# Rings of Saturn

In math, rings are well-defined algebraic forms that generalize complex fields: addition, division, multiplication, and division should not be distributive. Simply put, a ring is a geometrical structure equipped with two integral operations satisfying necessary properties analogous to those of multiplication and division of real numbers. To understand the essence of a ring, it is useful to think of a graph, with each point representing an angle, measure, or other geometric shape. The graph could be a parabola, theta (phi), or any other geometric shape. The points on the ring share common properties corresponding to their position on the graph, which gives them a metric meaning just like any point on the surface of a sphere.

In a similar way to the idea of a circle’s Cartesian equator, the definition of a ring also consists of a central point whose values surround it on all sides, such as a sphere’s orbit around the axis of rotation, or a torus around a point on its own spin axis. The rings on a calculator also represent a pointwise multiplication, as their values enclose the area of the calculator. The circle’s radii define the areas of multiplication. The concept of commutativity arises from the idea of an infinitely divisible whole, where any single value is considered to be a power of another. In algebra, a commutative ring can be thought of as the union of two ring functions, where the function on one side of the ring is defined by a function on the other side, so that if you pick a base number (let us call it r) and a function on the ring’s right side, and place them together, their values will define the values of the corresponding functions on both sides of the ring.

A similar type of ring particle is the moon. As it revolves around the earth, the moon indirectly reflects the Earth by reflecting off satellites and reflecting back heat from the surface of the moon. When amateur astronomers are drawing a picture of the moon using a telescope, they are referring to a large collection of tiny moon-sized (and occasionally bigger) rings of different colors that are floating around in space. One example is the prominence of “seashell” bands along the western coast of Africa. A more literal example would be to put a beach towel over a computer screen, make a ring of it around the screen, and then watch the resulting effect.

Rings of different shapes and sizes are often used, sometimes even representing the earth, sun, and moon themselves! For example, if you look at a map of the United States, what do you see? If you look at a map of the world made from maps of the actual places where continents and oceans meet, what do you see? The existence of continents and ocean liners was discovered by Captain James Cook in the 17th century, and Cook used his new knowledge to map the seas of the world for travelers and explorers.

Although it may seem like a small ring, the solar system itself is made up of many smaller rings of different compositions. The Earth’s orbit around the sun is affected by our location in its orbit around the sun, and many scientists have used these effects to map the distribution of continents, oceans, and landmasses in the solar system. Similarly, when we make a drawing of the rings of the earth using a globe or a flat sheet of paper, we are actually drawing a collection of shells and clumps of rocks that are arranged in a way that can be interpreted as a network of rings. The existence of plate tectonics is another example of how the evolution of our planet has led to the presence of rings in its crust.

How do you study the relationship between rings and the movement of stars in a solar system? In our own solar system, our location in orbit around the sun determines where the planets initially were. Studying other celestial objects in the outer solar system with similar elliptical orbit features, like the moon, assists in determining the positions of our planets. For instance, the distribution of moons around the inner solar system is similar to the distribution of planets for which information is available. Studying the distribution of stellar wind speeds can help astronomers determine the distribution of planetary rings around stars. Finally, if you’re interested in finding out whether rings have an impact on the formation of the solar system, it is necessary to study the distribution of comets around stars.