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

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In summary, the conversation discusses the topic of being pedantic and how it relates to social relationships. It also touches on the concept of the area of a circle and how it can be interpreted differently. The speaker suggests that it might be best to simply give a numerical answer in certain situations to avoid arguments.
  • #1
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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  • #2
Wow.
 
  • #3
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.
 
  • #4
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.
 
  • #5


I would respond with (2) as it provides a more thorough and accurate explanation of the concept. However, in a social setting, it would be more appropriate to simply respond with (1) as it is a commonly understood and accepted way of expressing the area of a circle. It is important to be aware of the context and the level of understanding of the person asking the question. In terms of becoming less pedantic in social relationships, it is important to be mindful of the language and level of detail you use in conversations and to adjust accordingly. Asking for feedback and being open to others' perspectives can also help in finding a balance between being accurate and being too technical in social interactions.
 

What is the formula for finding the area of a circle?

The formula for finding the area of a circle is A = π * r2, where π is a mathematical constant approximately equal to 3.14 and r is the radius of the circle.

What does the symbol π represent in the formula for the area of a circle?

The symbol π represents the ratio of a circle's circumference to its diameter. It is a mathematical constant that is approximately equal to 3.14, but can be calculated to more decimal places for greater accuracy.

Why is the formula for the area of a circle multiplied by the square of the radius?

The formula for the area of a circle is multiplied by the square of the radius because the area of a circle is directly proportional to the square of its radius. This means that as the radius increases, the area of the circle increases at a faster rate.

How is the formula for the area of a circle derived?

The formula for the area of a circle is derived using calculus and the concept of limits. It can also be derived geometrically by approximating a circle with a series of polygons and taking the limit as the number of sides approaches infinity.

What are some real-world applications of the area of a circle formula?

The formula for the area of a circle has many real-world applications, such as calculating the amount of paint needed to cover a circular surface, determining the size of a circular garden or pond, and designing circular objects such as wheels or gears. It is also used in fields such as engineering, architecture, and physics.

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