Sphere

Sphere

A Sphere is a geometric shape in three-dimensional space that is the surface of a completely round ball. It is analogous to a two-dimensional circle.

Definition

In mathematics, a sphere is defined as the set of all points in three-dimensional space that are located at a distance r (the radius) from a given point (the center). The longest straight line segment that connects any two points on the sphere passes through the center and its length is twice the radius.

Properties

A sphere has several important properties. It has the smallest surface area among all surfaces enclosing a given volume and it encloses the largest volume among all closed surfaces with a given surface area. The sphere is the only shape that has these two properties.

Equations

The standard equation of a sphere in Cartesian coordinates is x² + y² + z² = r². In spherical coordinates, the equation is simply ρ = r, where ρ is the radial distance from the origin.

Applications

Spheres have many applications in various fields such as physics, engineering, and astronomy. For example, the shape of planets and stars are often approximated as spheres due to their gravitational fields.

See also

• Circle
• Ellipsoid
• Oblate spheroid
• Prolate spheroid

References

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