Much of mathematics deals with maneuvering and manipulating numbers so that their value changes to match certain specifications, whether it is through algebra, calculus or standard arithmetic, the student of mathematics becomes aware of the fact that in order to solve problems, often times the numbers themselves need to change. Also, a lot of students that study at math faculties often need accounting hw help or advice how to solve some math tasks, because it’s quite hard task for them.
The mathematician also becomes readily aware, however, that there are some numbers which do not possess the virtue of “changeability.” These are numbers which must remain as they are, convenient or not.
These are the mathematical “constants.”
There are a great many of them, both in true mathematics and in other math-based sciences, particularly physics. These are some of the more common and important constants:
One of the most familiar and culturally significant of all constants, pi (π) is, as most people are aware, simply the ratio of a circle’s diameter to its circumference (roughly 3.14159).
What many people do not realize, however, is just how often pi tends to creep up as if by magic in nature itself, showing up in applications that don’t seem as if they have anything to do with circles. The examination of the real meaning behind pi has been one of the great sources of mathematical explanation throughout history.
The Imaginary Number
Denoted simply a lower case “i,” the imaginary number is precisely what its name suggests – a number that doesn’t actually exist. Specifically, it is “the square root of negative one.”
Worded in a different way, one could say that “The imaginary number is that which, when multiplied by itself, equals negative one.” Of course no such number can possibly exist.
So why, if the number doesn’t even exist, is it necessary for us to define it? Because it shows up all the time in mathematics. One of the things that student of math must come to terms with is the fact that just because a number doesn’t exist doesn’t mean it won’t be crucial to an equation which denotes something that does exist. Very often in complex algebra one ends up with an answer such as “x = √(-4),” which can be easily reduced by factoring out the imaginary number and receiving the simpler answer: x = 2i.
Also serving as the base of a natural logarithm, Euler’s number (e) possess, like pi, an irrational, yet real value (meaning that it continues forever after the decimal without ever repeating or ending, though it is a real number). It’s value has been estimated at about 2.71828…
While it is still uncertain to mathematician just why this number is so important, it surely is. It, also like pi, is used in a surprising number of real-world applications. It is the key, in fact, to such common mathematical problems as calculating compound interest – an important tool in the financial world.
The Golden Ratio
Another number that finds itself originating in nature, the golden ratio (denoted by the Greek symbol phi, φ, and calculated at around 1.61803) is roughly the ratio of height to width of a “golden rectangle;” a rectangle in which the ratio of its height to width is the same as the ratio of height + width to height.
While many have conjectured that this ratio possesses certain qualities that make it fundamentally more aesthetically appealing when used in art, architecture and other constructions, it is also found to a surprising extent in nature, especially when contemplated in conjunction with the “Fibonacci Sequence,” (1,1,2,3,5,8,13… where every digit is the sum of the two immediately preceding it), which proceeds according to the golden ratio (for reasons which can be mathematically deduced by a particularly clever reader).
These are just a few of the important mathematical constants, though in no way does this list even begin to do justice the dozens of others which exist. There are constants for many specific purposes – constants such as “c” (the speed of light) and “h” (Planck’s constant) which have almost limitless use in the world of physics; others which denote important engineering standards; some which are used by chemists; others which…. the list could go on and on.
An understanding of mathematical constants and how they work is essential to having a proper understanding to how math behaves and how it seeks to understand the world, for they enable the mathematician something concrete and unchangeable on which to stand – important in a field in which the entire purpose is change and manipulation.