- #1

pairofstrings

- 399

- 6

- 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.

Thanks.

You are using an out of date browser. It may not display this or other websites correctly.

You should upgrade or use an alternative browser.

You should upgrade or use an alternative browser.

- B
- Thread starter pairofstrings
- Start date

- #1

pairofstrings

- 399

- 6

- 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.

Thanks.

- #2

- 24,020

- 15,708

What do you think?

- #3

- 18,211

- 11,222

Can a 2D object be a surface?

- #4

pairofstrings

- 399

- 6

What do you think?

For 2D objects, like circle, the equation describes boundary..?Can a 2D object be a surface?

For 3D objects, like sphere, the equation: x ^2 + y ^2 + z ^2 = 1: describes surface..?

- #5

- 24,020

- 15,708

What's the definition of a boundary?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..?

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).

- #6

pairofstrings

- 399

- 6

Can a surface be a boundary?

I think that curve or a surface can have a boundary.Can a curve be 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?By the way, a circle is a 1D object (curve) and a sphere is a 2D object (surface).

Thanks.

- #7

- 24,020

- 15,708

A maths student is a 3d object!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.

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

- #8

pairofstrings

- 399

- 6

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.

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.

Last edited:

- #9

pbuk

Science Advisor

Homework Helper

Gold Member

- 4,084

- 2,411

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

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

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.

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

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.

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

- #10

pairofstrings

- 399

- 6

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?

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

Last edited:

- #11

pbuk

Science Advisor

Homework Helper

Gold Member

- 4,084

- 2,411

I don't like the word "shapes" here, perhaps you could use "plane figures".So, first there is a point then line/curve then shapes then solids according to ascending order of dimensions?

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

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.

Share:

- Replies
- 5

- Views
- 500

- Replies
- 5

- Views
- 2K

- Replies
- 3

- Views
- 595

- Replies
- 5

- Views
- 558

- Replies
- 29

- Views
- 628

- Last Post

- Replies
- 4

- Views
- 708

- Last Post

- Replies
- 8

- Views
- 1K

- Last Post

- Replies
- 6

- Views
- 1K

- Last Post

- Replies
- 1

- Views
- 587

- Last Post

- Replies
- 5

- Views
- 957