# Boundary or Surface?

pairofstrings
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Describing boundary or a surface?
Equation of circle: ##x ^2+y ^2=1##. Is this equation describing boundary or a surface?

Thanks.

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What do you think?

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Can a 2D object be a surface?

pairofstrings
What do you think?

Can a 2D object be a surface?
For 2D objects, like circle, the equation describes boundary..?
For 3D objects, like sphere, the equation: x ^2 + y ^2 + z ^2 = 1: describes surface..?

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For 2D objects, like circle, the equation describes boundary..?
For 3D objects, like sphere, the equation: x ^2 + y ^2 + z ^2 = 1: describes surface..?
What's the definition of a boundary?

Can a surface be a boundary?

https://en.wikipedia.org/wiki/Surface_(mathematics)

Can a curve be a boundary?

By the way, a circle is a 1D object (curve) and a sphere is a 2D object (surface).

• phinds
pairofstrings
Can a surface be a boundary?
Can a curve be a boundary?
I think that curve or a surface can have a boundary.
So, the boundary of a circle can be represented as ##x^2 + y^2=1##?

By the way, a circle is a 1D object (curve) and a sphere is a 2D object (surface).
I thought Sphere is considered as a 3D object. I was incorrect. So now, out of curiosity, please may I know what a 3D object could be like?

Thanks.

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I think that curve or a surface can have a boundary.
So, the boundary of a circle can be represented as ##x^2 + y^2=1##?

I thought Sphere is considered as a 3D object. I was incorrect. So now, out of curiosity, please may I know what a 3D object could be like?

Thanks.
A maths student is a 3d object!

Mathematically it's called a solid. A ball, sphere plus the interior, is a 3d object.

• pairofstrings
pairofstrings
Thanks.
I was looking into points, lines, curves, shapes, solids.
Lines and curves can be referred to as 1D objects ? There is a notion of boundary here?
Shapes, like Sphere, Cone, Cube, Cylinder can be considered as 2D objects? There is a notion of surface here? I can calculate Surface area here?
Solids are 3D objects. There is a notion of surface, volume here. I can calculate surface area, volume here?
Point is a zero dimensional object.

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I think things are getting rather confused here. Words like 'Sphere, Cone, Cube, Cylinder' have different meanings according to their context.

Lines and curves can be referred to as 1D objects ?
Yes.

There is a notion of boundary here?
A line segment is bounded by two points. The boundary of a 2D shape is a (closed) curve.

Shapes, like Sphere, Cone, Cube, Cylinder can be considered as 2D objects? There is a notion of surface here? I can calculate Surface area here?
Strictly speaking the word 'sphere' refers to a 2D surface, but I don't think that is helpful here. We normally consider shapes like triangles, squares etc. as 2 dimensional.

The shape of a coin is called a 'disk' and this is also a 2D object. The boundary of this shape is a 'circle' which, because it is a curve only has 1 dimension but we would not normally refer to a circle as a 1 dimensional object.

Solids are 3D objects. There is a notion of surface area, volume here. I can calculate surface area, volume here?
Yes. When we say sphere, cone, cube, cylinder or prism we are usually referring to a 3D object.

When we want to avoid confusion we say "the surface of a [sphere, cone, cube, cylinder or prism]" or "the interior of a [sphere, cone, cube, cylinder or prism]" to refer to the 2D and 3D objects respectively.

Point is a zero dimensional object.
Yes, a point has no dimensions.

pairofstrings
So, first there is a point then line/curve then shapes then solids according to ascending order of dimensions?

What is the point, line/curve, shape, solid collectively called? Are they called mathematical objects? Each one of them is a mathematical object?

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