Area of a Circle: Pi*R^2 - What Does it Mean?

  • Context: High School 
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Discussion Overview

The discussion revolves around the interpretation of the area of a circle, specifically the expression pi*r^2, and the implications of being pedantic in communication. Participants explore the balance between technical accuracy and social interactions.

Discussion Character

  • Conceptual clarification, Meta-discussion

Main Points Raised

  • One participant questions whether to respond with the formula pi*r^2 or to clarify that a circle itself does not have an area, suggesting that the area refers to the enclosed disc.
  • Another participant expresses a preference for providing a numerical answer to avoid potential arguments, indicating a more practical approach to communication.
  • A different participant shares a personal anecdote about being perceived as too pedantic in a domestic context, highlighting the tension between literal interpretation and conversational expectations.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the appropriate level of pedantry in communication, with differing views on the importance of technical accuracy versus social considerations.

Contextual Notes

The discussion reflects varying assumptions about the definitions of mathematical terms and the expectations in interpersonal communication, which remain unresolved.

Mkorr
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If someone asks me what the area of a circle is, should I respond:

(1) pi*r^2

(2) As a circle in the plane is defined as the set of all points in the plane that lie r units from O, so it does not technically have an area, but you probably mean the area of the surface that the circle encloses, alternatively the area of corresponding disc which is pi*r^2.

?

How pedantic can one reasonable be? Until others start complaining? How do I know? Should I ask? How can I become less pedantic in my social relationships?
 
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Wow.
 
If this were my girlfriend asking, I'd just calculate it in my head and give a numerical answer. It avoids all kinds of arguments and is probably what they really wanted to know anyway.
 
My wife claims that I'm too pedantic. For instance, I asked her if she would be home in time to cook dinner and she said yes. When she came home much too late I asked her about it but she said I took her too literally.
 

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