**Mathematics Has Become a Part In Our Modern Civilizations**

**The Introduction 01**

As many of us agree about Mathematics is not about problem-solving, this is the first thing we may need to understand, because once we treat Mathematics as problem-solving, then we will be stuck into an infinity loop about those thoughts on what other areas needed mathematics. Now, if we think Mathematics is the idea of surrounding about how our universe and everything in it behaves, it told us into such a form in what we as a human called geometry, numbers, pattern, etc. to help us human identified situations around us easily either in the form of us measuring it or else. Therefore, with that idea which part of our living environment isn't about the idea of living?

Fun fact let’s get back to the word “mathematics” comes from. It came from the Greek language in which is μάθημα, read as “*mathemata*” which mean something that is learn (Wikipedia, 2020), like a lesson (learned), or a knowledge (learning). Therefore, a study of mathematics not about problem-solving only, but a study of idea on the surrounding us neither in the living or non-living beings, we learned it from a geometry that happened, then translated into a number that we can know, with tools of operation that we can use to understand the message surround us in the form like a pattern of structure, order, quantity, relations, and many other forms of a pattern. The one we used in the school is the form of problem-solving to help us on the insight about mathematics is the study about those patterns of an idea that structured in concept on solving those type of similar questions, in which experimentally into a practical form that we found in our life to live. In which the Greeks in the past were using Mathematics on finding the form of sign from the Universe, that leads us into the learning of Astronomy, that we called the mathematical analysis on seeing the pattern of change in our Universe. Today, the area of Mathematics has spread to much more on helping us to a better understanding of our life to live and lightening our life to live.

Now, Modern Mathematics has spread topics into several minor topics that helped us with a better point of view. Firstly, we can see in the form of *Mathematics of Numbers*, or quantity. This mathematics of numbers will discuss mostly numbers as literally mentioned, the number of forms like `3` ; `3 1/2` ; or `3.5` . Once we use *the operations tools* like adding (`+`), subtracting (`-`), multiplication (`*`), and division (`/`) into those numbers, then we will do what we called the *calculation operation*. Sometimes, we are not only thinking about some number, but we will try to be finding some form of pattern in groups of numbers. We are analyzing and identifying a pattern that happened in those numbers without tools of operations. Like the form for group numbers `{1,3,5,7,9,11,...}` these types of groups numbers, that we will be called *odd numbers*, in which groups of numbers that unevenly divided, which lead us to an opposite group of numbers like `{2,4,6,8,10,12, ...}` as a group of numbers that evenly divided in which we called as *even number*. Now, Mathematicians have discovered more of these groups of numbers and those group's numbers classification has to help us more on organizing and learning the message of our universe.

On the other hand, in the loss of human records, Mathematician also learns about the connection among those numbers throughout the operation tools, which will be called Mathematics of Algebra. In Mathematics of Algebra, in short, called *Algebra*, we will get introduced the use of alphabetical as a form of random constants number, like in the form of below:

`(x+2)^2 = x^2 + 4*x + 4`

The alphabet of “`x`” in that calculation form has a meaning as a random constant number, that we can replace it with any numbers but a similar one, in terms, if you replace “`x`” by a number of 5, then the whole “`x`” in that calculation form will be replaced by 5, to become like:

` (5+2)^2 = 5^2 + 4*5 + 4 = 49`

Once we replace the alphabet of “`x`” by 5, then we will have a total value of 49 once we finished that’s calculation form. The connection from that calculation form, a mathematician will be called an *equation*. The relations in that equation will always remain the same if we replace the alphabet of “`x`” in that equation with any numbers, and of course, will lead us into a different value. Also, in the Mathematics of Algebra, Mathematician will introduce the use of symbols as identification of some form in the calculation of pattern. Like the form:

`(x+2)^2 = f(x)`

In which `f(x)` as a meaning for the function of `x`, in terms of each of “`x`” in that function can be replaced by any kind of numbers. Mathematics of Algebra has helped us with a simplification of calculation form, which also helps us with extending to more capability of calculation form.

In the form of what we called function, mathematicians can go back to our original idea on which we believe those numbers do exist after the form of geometry. After functions have to help us and organizing our information into two categories like a result as an independent variable or the output that always comes from the basis as the dependent variable or the input value. In which will help us to put it into a diagram that called as Cartesian Diagram, in which have two line perpendicular each other, one line represents as the output line and the other line represent as the input line.

In order to help us with more understand especially with shape, we have numbers, in which the study for Mathematics of Shape, we called Geometry, it was started by a dot, as one point, then once we have two dots, we can form a line, the more the dots the longer the line we will have. Mathematicians also learn about the character for each form, the relations among them, and how to calculate and measure them. In Geometry, we learned this dot (just an initial form), line (the form of more than one dot), and shape (the form of more than one line), like:

From the form of Shape, the Mathematician will let us know about a general idea of dimensions, which later on will be called a *Mathematics of Space*. The study about Mathematics of Space will be more on 3 dimensions object.

Trigonometry is one of the examples from the study for Mathematics of Shape. The discovery of this idea of trigonometry has been lead many mathematicians to the reality about if we know some side of the triangle then we will know the other sides of the triangle. Also, the hidden thing from this trigonometry also lead many Mathematicians to believe about Geometry taught us about the form does exist even though we don’t have accuracy in number, in this example like if we have adjacent and opposite sides of a triangle with the size of 1 unit then we will have our hypotenuse of roots of 2 units, in which the roots of 2 have unending decimals measurements, and we put this roots of 2 in the group of irrational numbers. Trigonometry has helped many of us the practitioner of Mathematics on solving many forms of the idea in living.

Analytic Geometry is the fancy name from other discoveries in Mathematics, which lead us to a combination of Algebra and Geometry that tell us about a coordinate of geometry or sometimes Mathematical practitioner called as Cartesian Geometry. The study of Analytic Geometry helping us about an object inside the space. This study of Analytic Geometry has to help ancient Mathematician on clearance discovery about the circle and the ellipse, by using the functions. For example, below, we can see the vertical line (sleeping line) and the horizontal line (standing line) have made a perpendicular line by the center is O, as in a group of numbers identified for the value of 0 (zero). To help us with the identification of line AB at the vertical line and horizontal line, then we need to name the vertical line as `x-`line and horizontal line as `y-`line, then we fill have a simple function like `f(x)=y` , which for each value of `x` will give `y` value, now if we look again to the image which called as a graph, we can see that for `x=2` then we have `y=1` , and for `x=4` then we have `y=2` , from that information, then our logic has informed us about this AB line have an equation like `y=1/2 x` and the form like:

to find about a half-circle, then we can use an equation like `x^2+y^2=16` , in which the form like:

**Reference**:

Wikipedia (2021, January 25). *Mathematics*. Retrieved from https://en.wikipedia.org/wiki/Mathematics [Accessed Feb 3, 2021]

Wiktionary (2020, December 16). μάθημα. Retrieved from https://en.wiktionary.org/wiki/μάθημα#English [Accessed Feb 3, 2021]

Encyclopedia Britannica (2021). *Function*. Retrieved from https://www.britannica.com/science/function-mathematics [Accessed Feb 4, 2021]

Math is Fun (2020). *What is a Functions*. Retrieved from https://www.mathsisfun.com/sets/function.html [Accessed Feb 4, 2021]

Encyclopedia Brittanica (2021). *Analytic Geometry*. Retrieved from https://www.britannica.com/science/analytic-geometry [Accessed Feb 3, 2021]

Technopedia Editorial (2021). *Analytic Geometry*. https://www.techopedia.com/definition/11236/analytic-geometry [Accessed Feb 3, 2021]