25 Nov '08 21:03

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?π

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podunk, PA26 Nov '08 03:08

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....π*Originally posted by sonhouse***And when a hypervolume is integrated?**- Joined
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26 Nov '08 14:25

You're quite right.*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....π**

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. π- Joined
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28 Nov '08 07:48

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

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...- Joined
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podunk, PA28 Nov '08 15:48

I will probably be wrong, but i would suspect an infinite amount more.......π*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...- Joined
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tinyurl.com/y2c6j2t328 Nov '08 17:00

That question can be answered in any number of ways.*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...

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.- Joined
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podunk, PA28 Nov '08 18:53

so i guess my above post was incorrect*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.

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..- Joined
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29 Nov '08 18:22Question: "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.- Joined
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01 Dec '08 09:17

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

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.- Joined
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podunk, PA01 Dec '08 13:35

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 sayingπ*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.- Joined
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01 Dec '08 13:41

2+?=6, yes, never thought of that...*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 sayingπ**

If so, then I have serious problem with [m]+(?)=[m2] π- Joined
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01 Dec '08 15:01the 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"