4 ms·
I think Eurler's identity is far more "interesting": e^(i * pi) + 1 = 0 It also connects "e" and "pi"; but on top of that also "i", "1" and "0". When I first
by cies 12y ago
I think Eurler's identity is far more "interesting":
e^(i * pi) + 1 = 0
It also connects "e" and "pi"; but on top of that also "i", "1" and "0". When I first read this equation it felt like a proof of God's existence :)
http://en.wikipedia.org/wiki/Euler's_identity http://en.wikipedia.org/wiki/Euler's_identity
- waynecochran 12y agoIt's true that this may be one of most startling equations, but its far from being the concoction of the arbitrary approximation in the OP. This is just the special case of Euler's more general formula e^{ix} = \cos{x} + i\sin{x}, which can easily be derived from Taylor series for e^x, sine, and cosine.
- mijoharas 12y agoOne thing I've never understood is why people write it that way round, I always think of it as: e^(i*pi) = -1 I don't understand why people switch it around all the time, I don't think it loses any elegance going that way round, I also feel it loses clarity being shuffled around because it's just one more (admittedly tiny) operation you need to do to see why it happens.
- waynecochran 12y agoBecause it involves all of the most important a constants: 0, 1, e, pi, i.
- deleted 12y ago[deleted]
- okamiueru 12y agoOf course Euler's identity is far more interesting. That's an actual mathematical insight. This is just a coincidence from playing around with irrational constants. Two entirely different things.