
#1
Feb612, 10:07 AM

P: 26

What does it mean to find the area? I've read somewhere and the person says, it means to find the space enclosed, but I still don't know what that means. I understand what area intuitively means, but not logically.




#2
Feb612, 10:34 AM

Sci Advisor
HW Helper
Thanks
P: 26,167

hi jaja1990!
area is a measure a measure gives a value µ(A) to any subset A, and obeys µ(A U B) = µ(A) + µ(B), for any two subsets A and B which do not overlap (see http://en.wikipedia.org/wiki/Measure_(mathematics) for more details) it could be area, or probability, or cost, or … for area, we define µ(any rectangle) to be the product of the sides of that rectangle 



#3
Feb612, 12:10 PM

P: 26

Thank you, that was a lovely answer.
I won't be able to fully understand the topic in the link yet, but it's on my todo list now. Can you explain a bit on: "a measure gives a value µ(A) to any subset A, and obeys µ(A U B) = µ(A) + µ(B)"? I understand what subset and union mean, but you didn't say what B is. Also, can you tell me how "obeys µ(A U B) = µ(A) + µ(B)" applies to finding the area of a rectangle? I hope I'm not being boring by asking these questions and reading more myself. Right now, because I'm short on time, I'm just trying to get a general idea, not delve deeply and look for exact answers. 



#4
Feb612, 12:30 PM

Sci Advisor
HW Helper
Thanks
P: 26,167

What does it mean to find the Area (e.g. area of a circle)?
hi jaja1990!
(i've now edited my previous post to correct that) we define its area to be the product of the sides … then we use µ(A U B) = µ(A) + µ(B) to define the area of any other shape (in the same way that the ancient greeks did) … we fill out the shape with rectangles, and add up the areas of the rectangles 



#5
Feb812, 09:06 AM

P: 26





#7
Feb812, 09:25 AM

P: 26

I understand how "we fill out the shape with rectangles, and add up the areas of the rectangles" applies to a circle, I was asking about:
"then we use µ(A U B) = µ(A) + µ(B) to define the area of any other shape (in the same way that the ancient greeks did) …" Specifically, I don't understand how we choose "A" and "B", I don't know how their values would look like for a circle. 



#8
Feb812, 11:59 AM

Sci Advisor
HW Helper
Thanks
P: 26,167

A B C D … are the areas of the 1st 2nd 3rd 4th … rectangles we add up the areas of as many rectangles as are needed, to get whatever degree of accuracy we want 



#9
Feb912, 09:52 AM

P: 26

I understand now, thank you for bearing with me!



Register to reply 
Related Discussions  
Area of a circle and pi and generally area  General Math  22  
Circumscribed circle  inscribed circle area formula  General Math  1  
Find how fast the radius of a circle get smaller as its area gets smaller  Calculus & Beyond Homework  2  
Find the area of trapezoid circumscribed about a circle?  General Math  6  
An odd Volume problem/how to find the area of a part of a circle  Introductory Physics Homework  12 