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- Thread starter abia ubong
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matt grime

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

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

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HallsofIvy

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

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saltydog

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

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saltydog

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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.

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matt grime

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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.

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

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lim c*x

x--> 0

rectangle becomes line and area becomes 0

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or hey sin0 = 0

triangle proof

did i just blow your mind?

triangle proof

did i just blow your mind?

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DaveC426913

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noslen answered this.abia ubong said:

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.

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