What Is the Space Entity with Quantity "Volume"?

[mani]

The space entity whose quantity is "Length" is the "Line"
The space entity whose quantity is "Area" is the "Surface"
The space entity whose quantity is "Volume" is the "?"
The term "solid" is not satisfactory, as the entity may be (the space occupied by) a body of liquid or gas.
Anyone knows the correct term?
I have been using the term "TRISP", short for "TRI - SPACE ", with my students for many years

 

[vincentchan]

volume volume volume volume volume volume volume
volume volume volume

 

[marcus]

you might try "room"

a cubical room, a conical room
a cylindrical room
occupied by whatever you want (solid, liquid, gas)
the measure of the room's size is volume

 

[Galileo]

It's space.
You're talking about the volume of a certain space as you''re talking about the the area of a certain surface.

 

[mani]

crisp new word

Volume is the quantity. Do we give the same name to the entity?

Space includes surfaces and lines. To be rigorous, we have to say "Three Dimensinal Surface". This long word is shortened first as Tri Space; and further as"Trisp"

 

[mani]

crisp new word

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Volume is the quantity. Do we give the same name to the entity?

What do we do when we want to denote a room (full of objects and air)?

Space includes surfaces and lines. To be rigorous, we have to say "Three Dimensinal Space". This long word is shortened first as Tri Space; and further as"Trisp"

 

[marcus]

The space entity whose quantity is "Length" is the "Line"
The space entity whose quantity is "Area" is the "Surface"
The space entity whose quantity is "Volume" is the "?"
The term "solid" is not satisfactory, as the entity may be (the space occupied by) a body of liquid or gas.
Anyone knows the correct term?
I have been using the term "TRISP", short for "TRI - SPACE ", with my students for many years

Mani, this is in the realm of linguistic invention. We are talking matters of taste.
You have taken to saying "Trisp" with your students. That sounds to me like an unattractive choice and I would not have wanted to use it when I was teaching. But DE GUSTIBUS NON DISPUTANDUM EST and if it works for you and they like it, then fine!

If I was teaching middle or high school students and they insisted on having a special word for a 3D region of space I would let them make up one and I personally would suggest saying threebus


Although I do not like your particular verbal invention, I think several of us understand the problem.

Going back to conventional language of, say, 1900

A Line had Length
A Surface had Area
A Space had Volume

(Also a "Solid Figure" was a conventional synonym for a 3D shape with volume. Sometimes the term "Body" was used for a 3D thing. Neither seems quite right though.)

THEN in the 20th century mathematicians started using "Space" very generally----a space of solutions, a space of functions, a topological space---and they began doing geometry in N-dimensions.

So "Space" lost its firm 3D connotation.

------misc. alternatives---------
threebus
container
room
pod
cubby
raum
box
package
block
holder
case
platz
bod
threebod

 

[jcsd]

You have line intergrals, you have surface intergrals and you have volume intergrals.

 

[marcus]

You have line intergrals, you have surface intergrals and you have volume intergrals.

that's right, in math-talk the word "volume" has the dual function of being the 3D analog of area

and also the 3D analog of surface

you can talk about a conical surface and ask about
"the area of that surface"

but if you have a spherical volume you have to ask about
"the volume of that volume"

We know how mathematicians talk and that they use "volume" to mean both the geometrical entity, the 3D region, AND the measure of it.

How mathematicians talk is not the issue.

this guy feels linguistically inventive and he doesn't like
how "what is the volume of that volume" sounds

he wants an nice-sounding 3D analog for
"what is the area of that surface?"

I am recommending to him that he and his students should say threebus


"there is a certain threebus bounded by a certain paraboloid of revolution
what is the volume of this threebus?"

If you are purely a mathematician you won't enjoy the discussion, you have to be part writer, or have an interest in English style, or want to invent words like he is doing.

 

[mani]

Mani, this is in the realm of linguistic invention. We are talking matters of taste.
You have taken to saying "Trisp" with your students. That sounds to me like an unattractive choice and I would not have wanted to use it when I was teaching.
... middle or high school students and they insisted on having a special word for a 3D region of space I would let them make up one and I personally would suggest saying threebus

Although I do not like your particular verbal invention, I think several of us understand the problem.
=========================================================
I note that you are not attracted by the word "trisp"
.
No, my students were not insisting on a new word. My own sense of symetry, and rigor, demanded it. You will appreciate this, as you state; " I think several of us understand the problem"
At first, I used "Three Dimesional space"; shortened it to " Three D Space" and occasionally just to "Three Space". One of my students suggested replacement of "Three" by "Tri". Another made this "Trisp". And a third quipped that the new word was "crisp".

But I will certainly go in for "Threebus". What I do not know about linguistics can fill up libraries. So please let me know about the"bus" part.

 

[jcsd]

Trisp is not cromulent.

 

[Janitor]

Aerospace engineers speak of 'ullage.' It means the unused volume in a tank of liquid, but maybe that term would do in a pinch.

 

[marcus]

At first, I used "Three Dimesional space"; shortened it to " Three D Space" and occasionally just to "Three Space". One of my students suggested replacement of "Three" by "Tri". Another made this "Trisp". And a third quipped that the new word was "crisp".

But I will certainly go in for "Threebus"...

If you are still teaching that age-group of students, and the students helped come up with the word as you say, that seems like a good reason to stick with trisp. It's nice to have some grassroots participation in deciding on language.

No serious reason to consider "threebus" I just like the sound. It strikes me as remarkably cromulent.

And it extends nicely to make a name for 4D chunks of spacetime:

a 4-simplex (the 4D analog of a tetrahedron) is a kind of "fourbus"


Indeed a square patch of surface or 2D disk or other 2D figure is a twobus

except we already call it a patch of surface.

----------
You asked (seriously or not) about the "bus" part of the word. All I can think of are echos of omnibus, rhombus, rebus, dingus (a word for thingamabob)
but maybe better justifications occur to you.

 

[Gokul43201]

I agree with jcsd and marcus. 'Volume integral' it is, is it not ?