that people like to repeat and I can't get behind it.
Maybe it's just not for me and I should just let other people like what they like.
- qq4 5y agoI feel this way as well. In fact every time I have tried to remember the "most beautiful equation" I had to think of it in the context of the unit circle and work it out by assigning pi to x. Otherwise I don't get any wow out of it.
- CamperBob2 5y agoIt doesn't really say anything meaningful or consequential The impressive aspect of that version of the equation is simply the idea that you can obtain a plain old integer (-1) using nothing but simple arithmetic operations on two random-looking transcendentals.
- jstx1 5y agoThe thing about that is that an imaginary power of a number isn't really simple - it's not like you can do repeated multiplication "i*pi times" and get a result. An imaginary power is defined as cosx + isinx (or the equivalent Taylor series). That's what I meant when I said that all people are impressed by is that cos(pi) = -1 or that sin(pi) = 0.