- TL;DR Summary
- Describing boundary or a surface?
Equation of circle: ##x ^2+y ^2=1##. Is this equation describing boundary or a surface?
What do you think?
For 2D objects, like circle, the equation describes boundary..?Can a 2D object be a surface?
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?
I think that curve or a surface can have a boundary.Can a curve be a boundary?
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).
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?
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?
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?
Yes, a point has no dimensions.Point is a zero dimensional object.
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?