The Beauty of Mathematics

Abstract
Mathematics is essentially a process of thinking that involves building and applying abstract, logically connected networks of ideas. Mathematic is the science of pattern and relationship. The one of examples of the kinds of mathematical pattern that are available is the nature and use of number. Numbers and relationships among them can be represented in symbolic statements, which provide a way to model, investigate, and display real-world relationships. Mathematics has some beauties side. Some of them are an interesting and lovely way to look at the beauty of mathematics, and of God, the sum of all wonders, and also the balance of the world.
Mathematic is the discipline knowledge which has relationship with the other knowledge such as science and technology. Science provides mathematic a several problem for it to investigate whereas the mathematic provides the science a tools to analyzing data to solve the problem. The science and mathematic are together discover the general pattern and relationship. The mathematic and technology have usefull relationship. The mathematic serve the design of programe technique to make software which will give advancement for technology.



Keywords : mathematics, universal, beauty, number, science, unique




CHAPTER I
INTRODUCTION
1. 1 Background
Mathematics relies on both logic and creativity, and it is pursued both for a variety of practical purposes and for its intrinsic interest. For some people, and not only professional mathematicians, the essence of mathematics lies in its beauty and its intellectual challenge. For others, including many scientists and engineers, the chief value of mathematics is how it applies to their own work. Because mathematics plays such a central role in modern culture, some basic understanding of the nature of mathematics is requisite for scientific literacy. To achieve this, students need to perceive mathematics as part of the scientific endeavor, comprehend the nature of mathematical thinking, and become familiar with key mathematical ideas and skills.
Mathematics is essentially a process of thinking that involves building and applying abstract, logically connected networks of ideas. These ideas often arise from the need to solve problems in science, technology, and everyday life—problems ranging from how to model certain aspects of a complex scientific problem to how to balance a checkbook.
In this case presents recommendations about basic mathematical ideas, especially those with practical application, that together play a key role in almost all human endeavors. Here, the focus is on seven examples of the kinds of mathematical patterns that are available for such modeling: the nature and use of numbers, symbolic relationships, shapes, uncertainty, summarizing data, sampling data, and reasoning.
1.2 Problem Formula
Below are the problem formula:
1. What is the define of mathematic?
2. What is the mathematical world?
3. What is the beauty of mathematic?
4. What are the relationships between mathematic, science and technology ?

1.3 Objective
Below are the objectives:
1. To know the definition of mathematic
2. To know the mathematical world
3. To know the beauty of mathematic
4. To know the relationship between mathematic, science and technology














CHAPTER II
THEORY
2.1 The Definition of mathematic
Matematic relies on both logic and creativity, and it ipursued both for a variety of practical purposes and for its intrinsic interest. Matematic as part os endeavor , process, or way thinking presented below. Mathematic is the science of pattern and relationship. There are two definition of mathematic. The first, mathematic as theoretical discipline explore the possible relationships among abstraction without concern for whether those abstractions have counterpart in the real world. The second is also an applied science. (Rutherford, 1990: 15).
The results of theoretical and applied mathematics often influence each other. The discoveries of theoretical mathematicians frequently turn out—sometimes decades later—to have unanticipated practical value. Because of its abstractness, mathematics is universal in a sense that other fields of human thought are not. It finds useful applications in business, industry, music, historical scholarship, politics, sports, medicine, agriculture, engineering, and the social and natural sciences. The relationship between mathematics and the other fields of basic and applied science is especially strong. (Rutherford, 1990).
2.2 The Matematical World
Mathematics is essentially a process of thinking that involves building and applying abstract, logically connected networks of ideas. These ideas often arise from the need to solve problems in science, technology, and everyday life—problems ranging from how to model certain aspects of a complex scientific problem to how to balance a checkbook.
This chapter presents recommendations about basic mathematical ideas, especially those with practical application, that together play a key role in almost all human endeavors. In Chapter 2, mathematics is characterized as a modeling process in which abstractions are made and manipulated and the implications are checked out against the original situation. Here, the focus is on seven examples of the kinds of mathematical patterns that are available for such modeling: the nature and use of numbers, symbolic relationships, shapes, uncertainty, summarizing data, sampling data, and reasoning.
2. 2. 1 Numbers
The one of examples of the kinds of mathematical pattern that are available is the nature and use of number. There are several kinds of numbers that in combinationwiyh a logic for interrelating abstract system and can be useful in a variety of very different ways. The first is The age-old concept of number probably originated in the need to count how many things there were in a collection of things. The second is The Arabic number system, as commonly used today, is based on ten symbols and rules for combining them in which position is crucial . The third is The roman number system, which is still used for some purposes, is made up of a few letters of the alphabet and rules for combining them. There are different kinds of numbers. The numbers that come from counting things are whole numbers, which are the numbers we mostly use in everyday life.A whole number by it self is an abstraction for how many things there are in a set but not for the things themselves. More flexibility in mathematics is provided by the use of negative numbers, which can be thought of in terms of a number line. Computation is the manipulation of numbers and other symbols to arrive at some new mathematical statement. These other symbols may be letters used to stand for numbers. Numbers have many different uses, some of which are not quantitative or strictly logical. In counting, for example, zero has a special meaning of nothing.



