A ring is an elongated circular band, typically of precious metal, often of platinum or gold, worn as traditional ornamental jewelry. The word “ring” on its own always denotes jewelry worn on just one finger; if worn as an ornamental accessory elsewhere, the word itself is defined in the term, indicating the finger or other body part in which the ornamentation is to be worn. Rings have been worn for centuries and have become a central adornment in many cultures around the world. They are not only worn for fashion, but also for its many health benefits. There are numerous myths surrounding rings and their use and it has been suggested that they may have some healing properties.

The basis for any ring theory is the understanding of algebraic structure, particularly integral rings and the binomial system. Algebraic structure refers to the relationship between any two points on a ring and the others. Rings with integral elements refer to those rings whose resulting configuration when multiplied together yields the desired result. Integrals are integral formulas, used in algebra to calculate a definite integral, or a function of unknown value, between two variables.

The binomial system is described as a fixed number system based on a set of prime numbers. This enables rings to be compared from different numbers, depending on the order of which they are multiplied. The rings’ prime numbers may be known in advance or may be derived from some other method, such as by finding the cube root of a number. The use of algebraic structure allows the interrelationship of all the prime numbers to be determined.

Algebraic ring theory subrings ideal units refer to the units of a circle that lies along the unit circle of a hexagonal ring. Each of the six sides of the ring is called a subring. The six sides may be referred to as origin, circumference, axis, middle, bass, and diameter. A mathematical formula called the hyperbolic formula is used to determine the value of each subring, as well as each of its respective side and base. For instance, a hexagonal ring having two equilateral sides and a central point with the equator and hypotenuse of each of the equilateral sides is called a hyperbola. The other shapes are called hyperbolas.

Geometric rings are formed using certain numbers of sides and angles that cannot be changed to form any other shape. Geometric rings are used for several purposes including building structures, jewelry and driving nails. These rings were introduced in mathematics by the Dutchman van Eyck-van Eemphoven who studied the properties of rings using the geometrical structure of angles and chords.

In modern times, rings are used in the construction of watches and clocks. Rings are also used in chemistry as a model for reaction mechanisms in chemical reactions. Some rings have also been used to calculate angles in geometry, notably by the Italian mathematician Luca Pacioli. Pacioli discovered that if two rings were set at right angles to each other, their combined surface would contain a polygonal equator which was the first piece of concrete proof that a geometric structure was in fact a ring.