Definition of Geometry.
Geometry (Greek; geo = earth, Metria = measure) is a part of mathematics that takes the issue of size, shape, and position as well as the nature of space. Geometry is one of the oldest sciences. Beginning a body of practical knowledge that is taking heavy with distance, area and volume, but in the 3rd century geometry is progressing on aksiometik form by Euclid, whose results are influential for the next several centuries.Geometry is one of the branches of the mathematical sciences. Science literally means geometry measurements of the Earth, which is the study of relationships in space. Indeed, the science of geometry already studied ancient Egyptian civilization, the people of the Indus River Valley and Babylonia.
This ancient civilizations known to have expertise in swamp drainage, irrigation, flood control and construction of buildings-large buildings. Most ancient Egyptians and Babylonians geometry is limited to the calculation of line segments length, area, and volume.
Brief History of Geometry.
There are at least six areas that can be seen as a 'source' geometry knowledge contributors, namely: Babylon (4000 BC - 500 BC), Greece (600 BC - 400 BC), Egypt (5000 BC - 500 BC), Jasirah Arabic (600 - 1500 AD), India (1500 BC - 200 BC), and China (100 BC - 1400). Of course there are still states that another contributor to the knowledge of geometry, however, is less significant or not recorded in the manuscript tradition.The Babylonians occupied the fertile region lying between the Euphrates and the Tigris in the Middle East region. At first, the area occupied by the Sumerians. At that time, 3500 BC, or about 5000 years ago has been living very advanced. Many buildings built as the town time now. Irrigation systems and rice farming has also grown. Geometry considered by engineers for development purposes.
Geometry is born and developed in Babylon is a result of the desires and expectations of government and religious leaders of the time. It is intended to be set up a variety of solid construction and great. Also hope for the king in order to control the land for the benefit of the tax revenue. Geometry techniques developed at that time in general is still rough and intuitive. However, quite accurate and can meet the needs of a variety of facts about the calculation of the techniques currently loaded geometry Ahmes Papyrus, written in approximately 1650 BC and discovered in the 9th century. Remains of this paper is a part of the goods stored by museums in London and New York. In this papyrus contained the formula of calculating the area of a rectangle, right triangle, trapezoid that has legs perpendicular to the base, as well as the approach to the calculation formula of the area of a circle. The Egyptians seem to have developed these formulas in their lives to calculate the area of cultivated fields.
In addition to continuing to develop geometry, they also developed a number system that we now know as 'sexagesimal' based 60. We still enjoy (and use) this system when talking about time.
They divided the day into 24 hours. One hour divided into 60 minutes. One minute divided into 60 seconds. We say, for example, is currently at 9 o'clock, 25 minutes, 30 seconds. When written will form at 9 25 '30 ", and in sexagesimal can be written as 9 5 25/60 30/3600. Systems has been using place value as we use today (in base 10 rather than in base 60).
The Babylonians developed a way of calculating area and volume. Among them calculate the circumference of a circle is equal to three times the length of its diameter. We know the price of these three approaches π price. Pythagorean formula has also been known at that time.
The Egyptians inhabit a very fertile region along the Nile. Agriculture is growing rapidly. The government needs a way to divide the rice plots fairly. Thus, the geometry developed here because it presents various polygon shapes that are customized to the situation in the region along the Nile river.
In Greece, the geometry experienced the 'emas' her. Around 2,000 years ago, found the theory that we know today by the name of axiomatic theories. Theory think that bases itself on the most basic things that we take for granted the truth. This kind of truth we call truth axiom. Axiom derived from a variety of basic arguments of the arguments and the arguments of both derivatives. From this era, we also share in the geometry book that has yet indisputable, namely Euclidean geometry. Geometry we teach formally in school is 'coffee-ness' of the Euclidean geometry.
In the early development of Islam, Islamic leaders encourage studying as much as possible. We learn to know as China. In that era, Islam spread in the Middle East, North Africa, Spain, Portugal, and Persian. The Islamic mathematicians contributed to the development of algebra, asronomi, and trigonometry. Trigonometry is one approach to resolving problems in algebraic geometry. We know her into analytic geometry. They also develop a polynomial.
