[loganc2342]

> The Pythagorean Theorem is arguably the most famous statement in mathematics, and the fourth most beautiful equation.

Just out of curiosity, which equations are considered the top three “most beautiful?”

[mauvia]

I know the top one is generally considered to be Euler's Equation.

e^(i * pi) + 1 = 0

It's considered incredibly elegant because it manages to combine multiple fundamental mathematical concepts into a single equation.

1 is the multiplicative identity, 0 is the additive identity, pi is the circle constant, e is euler's number, i is the square root of -1, the basic building block of complex numbers.

[travisjungroth]

IMO, it’s better with tau.

e^(i * tau) = 1

You lose the 0, but isn’t it a bit odd the 0 is there in the first place? Normally we’d reduce it to:

e^(i * pi) = -1

Which obviously isn’t as nice in this case.

And hey, if we’re allowed to break the conventions, you can have the 0 back easily.

e^(i * tau) = 1 + 0

[fasquoika]

Well you're on a website called ycombinator.com so maybe the fixed point combinator

    Y = λf.(λx.f(xx))(λx.f(xx))

https://en.m.wikipedia.org/wiki/Fixed-point_combinator

[boomboomsubban]

This seems to be the original source https://physicsworld.com/a/the-greatest-equations-ever/ but it doesn't actually rank the equations. The other source commenting on that does, but only the sample is available on Google Scholar. From that, first is Euler's identity, second is Maxwell's four electromagnetic field equations, and third isn't in the sample. The NYT article also commenting on it https://archive.ph/H7ujx suggests the theory of relativity, F=ma, or amusingly 1+1=2.

[BlueTemplar]

Maxwell's even better as a single equation :

http://www.av8n.com/physics/maxwell-ga.htm

[tapotatonumber9]

The most delicious is:

“(-1)^0.5 2^3 Σ π.”

[dotancohen]

You do realize that the volume of a Pizza with radius z and height a is:

  Pi ⋅ z ⋅ z ⋅ a

[zeroonetwothree]

Ask ten people you will get ten different answers.

[zabzonk]

not sure if you include physics, but newton, the gas laws, and einstien?

[Tao3300]

A = Pe^(rt)