2. 2. 2 Symbolic Relationships
Numbers and relationships among them can be represented in symbolic statements, which provide a way to model, investigate, and display real-world relationships. Such relationships between two quantity or category can be expressed by using pictures (typically charts and graphs), tables, algebraic equations, or words. Graphs are especially useful in examining the relationships between quantities.
Algebra is a field of mathematics that explores the relationships among different quantities by representing them as symbols and manipulating statements that relate the symbols. Sometimes a symbolic statement implies that only one value or set of values will make the statement true.
There are many possible kinds of relationships between one variable and another. A basic set of simple examples includes (1) directly proportional (one quantity always keeps the same proportion to another), (2) inversely proportional (as one quantity increases, the other decreases proportionally), (3) accelerated (as one quantity increases uniformly, the other increases faster and faster), (4) converging (as one quantity increases without limit, the other approaches closer and closer to some limiting value), (5) cyclical (as one quantity increases, the other increases and decreases in repeating cycles), and (6) stepped (as one quantity changes smoothly, the other changes in jumps).
Symbolic statements can be manipulated by rules of mathematical logic to produce other statements of the same relationship, which may show some interesting aspect more clearly. For example, we could state symbolically the relationship between the width of a page, P, the length of a line of type, L, and the width of each vertical margin, m: P = L+2m. This equation is a useful model for determining page makeup. It can be rearranged logically to give other true statements of the same basic relationship: for example, the equations L = P-2m or m = (P-L)/2, which may be more convenient for computing actual values for L or m.
Often, the quantity that interests us most is how fast something is changing rather than the change itself. In some cases, the rate of change of one quantity depends on some other quantity (for example, change in the velocity of a moving object is proportional to the force applied to it). In some other cases, the rate of change is proportional to the quantity itself (for example, the number of new mice born into a population of mice depends on the number and gender of mice already there)
2. 2. 3 Shapes
Fundamental geometrical shapes and relationships have corresponded symbolic representantion. The artifacts around us (such as buildings, vehicles, toys, and pyramida) and the familiar forms we see in nature (such as animals, leaves, stones, flowers, and the moon and sun) can often be caracterized in term of geometric form.
For many purposes, it is sufficient to be familiar with points, lines, planes; triangles, rectangles, squares, circles, and ellipses; rectangular solids and spheres; relationships of similarity and congruence; relationships of convex, concave, intersecting, and tangent; angles between lines or planes; parallel and perpendicular relationships between lines and planes; forms of symmetry such as displacement, reflection, and rotation; and the Pythagorean theorem.
Both shape and scale can have important consequences for the performance of systems. For example, triangular connections maximize rigidity, smooth surfaces minimize turbulence, and a spherical container minimizes surface area for any given mass or volume.
Geometrical relationships can also be expressed in symbols and numbers, and vice versa. Coordinate systems are a familiar means of relating numbers to geometry. For the simplest example, any number can be represented as a unique point on a line—if we first specify points to represent zero and one.
Coordinate systems are essential to making accurate maps, but there are some subtleties. For example, the approximately spherical surface of the earth cannot be represented on a flat map without distortion. Mathematical treatment of shape also includes graphical depiction of numerical and symbolic relationships. Quantities are visualized as lengths or areas (as in bar and pie charts) or as distances from reference axes (as in line graphs or scatter plots). Graphical display makes it possible to readily identify patterns that might not otherwise be obvious: for example, relative sizes (as proportions or differences), rates of change (as slopes), abrupt discontinuities (as gaps or jumps), clustering (as distances between plotted points), and trends (as changing slopes or projections). The mathematics of geometric relations also aids in analyzing the design of complex structures (such as protein molecules or airplane wings) and logical networks (such as connections of brain cells or long-distance telephone systems).
3. The Beauty of Mathematic
Mathematics, a simple word which not all people like with something related to its world. Mathematics is the natural home of both abstract thought and the laws of nature. Some people who dislike with mathematics will think that study about mathematic is not important and excited enough. They think that studying mathematics will make them find so many difficulties. But, actually we did not know another side of mathematics. Mathematics has some beauties side. Some of them are an interesting and lovely way to look at the beauty of mathematics, and of God, the sum of all wonders, and also the balance of the world. A. Einsteins said, “Do not worry about your difficulties in mathematics, I assure you that mine are greater.” So, let’s try to enjoy in the worlds.
Below are a little explanation about the beauty of mathematics:
1. Here is an interesting and lovely way to look at the beauty of mathematics, and of God, the sum of all wonders.

