The Meaning of Dividing an Area by a Length

[3trQN]

Is it meaningless to divide an area by a length?

 

[Tide]

That depends! What are you trying to do?

 

[3trQN]

What does it depend on?

Im not trying to do anything but understand and remove ambiguity in my understanding.

 

[Tide]

It depends on what you are trying to do. E.g., if you know the area of a rectangle and the length of one side then dividing that area by the length of the known side has meaning - it's the width of the rectangle.

 

[3trQN]

Sometimes i wonder why God does not number his Jigsaw puzzles. When your missing the starting peices, the rest just keeps falling apart.

Thx for the reply.

 

[DaveC426913]

Area of a chess board: 64 square inches.
Length of the chess board: 8 inches.
What is its width?

 

[SpongeBobRhombusHat]

It would also be meaningful if you were trying to maximize the ratio of the area contained within a curve to the length of the curve.

SBRH

 

[jasc15]

i think spongebob hit it pretty close to answering the original question. There is a comparitive way to use a length to area, or an area to volume ratio. For example, for a given volume, what shape has the smallest surface area? dimensionally, area divided by volume would give a result that is meaningless to understanding the answer to this question. I am sure there is a more rigorous answer to this, but i haven't studied it in any detail, so i have to rely on intuitive feel...

 

[rctrackstar2007]

area is a length squared so to divide an area by a length would only provide you with another length

 

[HallsofIvy]

area is a length squared so to divide an area by a length would only provide you with another length

Why "only"? That's a worthwhile result!

 

[dav2008]

Sometimes i wonder why God does not number his Jigsaw puzzles. When your missing the starting peices, the rest just keeps falling apart.

Thx for the reply.

What does that even mean?

 

[hypermonkey2]

If this is one of those "but what does it all MEAN??" questions, perhaps it should be on the philosophy board. Richard Feynman refrained from talking metaphysics, so i reckon trackstar gave a decent answer if your question was physical.

 

[rctrackstar2007]

If this is one of those "but what does it all MEAN??" questions, perhaps it should be on the philosophy board. Richard Feynman refrained from talking metaphysics, so i reckon trackstar gave a decent answer if your question was physical.

a very good idea on his part

"Why "only"? That's a worthwhile result!" because i think he might be talking about more than just numbers like it says above