Puzzle Description:

Euler's identity - beautiful! https://en.wikipedia.org/wiki/Euler%27s_identity

#1: CB Paul (cbpaul) on May 31, 2021 [SPOILER]

I minored in math (or as the Brits say, "maths"), but somehow this one never crossed my path. Check out the video in a series called "Equations Stripped". (And btw, that name is not just a name...)

Also, I would have pronounced it "u-lers", but apparently the Brits say "oilers". Weird.

Oh, oh, one more thing: all the online mentions of this have the i preceding the pi in the superscript. Just saying.

And, AM, it's a good solve, too!

Thanks Paul.

I noticed that too (that the "i" precedes the "pi" in online mentions). The reason I did it so is that generally complex numbers are represented as "a + bi", so "pi*i" seems more natural to me. Also, this is the form I learned and used, so saying it out loud with i before the pi feels wrong somehow :)

In fact the exact form I learned originally was "e^(pi*i) = -1", which I personally like better because it's slightly more compact, but may not be as "profound" since -1 is probably not considered to be as "fundamental" as 0 or 1.

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Pardon my ignorance, but what is e? In Einstein's theory it's energy, but here it seems like it must be a constant.

Belita, check this out: https://en.wikipedia.org/wiki/E_(mathematical_constant)

@CB Paul: Euler is a German name, "eu-" is pronounced "oi-" in German. "Die Eule" means "the owl", so I'm guessing that as a surname "Euler" would mean someone who works with owls.

Juli, thanks. Makes sense: something about wisdom. Even if he's not still working with owls, Euler knows stuff!

[And yes, knowledge and wisdom are not the same thing, but the overlap works here.]

Nice puzzle. Enjoyed the solve. Thanks

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Found to be solvable with moderate lookahead by infrapinklizzard.

Andrew, there is a solver that checks puzzles when they get published. It is very good at solving line-logical puzzles, so if the puzzle is not marked as line-logic solvable, it most probably isn't.

Even so, you should think of the assignments of solvability from the other direction. If it is marked "deep lookahead", that means that someone has found a way to solve it with a greater-than-normal amount of steps needed. Someone else may come upon a much shorter method and thus it is brought down to "moderate lookahead". Basically, we're defining the upper limit on how much work needs to be done to finish the puzzle.

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Oh yes, I should also probably reiterate that when I put a solve, that is just how *I* solved it, and is not necessarily the only or indeed best solve.

I think it's understood...at least I hope so because that's what I mean when I post a solve too :)

While this kind of puzzle is easy to solve, images are so much more fun.

No way am I going to try to figure out every possible way to solve a puzzle. I also just list my steps that I used. Sometimes I will go back and resolve to see if some earlier steps I took were necessary or not, but only if I find a less difficult step later that I probably should have seen.

Nice puzzle and I feel this is one of the most beautiful equations in mathematics.

As soon as I got most of the 'e', I knew what this was going to be.

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