Gömbfelületnek

Gömbfelületnek, which translates to "spherical surface" in English, refers to the set of all points in three-dimensional space that are equidistant from a fixed point called the center. This distance is known as the radius. A spherical surface is a two-dimensional manifold, meaning that in the immediate vicinity of any point on the surface, it resembles a flat plane. It is a fundamental geometric shape with many applications in mathematics, physics, and engineering.

The equation defining a spherical surface centered at the origin (0,0,0) with radius r is x^2 + y^2 + z^2 = r^2, where (x, y, z) are the coordinates of any point on the surface. If the center is at a point (a, b, c), the equation becomes (x-a)^2 + (y-b)^2 + (z-c)^2 = r^2.

Unlike a sphere, which is the solid region enclosed by the surface, the gömbfelületnek specifically refers to the boundary itself, having no thickness. Examples of spherical surfaces in the real world include the surface of a perfectly round ball or the surface of a planet. Its properties, such as surface area and curvature, are well-defined and extensively studied. The surface area of a gömbfelületnek is given by the formula 4πr^2, and its volume (the volume of the sphere it encloses) is (4/3)πr^3.