Yes, a polygon can conceptually grow from a zero-dimensional object, such as a point. By expanding a point outward in multiple directions, you can create a line segment (one-dimensional), and by further extending it into a closed shape, you can form a polygon (two-dimensional). This process illustrates how dimensions can evolve from simpler forms.
A point
A point has zero dimensions; a line has only one direction, which is length. Two-dimensional objects have length and width, and therefore area.
0. A triangle is a 2-dimensional object and so its volume - which requires a 3-dimensional object - is always zero.
A zero-dimensional geometric object is a point, which has no length, width, or height. It is defined by a specific location in space, typically represented by coordinates in a given coordinate system. Points serve as the fundamental building blocks in geometry, as they can be used to define more complex shapes and structures. Essentially, a zero-dimensional object exists solely as a position without any physical extent.
A zero-dimensional geometric object is a point. It has no length, area, or volume, and is defined solely by its position in space. In a coordinate system, a point is represented by its coordinates, but it does not occupy any space itself. This makes it the simplest form of a geometric entity.
A point
A zero-dimensional object cannot move along any dimension, so it (and everything else in this dimension) appears as one incredibly tiny speck. A point is zero-dimensional. A one-dimensional object is a step up from a zero-dimensional one, since objects can move in only in one direction, and objects appear along an impossibly narrow line. These include the line, ray, and segment.
A point has zero dimensions; a line has only one direction, which is length. Two-dimensional objects have length and width, and therefore area.
Points are the only such objects.
0. A triangle is a 2-dimensional object and so its volume - which requires a 3-dimensional object - is always zero.
A zero-dimensional geometric object is a point, which has no length, width, or height. It is defined by a specific location in space, typically represented by coordinates in a given coordinate system. Points serve as the fundamental building blocks in geometry, as they can be used to define more complex shapes and structures. Essentially, a zero-dimensional object exists solely as a position without any physical extent.
One-dimensions objects
An ellipse is a 2-dimensional object and so its volume must be zero!
A square is a 2-dimensional shape whereas volume is a property of a 3-dimensional object. So it makes no sense to talk about a square having volume. However, a 2-dimensional shape can also be considered as a 3-dimensional object with either a zero or infinite third dimension; so the volume of a square can be considered as either zero or infinite.
A circle being a two dimensional object has zero length in the third dimension so its volume is always zero.
A zero-dimensional geometric object is a point. It has no length, area, or volume, and is defined solely by its position in space. In a coordinate system, a point is represented by its coordinates, but it does not occupy any space itself. This makes it the simplest form of a geometric entity.
Negligible, though not exactly zero.