Sferoïde

sferoïde is the French term for a spheroid, a geometric shape that is generated by rotating an ellipse about one of its principal axes. Depending on which axis is chosen, the resultant shape is either an oblate spheroid, such as the Earth or a flattened planet, or a prolate spheroid, like a rugby ball or certain celestial bodies. The geometry of a spheroid is fully described by two radii: the equatorial radius a and the polar radius c. The sferoïde satisfies the equation (x²+y²)/a² + z²/c² = 1, which reduces to a sphere when a equals c.

In astronomy, sferoïde models are crucial for understanding the shape, mass distribution, and gravitational field of planets and asteroids. The flattening factor, defined as (a−c)/a, quantifies the deviation from perfect sphericity. For Earth, flattening is 1/298, indicating a slight equatorial bulge due to rotation. Geodesists use spheroidal baselines to define reference ellipsoids, such as GRS80 or WGS84, for geospatial mapping.

Sferoïde theory also informs the design of engineering structures like pressure vessels and aerodynamic bodies. Because the curvature is asymmetric, performance analyses often employ differential geometry to derive normal stresses and streamline patterns. In computer graphics and 3D modeling, rendering a spheroid requires parametric equations expressing coordinates as functions of two angles, enabling accurate shading and collision detection. Thus, the sferoïde remains a foundational concept across physics, astronomy, engineering, and digital visualization.