In the eastern region, India and China are known contributor reliable mathematical knowledge. In India, the mathematician has the duty to make a variety of buildings burning to the victim at the altar. One of the conditions is a form of be (even should) be different but should be the same breadth. For example, create a burning building consisting of five levels and each level consists of 200 bricks. In between the two levels of the order should not be exactly the same brick. When it appeared geometry expert in India. Of course, the building was also equipped with a roof. The roof is also part Indian mathematician task. This is where developing theories of geometry.
Like the branches of other science, math (including geometry) also developed by Chinese scientists since 2000 BC (or about 4,000 years ago). While in Europe there is a book 'Elements', Euclidean geometry is able to penetrate the time 2000 years unchallenged, in the east, the Chinese are the Nine chapters on mathematical' created around the year 179 by Liu Hui. This book contains a lot of geometry problems. Among them calculate the area and volume. In the book explores the law of Pythagoras. Also a lot of talk about polygons.
At the mid-day, the Muslim mathematician contributed much on the development of geometry, especially algebraic geometry and algebraic geometry. Al-Mahani (1853) got the idea to describe the problem geometry as copying the cube to problems in algebra form. Thabit ibn Qurra (known as a Thebit in Latin) (836-901) arimetikal control to control the ratio of the quantity given to the geometry, and contribute on the development of analytic geomeri. Omar Khayyam (1048 -1131) for resolution geometry to find a cubic equation, and further investigation is the development of the largest Euclidean geometry instead.
In the early 17th century, there were two important developments in geometry. The first, and most important, is the creation of analic geometry, or geometry with coordinates and equations, by René Descartes (1596-1650) and Pierre de Fermat (1601-1665). This was the beginning that the need for the development of calculus. The second is a geometric progression systematic investigation of projective geometry by Girard Desargues (1591-1661). Projective geometry is geometry without measurement probe, Just by probing how the relationship between each other.
Two developments in geometry in the 19th century, changed the way he had learned previously. This is not Euclidean Geometry discovery by Lobachevsky, Bolyai and Gauss and of the formulation of symmetry as a primary consideration in the Erlangen Programme of Felix Klein (which concludes Euclid Euclidean geometry and not). Two of the experts geometry at that time was Bernhard Riemann, working in mathematical analysis, and Henri Poincaré, as the originator of the theory of geometric topology algebraik and dynamics of the system.
As a result of these major changes in the conception of geometry, the concept of "space" became something rich and distinct, and the background was originally only different theories such as complex analysis and classical mechanics. Traditional type of geometry has been known for sure as of a homogeneous space, namely the space it has a sufficient stock of symmetry, so that from the point to the point they look the same.
Characters Geometry.
1. Thales (640-546 BC).
At first geometry based solely born by experience. But the mathematician who first felt dissatisfied with the method based solely on experience is Thales (640-546 BC). Thales Mathematical Society now appreciate as a person who always say "Prove it" and even he was always doing that. Of the many theorems are:- The corners of the base of an isosceles triangle are congruent,
- The corners of the bracket is congruent,
- An angle that is expressed in a semi-circle is a right angle.
The work and principles Theles clearly have marked the beginning of an era of advancement of mathematics that develop deductive proof as logical reasons can be accepted. Deductive proof of the theorem is necessary to derive postulates. Furthermore, to formulate a new statement is logical.
2. Pythagoras (582-507 BC)
After the death of Thales came Pythagoras (582-507 BC) following his followers, known as the Pythagorean proceed step Thales. The Pythagorean method of proof is not only to develop the Pythagorean Theorem, but also to the theorems the angles in a polygon, the properties of parallel lines, theorems about the amounts are not comparable, and theorems about five solid wake irregular.3. Euclid (300 BC)
Not many people are lucky to have a lasting fame as Euclid, Greek geometer great. Although during his lifetime such figures as Napoleon, Martin Luther, Alexander the Great, far more famous than Euclid but in the long run may surpass all their fame called it.Besides fame, almost no detailed information about Euclid's life that can be known. For example, we know he's been active as a teacher in Alexandria, Egypt, around 300 BC, but when he was born and when he died really dark. In fact, we do not know in what continent and in what city he was born. Although he wrote several books and left them still there, its place in history is mainly located in the great book on geometry called The Elements.
