authalic sphere describes a sphere that has the same surface area as the earth's spheroid.
Cartographers use a value for the spherical circumference of the Earth called the authalic sphere. A real (meaning "area-preserving") sphere is a sphere with the same surface area as the oblate ellipsoid used.
Spheres are fundamental objects in many areas of mathematics. Spherical and near-spherical shapes also occur in nature and industry. Bubbles, like soap bubbles, are spherical in equilibrium. The Earth is often approximated as a sphere in geography, and the celestial sphere is an important concept in astronomy. Manufactured objects such as pressure vessels and most curved mirrors and lenses are based on spheres. Most balls used in sports and toys are spherical, as are their bearings because the ball rolls smoothly in any direction.
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