1 x 8 + 1 = 9
12 x 8 + 2 = 98
123 x 8 + 3 = 987
1234 x 8 + 4 = 9876
12345 x 8 + 5 = 987 65
123456 x 8 + 6 = 987654
1234567 x 8 + 7 = 9876543
12345678 x 8 + 8 = 98765432
123456789 x 8 + 9 = 987654321


1 x 9 + 2 = 11
12 x 9 + 3 = 111
123 x 9 + 4 = 1111
1234 x 9 + 5 = 11111
12345 x 9 + 6 = 111111
123456 x 9 + 7 = 1111111
1234567 x 9 + 8 = 11111111
12345678 x 9 + 9 = 111111111
123456789 x 9 +10= 1111111111


9 x 9 + 7 = 88
98 x 9 + 6 = 888
987 x 9 + 5 = 8888
9876 x 9 + 4 = 88888
98765 x 9 + 3 = 888888
987654 x 9 + 2 = 8888888
9876543 x 9 + 1 = 88888888
98765432 x 9 + 0 = 888888888
Brilliant, isn’t it?

And look at this symmetry:
1 x 1 = 1
11 x 11 = 121
111 x 111 = 12321
1111 x 1111 = 1234321
11111 x 11111 = 123454321
111111 x 111111 = 12345654321
1111111 x 1111111 = 1234567654321
11111111 x 11111111 = 123456787654321
111111111 x 111111111 = 12345678987654321
Now, take a look at this…
101%
From a strictly mathematical viewpoint:
What Equals 100%?
What does it mean to give MORE than 100%?
Ever wonder about those people who say they are giving more than 100%?
We have all been in situations where someone wants you to
GIVE OVER 100%.
How about ACHIEVING 101%?
What equals 100% in life?
Here’s a little mathematical formula that might help
Answer these questions:
If:
A B C D E F G H I J K L M N O P Q R S T U V W X Y Z
Is represented as:
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26.
If:
H-A-R-D-W-O-R- K
8+1+18+4+23+15+18+11 = 98%
And:
K-N-O-W-L-E-D-G-E
11+14+15+23+12+5+4+7+5 = 96%
But:
A-T-T-I-T-U-D-E
1+20+20+9+20+21+4+5 = 100%
Then, look how far the love of God will take you:
L-O-V-E-O-F-G-O-D
12+15+22+5+15+6+7+15+4 = 101%
Therefore, one can conclude with mathematical certainty that:
While Hard Work and Knowledge will get you close, and Attitude will
Get you there, It’s the Love of God that will put you over the top!
(Darvish Blog, accessed on March, 27th 2011)
2. The balance of the world
Mathematics has the main role in the balance of the world. It will not be a liar, because mathematics serve definite value. For instance, days total in a year is 365, everyday the earth rotate the sun is always during 24 hours, means that is not more than 24 hours. If there is a fault happen, the balance of the world will be interfered.

2. 3 Matematics, Science, and Technology
Mathematic is the discipline knowledge which has relationship with the other knowledge such as science and technology. The mathematic is abstracness so the mathematic is universal in sense so it could make a role to other field. Science provides mathematic a several problem for it to investigate whereas the mathematic provides the science a tools to analyzing data to solve the problem. The science and mathematic are together discover the general pattern and relationship. The mathematic also play role as science language so the idea science ideas have no unambiguously meaning. Mathematic and science have many common feature those are a belief in understandable order, an interplay of imagination and rigorous logic, ideals of honesty and opennes, the critical importance of peer criticism, the value placed on being the first to make key discovery, being international in scope (Rutherford, F. James, 1924: 18).