In the Elements, Euclid combine school work he has to know with all the mathematical knowledge that he knew in a systematic comparison to be an amazing result. Most of the work is original, as the deductive method he demonstrated most of the required knowledge through reasoning. In Euclid's Elements was explaining algebra and number theory as well as he describes the geometry.
The importance of the book The Elements does not lie in the personal statement formulas are flung. Almost all theory contained in the book was never written one before, and also can be verified. Donations Euclid lies in the way of setting materials and problems as well as the overall formulation in planning the preparation of the book. Here involved, the most important, the selection of the arguments and the calculations, for example, about the possibility of drawing a straight line between two points.
Subsequently carefully and cautiously he set up the arguments so easily understood by the people afterward. When necessary, she provides instructions on how to split things unsolved and develop experiments to problems missed. It should be noted that the book The Elements other than primarily a development of rigorous geometry, also in addition it contains the parts about following extensive algebraic summation theory.
Books of The Elements is already the standard handbook of over 2000 years and is the most successful book ever compiled humans. Euclid compiled his book so great that from the shape alone is able to get rid of the books that never made before.
As a trainer tool logic of the human mind, the book The Elements is much more powerful than all the treatises of Aristotle's logic. The book is a complete example about the structure of deductive thinking and is a stunning piece of all the creations of the human brain.
Fair to say that the book of Euclid is an important factor for the growth of modern science. Science is not just a collection of observations carefully and not just generalize too sharp and wise. The results are taken large modern science comes from a combination of empirical investigation work and experiments on the one hand, with careful analysis and conclusions which have a strong base on the other.
Euclid influence on Sir Isaac Newton are felt at all, since Newton wrote the famous book by the name of The Principia in the form of geometry, similar to the Elements. Various scientists are trying to identify with the way Euclid shows how all of their conclusions logically originated from the original assumptions. Not unless what is done by mathematicians such as Russell, Whitehead and philosopher Spinoza.
Now, mathematicians already understand that the geometry of Euclid. is not the only system of geometry that is so basic and firm grip, and that can be planned as well, they also understand that during the last 150 years many people who formulate the geometry is not a la Euclid. Actually, since Einstein's theory of relativity was accepted by, the scientists realized that Euclidean geometry is not always true in the real application of the horizon problem.
At about the proximity of "black hole" and a neutron star - for example - which are in a high degree of gravity, Euclidean geometry does not give a thorough picture of the world, or do not show the exact translation of the space as a whole. However, these examples are rare, because in many ways the work of Euclid provides a probability estimate is closer to reality. Recent advancement of human knowledge is not the result of intellectual effort reduces both Euclid and of the importance of his position in history.
4. Scientists-Muslim Scientists
In the era of the Islamic Caliphate, Muslim scientists also helped develop the geometry. In fact, in the medieval era, the geometry is controlled by the Muslim mathematician. No wonder the Islamic civilization contributed a significant contribution to the development of that branch of modern mathematics.Achievement in the golden era of Islamic civilization in the field of geometry is extremely amazing. Why not. Researchers in the United States (U.S.) found that in the 15th century AD, Muslim scholars have used the crystal-like geometric patterns. In fact, modern mathematicians only recently discovered the pla design geometry in the 20th century AD
According to a study published in the journal Science, the golden era of Muslim mathematicians have demonstrated an important breakthrough in the field of mathematics and art design in the 12th century AD "It's very impressive," said Peter Lu, researchers from Harvard, the U.S., told the BBC.
Peter Lu revealed, the mathematicians and designers in the Muslim Caliphate era have been able to make the design of walls, floors and ceilings using tiles that reflect the use of mathematical formulas so sophisticated. '' Theory of the newly discovered 20 or 30 years ago, "he said.
Design in Islamic art uses geometric rules with crystal-like shape using polygon shape to create a symmetrical pattern. Until now, the general view is outstanding and intricate patterns star shaped polygon in Islamic art design is achieved by using a zigzag line drawn with a ruler and compass.
