# Its strange

1. Apr 27, 2005

### 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

2. Apr 27, 2005

### matt grime

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

3. Apr 27, 2005

### JonF

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

Last edited: Apr 27, 2005
4. Apr 27, 2005

### HallsofIvy

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

5. Apr 27, 2005

### 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?

6. Apr 27, 2005

### hypermorphism

7. Apr 27, 2005

### saltydog

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. Apr 28, 2005

### abia ubong

hey hallsofivy is there a proof that their ares are zero if there is send me a private pls same goes 2 any one who beleives the area is zero.for u jon f wats the meaning of d.n.e?

9. Apr 28, 2005

### 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.

10. Apr 28, 2005

### 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

11. Apr 28, 2005

### 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 with out meaning.

It’s the same idea as this question being meaningless “what color is loud”.

12. Apr 29, 2005

### noslen

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

lim c*x
x--> 0

rectangle becomes line and area becomes 0

13. Apr 29, 2005

### noslen

or hey sin0 = 0

triangle proof

did i just blow your mind?

14. Apr 29, 2005

### 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

15. Apr 29, 2005