The mathematic and technology have usefull relationship. The mathematic serve the design of programe technique to make software which will give advancement for technology. The technology also give the valuable contribution to the mathematic to solve the problem of mathematic.( Rutherford, F. James, 1924: 18)

















CHAPTER III
THE RESULT OF OBSERVATION

In this paper we have observation and asking to people around about the designed world for human life.
Location : Biology
Informant : Drs. Sulisetijono, M.Si
1. What is he definition of Mathematic?
Mathematic is number, universal. All the thins can be numbered although it will give different interpretation.
2. What are the relationships between Mathematic and science?
The basic of Mathematic is number, by using mathematic “number” we could fonish problems in science. In Biology, mathematic use to solve the biology problem that related with mthematic especially statistic
3. What is the common feature of mathematic and science especially in Biology?
The mathematic and Science especially Biology have the common feature, those common feature such as both of them have number although the number have different meaning for each. The mathematic and science both have logic thinking, in addition they also have imaginary thinking
4. What are the beauty of mathematics?
Some people will think that mathematics is very complicated. But actually, mathematic is universal it means that every things will include math on it world. Matematic has beauty and unique sides. For instance, in mathematical world there is pattern of number (aritmetic and geometric pattern). Thi is a beauty ‘unique’ side of mathematic but need extraordinary skill. Not only that, we know that time is an imaginary thing which can be revealed by using number.
Inquiry from Biology programe
Inquiry from Mathematics programe
There are 9 responndence:

INQUIRY
1. Do you like mathematics?
a. Yes
b. No
- Why?
*........................................................................................................................
2. What do you think about mathematics?
a. Mathematics is number c. Mathematics is universal
b. Mathematics is science d. A, B, C true all

3. Whats on your mind when you heard mathematics?
a. Wonderful c. Scary
b. Unique d. Complicated
4. Is mathematics important to be studied?
a. Yes
b. No
- Why?
*.....................................................................................................................

