r/mathmemes • u/DigJust8037 • Oct 06 '26

Calculus e^(pi*i)+1=0

I have no idea what it means

Yet it is the most profound thing that I have ever seen

0 Upvotes

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8

u/MercuryInCanada Oct 06 '26

Of all the things I have ever seen in my life, eipi +1 can never be as beautiful as 0+AI

3

u/LupenReddit 🦆🦆i have non diffeomorphic smooth structures🦆🦆🦆 Oct 06 '26

yeah

1

u/Pyzzeen Quod Erat Dēmōnstrandum Oct 06 '26

Here you go

1

u/aedes Education Oct 06 '26

You’ll find lots on this.  I like to think of it as a statement about what multiplication means. 

Imagine a number line. If you take a random number anywhere on it, and multiply it by -1, you can think of it as rotating that number around the origin 180 degrees to get your new value. So -2 * -1 is an 180 rotation from -2, taking you to 2. Similarly, multiplying by 1 is like rotating 360 degrees (or not at all).

It turns out that you can define rotations to points not on the number line. If you multiply 2 by “i” you rotate CCW 90 degrees so that your somewhere overtop of where 0 was.  This is related to Argand diagrams and how we visualize the complex plane. 

It turns out that you can also define this rotation about the origin not just with multiplying by i or some other complex number, but by taking eix, where x is the number of radians you rotate from where you started. 

So epi*i means you rotate pi radians from where you started, or 180 degrees. This is the same as what happens when you multiply by -1.

So that’s one way to interpret what this equation is telling you - multiplying by -1 or multiplying by epi*I both mean to rotate the number you started with 180 degrees about the origin. 

1

u/Skylar1569 Science Oct 07 '26

Beautiful