curiosity killed the cat

So,..when a line is integrated the result is an area, when an area is integrated a volume is obtained, so naturally, what is obtained from the integration of a volume?😕

hypervolume

http://mathworld.wolfram.com/Content.html

Originally posted by David113
hypervolume

http://mathworld.wolfram.com/Content.html

And when a hypervolume is integrated?

Originally posted by sonhouse
And when a hypervolume is integrated?

unless i am misunderstanding, a hypervolume of order n+1 is obtained when a hypervolume of order n is integrated....so it will always be a hypervolume after this point.....Like I said , I have very limited knowledge on the subject, so my assumption may be incorrect....😕

Originally posted by joe shmo
unless i am misunderstanding, a hypervolume of order n+1 is obtained when a hypervolume of order n is integrated....so it will always be a hypervolume after this point.....Like I said , I have very limited knowledge on the subject, so my assumption may be incorrect....😕

You're quite right.

As a distance is measured in meter, m
an area is measured in meter squared, m2
a volume is measured in meter qubed, m3
and this is what we deal with in our lives.
But we can go further:
A hypervolume is measured in a hypermeter, m4
The next ones is m5, m6, and m7 etc.
but there are no proper word for it.
Try to buy a hypermeter of water and see the result. 🙂

Originally posted by FabianFnas
You're quite right.

As a distance is measured in meter, m
an area is measured in meter squared, m2
a volume is measured in meter qubed, m3
and this is what we deal with in our lives.
But we can go further:
A hypervolume is measured in a hypermeter, m4
The next ones is m5, m6, and m7 etc.
but there are no proper word for it.
Try to buy a hypermeter of water and see the result. 🙂

So, now when we know the correlence between meter, meter squared, meter qubed, and meter hypered...

A joke:
- Look at the sea! So much water!
- Yes indeed, and yet you only see the surface...!

Question: How much more is a qubic meter of water volume, compared with a square meter of water surface?

And, yes, there is an answer...

Originally posted by FabianFnas
So, now when we know the correlence between meter, meter squared, meter qubed, and meter hypered...

A joke:
- Look at the sea! So much water!
- Yes indeed, and yet you only see the surface...!

Question: How much more is a qubic meter of water volume, compared with a square meter of water surface?

And, yes, there is an answer...

I will probably be wrong, but i would suspect an infinite amount more.......😕

Originally posted by FabianFnas
So, now when we know the correlence between meter, meter squared, meter qubed, and meter hypered...

A joke:
- Look at the sea! So much water!
- Yes indeed, and yet you only see the surface...!

Question: How much more is a qubic meter of water volume, compared with a square meter of water surface?

And, yes, there is an answer...

That question can be answered in any number of ways.

You could calculate the number of molecules that would cover the surface, compared to the number in the cubic meter.

Wait, qubic? Huh?

You could say there is 1 cubic meter more water in the cubic meter, since there is no volume on the surface.

You could say thay there is another dimension in the cubic meter.

There is no clear answer.

Originally posted by AThousandYoung
There is no clear answer.

Yes there is. But perhaps we should think outside the box.
But it's not a joke problem. It is a very serious question.

Originally posted by FabianFnas
Yes there is. But perhaps we should think outside the box.
But it's not a joke problem. It is a very serious question.

so i guess my above post was incorrect

I reasoned that the volume could be broken into "n" crosssectional volumes of width x, so as "n" approaches infinity x approches zero...so there are an infinate number of crossectional areas in any given volume..

Question: "How much more is a qubic meter of water volume, compared with a square meter of water surface? "

Another question that is much easier to answer, yet exactly the same type of question:

Q2: "How much more is 6 compared with 2?"

Reason how you came up with the correct answer, and bring in all intermediary steps.

Originally posted by FabianFnas
Question: "How much more is a qubic meter of water volume, compared with a square meter of water surface? "

Another question that is much easier to answer, yet exactly the same type of question:

Q2: "How much more is 6 compared with 2?"

Reason how you came up with the correct answer, and bring in all intermediary steps.

Q2: "How much more is 6 compared with 2?"

Let's set up the equation (2) * (?) = (6).
The ? is the answer of how much 6 is compared to 2.
If we turn ? to 3 at the left, we see that (2) * (3) = (2 * 3) = (6), right?
So we see that six is three times two. Simple mathematics.

Now:
Q1: "How much more is a qubic meter of water volume, compared with a square meter of water surface?"
or simpler
"How much more is 1 m2 compared with 1 m?"

Let's set up the eequation (1) [m] * (?) = (1) [m2].
The ones we can get rid of, they doesn't change the equation.
[m] * ? = [m2].
The right side [m2] = [m*m] = [m] * [m] so we get [m] * (?) = [m] * [m].
So if we change (?) into [m] we get [m] * [m] = [m] * [m].
The conclusion will be: A square meter is exactly a meter more than a meter.

Back to the question: "How much more is a qubic meter of water volume, compared with a square meter of water surface?" the answer will simply be "A meter!".

The qustion and the answer, and the resoning is serious. It is done in a comparable method to that shows that E=mc2 and not E=mc3. It's called dimensionanalysis.

Originally posted by FabianFnas
Q2: "How much more is 6 compared with 2?"

Let's set up the equation (2) * (?) = (6).
The ? is the answer of how much 6 is compared to 2.
If we turn ? to 3 at the left, we see that (2) * (3) = (2 * 3) = (6), right?
So we see that six is three times two. Simple mathematics.

Now:
Q1: "How much more is a qubic meter of water volume, compared with ...[text shortened]... able method to that shows that E=mc2 and not E=mc3. It's called dimensionanalysis.

well, that is very straight forward. but the equation "how much more is the answer 6 compared with 2" could also be thought of as 2+?=6...just messing with you..I get what your saying🙂

Originally posted by joe shmo
well, that is very straight forward. but the equation "how much more is the answer 6 compared with 2" could also be thought of as 2+?=6...just messing with you..I get what your saying🙂

2+?=6, yes, never thought of that...
If so, then I have serious problem with [m]+(?)=[m2] 🙂

the major issue here is we have to define what kind of comparison we are looking at: a proportional comparison or something more like a "discrete" or an "absolute" comparison (i'm having trouble finding a good word to fit what i mean there, ask if it needs clarification). just like you guys said - is the question "by what factor do we multiply to get from area to volume" or is it "what measurement water do i have to ADD to get from an area to a volume?"

it seems like a ludicrous idea to compute the amount of water to ADD, since volume and area are different spatial measurements (like asking someone to combine x with x^2), however as was mentioned earlier, you could probably break it down to the number of molecules of water. in this case the application of sum/difference makes legitimate sense.

in other words, this is quite a quandry and requires further definition of the question we're trying to answer! as phrased, i think the question may be a little too vague to be called "answerable"