"You can see the development of these sophisticated geometric design. So they start with a simple design patterns, and long into the more complex," added Peter Lu. Peter Lu's discovery proves that Islamic civilization has been able to achieve remarkable progress in the field of geometry.
So how Muslim mathematicians developed the geometry? In the 9th century AD, the Muslim mathematician named Khwarizmi has developed geometry. Initially, studied the geometry of the leading mathematicians of the book entitled The Elements of Euclid's work. He then developed a variety of geometries and find new things in the study of relationships in space. Al-Khwarizmi invented the term secans and tangent in trigonometry and astronomy investigation. He also found a number system that is essential for the modern number system. In the Number System, al-Khwarizmi contains cosine terms, Sine and tangent to solve trigonometric equations, isosceles triangle theorem, calculation of area of a triangle, square and circle area calculation in geometry.
The study of al-Khwarizmi is considered as a major revolution in the world of mathematics. He connects the geometric concepts of ancient Greek mathematics into a new concept. Studies of al-Khwarizmi generate a combined theory that allows rational numbers / irrational, geometry quantities are treated as objects of algebra.
The study of al-Khwarizmi allow systematic application of algebra. For example, the application of arithmetic to algebra and vice versa, and the opposite algebra to trigonometry, algebra to number theory, algebra to geometry and vice versa. These studies underlie the creation of polynomial algebra, combinatorial analysis, numerical analysis, numerical solutions of equations, number theory, geometry and construction of the equation. The concept of geometry in mathematics introduced by al-Khwarizmi also very important in the field of astronomy. Because Astronomy is the science that studies the stars including position, movement, and interpretation related to the star. In order to calculate the position of the earth requires the calculation geometry.
Muslim scientists who contributed to developing the geometry of Thabit Ibn Qurra is. Muslim mathematician known as Thebit call it is also one of the leading Islamic scholars in the field of Geometry. He did important discoveries in the field of mathematics as integral calculus, trigonometry, analytic geometry, and the geometry of non-Eucledian.
One of the works of Thabit phenomenal in the field of geometry is his book The composition of Ratios (composition ratio). In the book, Thabit apply to the ratio between the quantity of arithmetic geometry. This thinking, far beyond the discovery of the ancient Greek scientist in the field of geometry.
Thabit donations to other geometry that is, the development of the theory of Pythagorean geometry in which he developed it from a right-angled triangle special to all right-angled triangles. Thabit also studied geometry to support the discovery curve required to form an image of the sun.
In addition, other Muslim scientists who contributed to developing the geometry is Ibn al-Haitham. In the field of geometry, Ibn al-Haitham develop analytical geometry linking geometry to algebra. In addition, he also introduced the concept of motion and transformation in geometry. Ibn al-Haitham theory in a square field is the first time that the theory of elliptic geometry and hyperbolic geometry. This theory is considered as a sign of the emergence of non-Euclidean geometry. The works of Ibn al-Haitham it affects the work of experts such as the geometry of the Persian Nasir al-Din al-Tusi and Omar Khayyam. However, the influence of Ibn al-Haytham do not stop in Asia alone. A number of European experts geometry as Gersonides, Witelo, Giovanni Girolamo Saccheri, John Wallis was affected and thought of al-Haitham. One of his leader in the science of geometry is Kitab al-Tahlil wa al'Tarkib.
Other Muslim scholars who contributed to developing Abu Nasr Mansur geometry is Ibn Ali ibn Iraq or commonly referred to as Abu Nasr Mansur. He merupakana one expert who studied the geometry of spherical geometry (geometry related to astronomy). Spherical geometry is very important to solve difficult problems in the Islamic astonomi. Muslims need to determine the proper time for prayer, Ramadan, as well as a good feast of Eid al-Adha and Eid. With the help of spherical geometry, Muslims are now able to estimate these times with ease.
So, thank you for reading this article. Written and posted by Bambang Sunarno.
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DatePublished: February 14, 2014 at 20:49
7MHPNPADAEFWTag ; Did you know Geometry History, geometry.
