Ellipsoidal vs. Elliptical — What's the Difference?

Ellipsoidal shapes are three-dimensional with symmetrical curves around multiple axes, commonly seen in applications requiring a volume-centric approach such as in astronomy or physics. Whereas elliptical refers typically to two-dimensional forms, primarily used to describe flat, oval shapes like those of planets' orbits or the outline of an ellipse in mathematics.

Ellipsoidal structures often have practical implications in design and engineering, particularly when aerodynamics or light distribution is a concern, offering a continuous surface without edges. On the other hand, elliptical forms are frequently utilized in graphic design and architecture for their aesthetically pleasing curves and simplicity.

In geometry, an ellipsoidal figure is defined by equations that take into account its three axes (major, minor, and intermediate), which are crucial for understanding its shape in three-dimensional space. Elliptical, however, is described with just two axes (major and minor), simplifying calculations and visualizations in a flat plane.

Ellipsoidal coordinates are used in physics and mathematics to solve problems involving three-dimensional space where symmetrical properties about more than one axis are considered. Elliptical coordinates simplify these issues in two dimensions, often used in problems involving perimeter or area.

When manufacturing lenses and mirrors, ellipsoidal surfaces are crucial for focusing light correctly in devices like telescopes and projectors, exploiting their volumetric properties. Elliptical surfaces, however, are used in simpler optical devices, such as magnifying glasses, where the focus is more on the direct manipulation of flat surfaces.