Determining Areas of Lines & Points: Suggestions Welcome

In summary, the area of a straight line or point is declared to be zero. This is because area requires two dimensions and a line or point only has one. This is true for any reasonable definition of area. Even when dealing with fractal curves or space-filling curves, the area is still considered to be zero. It is impossible to prove otherwise using a triangle since a line or point does not have a measurable area.
  • #1
abia ubong
70
0
i was thinking can anyone findv the area of a straight line and also can anyone determine the area of a point or dot as the case maybe ,any suggestions wiil be appreciated
 
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  • #2
Areas of such things are declared to be zero, as I suspect you know.
 
  • #3
The area for any line or point is DNE. Area requires exactly two dimensions.
 
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  • #4
Using any reasonable definition of area, the area of a 1 dimensional set is 0.
 
  • #5
What happens when the dimension of a curve exceeds 1? An example is the fractal curves of Weierstrass. This curve zig-zags so much that it has infinite slope at every point in its domain. Doesn't this sound like the curve is taking on the "character" of "width" as exhibited by it's fractal dimension which is greater than 1?
 
  • #6
  • #7
hypermorphism said:
Also, check out the fun things that are called space-filling curves.

I'm familiar with the curves. Someone here in the group is suppose to be I think proving that the curve fills the plane. I'd like to see that proof.
 
  • #8
hey hallsofivy is there a proof that their ares are zero if there is send me a private pls same goes 2 anyone who beleives the area is zero.for u jon f wats the meaning of d.n.e?
 
  • #9
dne is does not exist.

abia, the area is "declared" to be zero, ie it is a deinition that the area of a point is zero, as is the area of a straight line. This makes sense: the area of a rectangle of sides a and b is ab. A line can be thought of as a rectangle of sides a and 0, so the area is zero. If you want to think about an infinitely long line, then we need to invoke some other theory of what areas are, but in any reasonable sense a straight line has zero area. Areas are usually integrals over the set whose area you want to find.
 
  • #10
matt ,can this be proven using a triangle,at least u used a rectangle,pls tell me if a triangle can be used to prove the value
 
  • #11
Area is a property of a 2 dimensional shape. Lines are one-dimensional shapes. So to talk about the area of a line is without meaning.

It’s the same idea as this question being meaningless “what color is loud”.
 
  • #12
given a rectangle c long (constant) and x wide ...

lim c*x
x--> 0

rectangle becomes line and area becomes 0
 
  • #13
or hey sin0 = 0

triangle proof

did i just blow your mind?
 
  • #14
not really noslen i still need more proof,my friend says he has a proof that its 0 using a triangle,so can u help
 
  • #15
abia ubong said:
not really noslen i still need more proof,my friend says he has a proof that its 0 using a triangle,so can u help
noslen answered this.

The angle between the two long sides of this "triangle" is zero degrees.
sin(0) = 0, meaning the opposite side of the "triangle" is of length zero.
Measure the area of the "triangle" (1/2L*H).
The height is zero, thus the area is zero.
 

Related to Determining Areas of Lines & Points: Suggestions Welcome

1. How do you determine the area of a line?

The area of a line cannot be determined, as a line is a one-dimensional object with no surface area.

2. What is the difference between a line and a point?

A line is a one-dimensional object that extends infinitely in two directions, while a point is a specific location in space with no size or dimension.

3. How do you calculate the area of a point?

A point has no area, as it is a single location with no size or dimension.

4. Can the area of a line or point be measured?

No, the area of a line or point cannot be measured, as they do not have any physical size or dimension.

5. What is the purpose of determining the area of lines and points?

The concept of determining the area of lines and points is used in mathematics and science to understand and analyze geometric shapes and their properties. It is also used in real-world applications such as mapping and surveying.

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