Therefore, the shape is an **ellipse** (in a meridional plane), and the surface is a **surface of revolution of an ellipse**, but since it's symmetric, it's a **3D ellipsoid**.
["The Ellipse in the Meridional Plane: Natural Geometry Behind the 3D Ellipsoid Surface", "When exploring the elegant shapes of geometry, few figures embody symmetry and mathematical purity like the ellipse. In the context of 3D geometry, the ellipse transforms into a powerful surface through revolution—giving rise to the ellipsoid, a cornerstone shape in both pure mathematics and real-world applications.", "### Therefore, the Shape Is an Ellipse in the Meridional Plane", "In geometrical terms, the meridional plane refers to a plane that contains a line of symmetry — often the axis of revolution. When we say the shape is an ellipse in this plane, we describe a perfectly closed, flattened circle stretched along two equal semiaxes. An ellipse is defined mathematically by the equation:", "[\n\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1\n]", "where (a) and (b) represent the semi-major and semi-minor axes, respectively. This equation governs the extent of the curve, illustrating how the geometric constraint of elliptic symmetry establishes a curved boundary in two dimensions — the foundation for building more complex 3D forms.", "### Surface of Revolution: From Ellipse to Ellipsoid", "Rotating this ellipse about its major axis (the meridional plane) produces a surface of revolution, a smooth, surface-filling shape symmetric about its central axis. This process converts a 2D ellipse into a 3D ellipsoid — a surface where every point maintains consistent rotational symmetry. The resulting three-dimensional object, known as an ellipsoid, extends uniformly in all directions defined by the ellipse’s shape.", "Because of the ellipse’s aspect ratio ((a <br/>\neq b)), the surface varies smoothly—neither spherical nor highly elongated—offering unique geometric properties such as varying curvature and isotropic dimensional balance around the rotational axis.", "### Why the Ellipsoid (Surface of Revolution of an Ellipse) Matters", "The concept of revolving an ellipse into an ellipsoid is more than a mathematical curiosity. It exemplifies how symmetry and transformation produce complex, practical forms. In physics, engineering, and computer graphics, ellipsoids model natural phenomena (e.g., planetary shapes, cell nuclei) and optimize structural designs. Their predictable curvature enables efficient stress distribution and fluid dynamics modeling.", "In summary:\n- The ellipse in the meridional plane defines the boundary of symmetry.\n- Revolving this ellipse forms a smooth, rotate-invariant ellipsoid surface.\n- This elegant transformation connects 2D geometry with 3D space, blending beauty and utility in mathematical design.", "Explore the ellipse, embrace its rotational symmetry, and discover how the surface of revolution elevates geometry into real-world relevance — a classic shape defined by simplicity and symmetry, yet rich with application potential."]
