In geometry, rings are geometrical structures which generalize the multiplication: addition does not need to be additive and multiplicative reciprocity inverses are not needed. Simply put, a circle is a group equipped with two definite operations equivalent to the natural multiplication of numbers, corresponding to the operations of addition and subtraction of real numbers. A conic section is the angle formed by two points on the circle, and a parabola is the curve which follows a similar path. The properties of the circle and parabola are also the properties of the real world, so a perfect circle is a sphere with definite radius on each of its radii.
Rings in algebraic structure have similar properties to those obtained from algebraic equations, so they are often studied together. For instance, when working with real numbers, one uses a ring theory ring to multiply by real integral formulas. A number can be thought of as a complex number (i.e. a number that does not have a simple root in finite numbers), so a ring theory ring will represent a group of complex numbers together with their multiplication by any number that satisfies the properties of unity, additive prime number, and quotient. These rings are sometimes referred to as “algebraic rings” owing to their resemblance to algebraic equations.
In higher mathematics, a ring theory ring is used to represent a symmetric binary operation on a finite field. Here, one uses a series of rings to represent the binary operations of addition, subtraction, and multiplication. For instance, there are four rings which, when added together, give rise to the complete binary formula for the calculation of the square root of a positive number. A similar type of series is used to represent multiplication and division of natural numbers.
In computer science, there are two types of rings: the null ring and the commutative ring. The null ring occurs when a number is represented by one or more null bits. For instance, the number 6 comes between a null and a zero. The null ring has no other property than the existence of zero and one bit for each number. The commutative ring, on the other hand, has a unique property of being the exact reverse of its complement (i.e., a number can be represented by one or more Commutatives).
There are two classes of rings that exist in nature. One is the “galactic ring” which is formed when a planet orbits the nearest star in a fixed orbit. The second class of ring is the “solar system” rings that are formed by the movement of a planet around a star. Many of these rings have fuzzy edges which give them an appearance of halo blurs around bright stars. The fuzzy edges are caused by disturbances in the space-time continuum caused by passing dust and light. Astronomy textbooks use fuzzy rings to represent the distribution of planets in the solar system.
A fuzzy ring may also be created from perturbations in a gas giant’s orbit. perturbations cause ripples in the gravitational field of a gas giant. This perturbation can become so strong that the gas giant will move away from the sun at great speeds. When this happens, the moon becomes a close planet in its orbit around the gas giant. Thus, it is possible to see the moons surrounding a gas giant rotating around the giant, much like the rings of Saturn’s ocean.