Should it be upside or downside

  • Thread starter MathematicalPhysicist
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In summary, the triangle symbol in Helmholtz Equation can be represented by either \nabla^2 or \Delta and they are both equivalent. Some prefer \nabla^2 for clarity and consistency, while others use \Delta due to its frequent use in mathematics. However, in the Helmholtz equation, \nabla^2 is considered to be more symmetrical. It should also be noted that in loop quantum gravity, while \nabla^2 and \Delta are the same, \nabla and \Delta are not.
  • #1
MathematicalPhysicist
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how does the triangle symbol in Helmholtz Equation should be?
is it like the attach file in here.
 
Last edited:
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  • #2
or like this attach file.

btw, can you attach more then one file in here?
 
Last edited:
  • #3
If I remember correctly, then they are both the same. nabla squared is sometimes denoted as a triangle with the sharp side up.

So:

[tex]\nabla^2 \equiv \Delta[/tex]
 
  • #4
I've always seen it point down.

Njorl
 
  • #5
I also usually see [itex]\nabla^2[/itex]. But [itex]\Delta[/itex] is perfectly valid.

Personally I prefer [itex]\nabla^2[/itex]. 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 [itex]\Delta[/itex] is already used enough anyway.

In the Helmholtz equation in particular [itex]\nabla^2[/itex] looks better.
[itex]\nabla^2\psi+k^2\psi=0[/itex] is more symmetric.
 
  • #6
loop quantum gravity: note well it is [tex]\nabla^2[/tex] and [tex] \Delta[/tex] that are the same not [tex]\nabla [/tex]and [tex] \Delta[/tex]!
 

1. Should I conduct my experiment with the object upside down or downside up?

The orientation of the object depends on the specific experiment you are conducting. Consider the purpose of your experiment and the variables you are testing to determine the best orientation for accurate results.

2. Are there any advantages to having the object upside down?

In some cases, having the object upside down may provide better visibility or accessibility for certain measurements or observations. However, it ultimately depends on the experiment and the object itself.

3. Is there a specific rule for when an object should be placed upside down or downside up?

There is no universal rule for object orientation in scientific experiments. It is important to consider the purpose of the experiment and make a decision based on the specific objectives and variables involved.

4. Can the orientation of the object affect the outcome of my experiment?

Yes, in some cases, the orientation of the object may impact the results of your experiment. It is important to carefully consider the orientation and make sure it does not introduce any bias into your data.

5. Are there any safety concerns when working with an object that is upside down?

Safety should always be a top priority when conducting experiments. If the object is unstable or could potentially cause harm when upside down, it is important to take necessary precautions or consider changing the orientation of the object.

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