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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.
Thanks.
PeroK said:What do you think?
For 2D objects, like circle, the equation describes boundary..?phinds said:Can a 2D object be a surface?
What's the definition of a boundary?pairofstrings said: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 said:Can a surface be a boundary?
I think that curve or a surface can have a boundary.PeroK said: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?PeroK said: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!pairofstrings said: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.
Yes.pairofstrings said: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.pairofstrings said: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.pairofstrings said: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.pairofstrings said: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.pairofstrings said:Point is a zero dimensional object.
I don't like the word "shapes" here, perhaps you could use "plane figures".pairofstrings said: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".pairofstrings said:What is the point, line/curve, shape, solid collectively called? Are they called mathematical objects? Each one of them is a mathematical object?
The equation of a circle is (x-h)^2 + (y-k)^2 = r^2, where (h,k) is the center of the circle and r is the radius.
The equation of a circle is for the boundary of the circle, as it represents all the points that are equidistant from the center.
The center of the circle, represented by (h,k), is the point that is equidistant from all points on the boundary of the circle. It is the midpoint of the circle.
To find the center and radius of a circle using the equation, you can compare it to the standard form (x-h)^2 + (y-k)^2 = r^2 and identify the values of h, k, and r. The values of h and k will give you the coordinates of the center, and r will give you the radius.
No, the equation of a circle is specifically for circles in two-dimensional space. In three-dimensional space, the equation for a circle is (x-h)^2 + (y-k)^2 + (z-j)^2 = r^2, where (h,k,j) is the center of the circle and r is the radius.