pyöreäellipsoideja

Pyöreäellipsoidi, sometimes referred to as a spheroid or a slightly flattened sphere, is a type of quadric surface that is formed by rotating an ellipse about one of its principal axes. If the ellipse is rotated about its major axis, the resulting shape is an oblate spheroid, which is flattened at the poles. If the ellipse is rotated about its minor axis, the result is a prolate spheroid, which is elongated along the axis of rotation.

The mathematical equation for a pyöreäellipsoidi centered at the origin is typically given by (x^2 / a^2) + (y^2 / b^2) + (z^2 / c^2) = 1. For a pyöreäellipsoidi, two of the semi-axes (a, b, c) are equal. For instance, an oblate spheroid might have the equation (x^2 / a^2) + (y^2 / a^2) + (z^2 / c^2) = 1, where a > c. A prolate spheroid would have a < c.

Pyöreäellipsoidit are common in nature and have applications in various fields. For example, planets and other celestial bodies are often approximated as oblate spheroids due to their rotation, which causes them to bulge at the equator. In computer graphics and physics, they are used as simplified models for more complex shapes. The term itself is Finnish, with "pyöreä" meaning round or circular and "ellipsoidi" meaning ellipsoid.