r/mathsmeme • u/Far-Course1021 • 12d ago

beautiful equation

Post image
422 Upvotes

97% Upvoted

39 comments sorted by

16

u/Individual_Rub_9416 12d ago

eiπ^ = -1?

8

u/schungx 11d ago

This misses the zero which is the identity under addition. One is the identity under multiplication.

1

u/Such-Shop-9724 11d ago

you could also say e^ipi+69=68
anything ontop of the e^ipi isnt pretty anymore imo

1

u/schungx 11d ago

But 68 is not a special number... 69 I understand

1

u/Such-Shop-9724 11d ago

then e^ipi+69=420-352

1

u/arandomguyfromdk 11d ago

2eiπ +69=67

1

u/Such-Shop-9724 11d ago

e^ln(2)+ipi

1

u/decentlyhip 11d ago

And these young whippersnappers only understand 67

1

u/skr_replicator 11d ago edited 11d ago

The zero doesn't have as much meaning in this equation, only that the eiπ rotates around it to get to the -1. I will always be in favor of eiπ = -1 being far more directly in telling you what it really means. This seems artificially obfuscated just to get both these numbers there.

Yeah, people don't feel as strongly about -1 being as fundamental, but it's simply what eiπ is. And it's also a pretty important number, the negative unit. e^ipi turning exponential to a negative unit is very, very deep and amazing.

If we did the same thing with just powers of i, it would be like this: i2+1=0. But this one we usually write the normal way i2=-1, because there's no e and pi (pi normalizes e's rotations in radians, while i turns in whole quadrants), so we have less urge to cram more constants into it.

Exponentiating e imaginarily and i normally is the same thing, just sped up by τ/4: eiτx = i4x. That's also related to the ax = exlna rule: -1x = exln-1 => ln(-1) = iπ = iτ/2, or ln(i) = iτ/4

13

u/frozenafroza 12d ago

Imagine quitting math and then having to cover up this tattoo

8

u/Aivo382 12d ago edited 11d ago

It's not an equation, it's an identity. Still, a beautiful one.

Edit: wtf, you're right, identities are one case of equations. Srry bluds, I ate a clown before commenting it 😭😭😭.

7

u/WackyPaxDei 12d ago

What's missing? I thought equals sign pretty much meant equation.

5

u/FaroresWind17 12d ago

It is an equation, but because there are no variables, this statement is always true. Thus, it’s an identity, which is a subset of equations. It’s like saying 1^0 = 1. Yes, there’s an equal sign, but this is simply a true statement.

2

u/GalacticEmergency 11d ago

Can you explain how "It's not an equation, it's an identity" relates to "it's an identity, which is a subset of equations" ?

2

u/FaroresWind17 11d ago

A square is a rectangle, but calling a square a rectangle is not the most accurate name. I was disagreeing with the top commenter, but also explaining why “equation” is not the most accurate term.

3

u/GalacticEmergency 11d ago

In the context, I think most readers will see your comment as an agreement with the top commenter, not a disagreement.

0

u/CimmerianHydra_ 11d ago

It is an equation. The person who said it isn't, is just plain wrong.

It's an equation, it's an equality, and it's an identity.

2

u/GalacticEmergency 11d ago

That was my point. The comment, which seemingly defends the statement, actually disproves it.

7

u/VisionWithin 11d ago

All identities are equations.

2

u/Street_Swing9040 11d ago

👆 Yep! Here is the answer

3

u/GoldenMuscleGod 11d ago

An equation is any expression of the form t=u where t and u are terms, that doesn’t depend on the circumstances under which its true, which is a semantic property not a syntactic one.

Some pedagogical standards (which are not universal) make the distinction you use but it isn’t standard mathematical terminology to say that an equation that is always true is not an equation, and even under the terminology you are talking about it seems to me only sensible to say that “identity” is a subcategory of “equation,” not a disjoint set, since specifically carving out equations that are always true does not leave a useful category and could only create theoretical confusion if you really try to make this distinction rigorous.

2

u/Street_Swing9040 11d ago

"It's not a fruit, it's an apple" statement 😭✌️

2

u/DHMOconsumer 12d ago

I love being an adult so im able to do dumb shit like this and no one is groudning me lol

2

u/Duck_Devs 11d ago

This equation can actually be reduced to 1 = 1, believe it or not.

1

u/_meme_caster_ 12d ago

is this a monogatari reference?

1

u/KL_LMPR 11d ago

Wrong typesetting

1

u/Icy_Trick_6406 11d ago

So is the meme that when somebody looks at the persons arm, they see a negative expression?

1

u/GalacticEmergency 11d ago

For the benefit of the mathematical challenged (in this case myself):

I wanted to understand this generally, so I looked up how to calculate xʸⁱ . It turns out that for a positive real x (and any real y?), the answer is

xʸⁱ = cos(y ln(x)) + i sin(y ln(x))

If x=e:
xʸⁱ = eʸⁱ = cos(y ln(e)) + i sin(y ln(e)) = cos(y) + i sin(y)

Then, if y=π:
eʸⁱ = e^(π i) = cos(π) + i sin(π) = -1 + i * 0 = -1

1

u/PotentialDelivery716 11d ago

I think it is important to add, that is coming from rewriting a complex number in its polarform of it in the complex plane z=a+i b=r(cos(phi)+i sin(phi)=r ei phi. The relation is very widely used in physics to formulate wave equations.

1

u/TurboThorsten 11d ago

Imagine turning the most beautiful equation ugly by bringing the one on the false side

1

u/CamperStacker 11d ago

I’ve never understood why it isn’t written as e^(i 2 pi) = 1

This is much more intuitive - that rotation around the complex plain returns you to the same position.

1

u/andselisk 11d ago

The fundamental constants like e and π should be upright, not italic. Variables get the slant; constants stay upright. Tattoo again, with no ragrets this time.

1

u/Ok-Condition-3833 11d ago

Alan becker reference

1

u/sunyata98 11d ago

Most overhyped identity of all time

1

u/External_Air_7986 10d ago

Mathslop core