Should it be upside or downside

[MathematicalPhysicist]

how does the triangle symbol in Helmholtz Equation should be?
is it like the attach file in here.

 

[MathematicalPhysicist]

or like this attach file.

btw, can you attach more then one file in here?

 

[suyver]

If I remember correctly, then they are both the same. nabla squared is sometimes denoted as a triangle with the sharp side up.

So:

$$\nabla^2 \equiv \Delta$$

 

[Njorl]

I've always seen it point down.

Njorl

 

[master_coda]

I also usually see $\nabla^2$. But $\Delta$ is perfectly valid.

Personally I prefer $\nabla^2$. It makes it more clear what operation you're actually performing. Plus it help avoid defining a new symbol for every single mathematical operation. And $\Delta$ is already used enough anyway.

In the Helmholtz equation in particular $\nabla^2$ looks better.
$\nabla^2\psi+k^2\psi=0$ is more symmetric.

 

[HallsofIvy]

loop quantum gravity: note well it is $$\nabla^2$$ and $$\Delta$$ that are the same not $$\nabla$$and $$\Delta$$!