On two-dimensional geometric objects with round or curved edges
In the context of planar shapes, the term round of course refers primarily to the circle, though here it is understood in a more general sense that encompasses any type of curvature. Shapes are considered round if at least one part exhibits such curvature, even if other parts are straight. A simple example of a shape with both a curved and a straight section is the semicircle. Shapes involving curvature not derived from a circle, such as the ellipse and forms based on this, are generally more complex to calculate. Calculations involving circles are simplified by the constant pi, usually represented by the Greek letter π. While calculating this number is not trivial, its value is known with great precision, allowing us to skip that step in circle-related calculations. The value of π is approximately 3.1415927. It is an irrational and transcendental number, meaning it has an infinite, non-repeating decimal expansion and is not the solution to any algebraic equation with rational coefficients. π appears frequently in geometry whenever a circle is involved.
The boundary of a two-dimensional shape consists of one or more one-dimensional curves. When these curves are closed, they enclose an area. This area constitutes the corresponding two-dimensional shape.
In geometry, references to two-dimensional shapes without further qualification generally imply Euclidean geometry, that is geometry on a flat plane. However, there are also geometries on other types of surfaces, such as elliptic and hyperbolic geometries. Examples of shapes from such non-Euclidean geometries include the antipodal digon and the spherical triangle. These belong to the elliptic geometry of a sphere's surface. Non-Euclidean objects are at the end of this list.