The Meaning of Dividing an Area by a Length

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Discussion Overview

The discussion revolves around the concept of dividing an area by a length, exploring its meaning and implications in various contexts. Participants engage in clarifying the conditions under which such a division is meaningful, including mathematical and conceptual interpretations.

Discussion Character

  • Exploratory
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • Some participants suggest that the meaning of dividing an area by a length depends on the context and purpose of the operation.
  • One example provided is dividing the area of a rectangle by the length of one side to find the width, indicating a specific scenario where the operation has meaning.
  • Another participant mentions maximizing the ratio of area to length as a meaningful application of this division.
  • There is a discussion about the dimensionality of area and length, with some asserting that dividing an area (length squared) by a length results in another length.
  • Concerns are raised about the philosophical implications of the question, with suggestions that it may belong in a different context, such as philosophy.

Areas of Agreement / Disagreement

Participants express varying views on the meaningfulness of dividing an area by a length, with no consensus reached on whether it is inherently meaningful or context-dependent. Some agree on specific scenarios where it is meaningful, while others question the broader implications.

Contextual Notes

Participants highlight the importance of context and purpose in determining the meaning of the division, indicating that assumptions about the application may vary.

3trQN
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Is it meaningless to divide an area by a length?
 
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That depends! What are you trying to do?
 
What does it depend on?

Im not trying to do anything but understand and remove ambiguity in my understanding.
 
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.
 
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.
 
Area of a chess board: 64 square inches.
Length of the chess board: 8 inches.
What is its width?
 
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
 
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...
 
:confused: area is a length squared so to divide an area by a length would only provide you with another length
 
  • #10
rctrackstar2007 said:
:confused: 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!:smile:
 
  • #11
3trQN said:
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?
 
  • #12
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.
 
  • #13
hypermonkey2 said:
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 :smile:

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

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