5. What important mathematics in your live?
a. 0 - 25 % c. 56 - 75 %
b. 26 - 50 % d. 76 - 100 %

Conclusion :
Question 1
- there are 5 persons answer yes and 4 person answer no

Question 2
- there are 4 persons answer d, 3 persons answer a, and 2 persons answer c
Question 3
- there are 4 persons answer a, 3 persons answer d, 1 person answer c, and 1person answer b

Question 4
- there are 8 persons answer a and 1 person answer b

Question 5
- there are 3 persons answer c and d, 2 persons answer b, and 4persons answer a

Date of interview: 28 Maret 2011
Interviewer : - Anisa Khumairo
- Dwi Tika Ratnasari
- Hikmah Maulidiya
- Lindawati P.
- Lutvi Riskita
Resource person : Bp. Abdurrahman Ashari

1. Whyt the mathematic is called has an universality?
Mathematic called has universality because it is not based on sense, by who, where, and to who but only bases on logic. The theory in mathematic could hold out if it can accepted by logic mind. So it can occur in the universe place.
2. What the mean of creativity in Mathemartic?
The word creativity derived from word create which in Indonesian languge mean ‘mencipta’. The mathematic is creative because it always to attempt to find the new pattern to create new theory.
3. What are the beauty of Mathematic?
There are many symmetri. We could see the bauty of Mathematic by see the pattern of this number below:
1 x 11+1= 12 has beautifull with 2 x 11 + 1= 23, and 3 x 11+1= 34. From those example we know that there is a pattern in the relationship. In other those, Mathematic also could change any compex thing to the simple thing.
4. How the mathematic formula could be found?
The mathematic formula could be found by experiment without thing. The mathematic always found it formula with the trial and error
7. How we could determinate that our formula is correct?
We could determinate that our formula is correct with use our blogic. As long as that theoty could be accepted by our logic so it is the correct theory. To proof that the theory is correct also could other way, i is to related many pattern. If by those pattern we could find the same yield with our formula so our formula is correct.
8. What the relation between symbol and number in mathematic?
Actually the number which we use in universal are a symbol, That symbol be agreed to be a tool to reveale the thing. The symbol also help us to reveslr sny thing in mathemstic which in the beginner visible complex be easier and simple.
9. What the relation of mathematic with advance of technology?
For intance, In the Belanda ever did an experiment to knew how much the microorganism are sucked by dengue mosquito with the microorganism that injected by mosquito bite. This experiment did to know the high possible for human contaminated the bleed fever. The mathematic helped to know the trth of hypotesis. This experiment has given the valuable contribution for the medical world.
10. What the definition of science in resource opinian?
The mathematic is learning of pattern.











CHAPTER IV
CLOSING


A. Conclusion

Be based on the study and discussion we done can conclude that:
Matematic relies on both logic and creativity, and it ipursued both for a variety of practical purposes and for its intrinsic interest. Mathematics is essentially a process of thinking that involves building and applying abstract, logically connected networks of ideas. The one of examples of the kinds of mathematical pattern that are available is the nature and use of number. Numbers and relationships among them can be represented in symbolic statements, which provide a way to model, investigate, and display real-world relationships. Fundamental geometrical shapes and relationships have corresponded symbolic representantion. Mathematic is the discipline knowledge which has relationship with the other knowledge such as science and technology.

B. Suggestion

1. Suggest that the mathematicians become more creative to produce new theory which could develope world.
2. Suggest that mathematicians will use mathematics in the right way.




RESOURCES
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J.Glen, John. 1987. Mathematical Models in Farm Planning: A Survey. (online), (http://JSTOR Operations Research, Vol_ 35, No_ 5 (Sep_ - Oct_, 1987), pp_ 641-666.mht), diakses 14 Maret 2011.
Ackermann W. 1928 Zum Hilbertschen Aufbau der reellen Zahlen. Mathematische Annalen 99 118–133. doi:10.1007/BF01459088
Aczel, P. & Rathjen M. (2001). Notes on constructive set theory. Technical report, Institut Mittag-Leffler. http://www.ml.kva.se/preprints/meta/AczelMon_Sep_24_09_16_56.rdf.html.