Can a straight line or point have area?

[abia ubong]

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

 

[matt grime]

Areas of such things are declared to be zero, as I suspect you know.

 

[JonF]

The area for any line or point is DNE. Area requires exactly two dimensions.

 

[HallsofIvy]

Using any reasonable definition of area, the area of a 1 dimensional set is 0.

 

[saltydog]

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?

 

[hypermorphism]

Also, check out the fun things that are called space-filling curves.

 

[saltydog]

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.

 

[abia ubong]

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?

 

[matt grime]

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.

 

[abia ubong]

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

 

[JonF]

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”.

 

[noslen]

given a rectangle c long (constant) and x wide ...

lim c*x
x--> 0

rectangle becomes line and area becomes 0

 

[noslen]

or hey sin0 = 0

triangle proof

did i just blow your mind?

 

[abia ubong]

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

 

[DaveC426913]

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.