Equation of Circle: Boundary or Surface?

[pairofstrings]

TL;DR Summary

Describing boundary or a surface?

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

Thanks.

 

[PeroK]

What do you think?

 

[phinds]

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..?

 

[PeroK]

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).

 

[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.

 

[PeroK]

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]

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.

 

[pbuk]

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?

 

[pbuk]

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

I don't like the word "shapes" here, perhaps you could use "plane figures".

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

No, the term "mathematical object" does not have any generally accepted meaning, and there isn't really a collective noun for these geometrical concepts except perhaps each of them could be called a "figure".

If you want to learn about geometry then you should learn about things that are important; asking random questions about things that may not be important will not help you learn. Khan Academy has a suitable set of courses in basic geometry.