What Is Geometry? Different Kinds Of Geometry and History Of Geometry

What is Geometry?

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Geometry is a branch of mathematics where research is done between the size and shape and the correlation of the various related objects. Geometry can be considered as a place or a science in the world. As we learn about the counting of our experience in the census, the description and explanation of our experience in space or the world in geometry is explained. Using the initial geometry, it is possible to calculate the area and range of two-dimensional different shapes and range of surfaces and the surface of the three-dimensional objects.

The most known of these undesirable concepts is the idea of ​​point, line and plane.

These basic ideas arise from our daily life experience. Where is an object? - In response to this question, we have to think about a specific, stable position. The term "dot" refers to the concept of our intuitive, fixed, fixed position. Many physical objects mark the point of the point. Such as the edges of a block-shaped object, the tip of the pencil, or the scrape on the paper. These things are considered to be the real, abstract, or model of the point-of-mind, abstract concept. Likewise, a tilt yarn, table edge, flank bar, etc., indicate many points in succession.

Different kinds of geometry

• Analytical geometry

Anthrax geometry is born from this perception, with some numerical and algebraic equations, point, line, and other geometric shapes can be pointed out. Using axes and coordinates, it is possible to point to points, lines and other shapes by drawing illustrations of the equations. For example, it is possible to pinpoint the position of a point by indicating distance from two axes in a perpendicular position. If a point is located 5 units away from the x-axis and 7 units from the y-axis, then its position is x = 7, y = 5, it is possible to point out the two equations. Similarly, a straight line is always indicated by an equation of ax + by + c = 0. There are more complex equations for circle, ellipsis, angle intersection and other shapes.

There are two types of problems in analytical geometry that are very common. The geometric details of how many points are given in the first type of problem, and from that point there is an algebraic equation that boils down to these points. The opposite of the second type of problem: From a given algebraic equation, there is a point combination that follows a geometric statement. For example, a circle with a radius of 3 whose coordinates of the x and y axis at the root point of the axis, all the points in it, will follow the x2 + y2 = 9 equation. Using such equations, other geometrical problems such as to find the right angle of an angle or segment, or to be perpendicular to a given point of a line, to draw the circle through three given inequal points, etc.

Likewise it is possible to point out points, lines and other images in three dimensions using three axes. In this case, the third axis or z axis is then perpendicular to the two axes.

Analytical geometry plays an important role in the development of mathematics. It combines geometry and spatial relationships with the relation of anthropometric mathematics. Analytical geometry strategies make geometric representation of numbers and algebraic expressions possible. As a result, there is a chance to see the new light in terms of calculus, function theory, and other higher mathematical problems. Non-Euclidean geometry and analysis of more than three dimensional geometries without analytical geometry could not be feasible.

• Insulator geometry

German mathematician Carl Friedrich Gauss started the insulatory geometry branch while solving the practical problems related to land surveys and geodesy. In this he used insulin calculus to identify the characteristics of curves and curves. For example, he has been mathematically demonstrating that the intrinsic curvature of a roller is the same as the curvature of a plane, because a hollow belon is cut into a plane after it is cut into a plane, but it can not be done without forming a sphere.

• Non-Euclidean Geometry

Euclid's fifth autocomplete is that it is possible to draw only one line parallel to that line by drawing an outer point of a given line, and this parallel line will never touch the given line, it will continue parallel to the infinite. At the beginning of the 19th century, German mathematician Carl Friedrich Gauss, Russian mathematician Niklai Ivanovich Lobachevsky and Hungarian mathematician Yonesh Balaiyyi independently show that it is possible to form a consistent geometric arrangement where this fifth assertion of Euclid can be replaced with another self-evident, which says that The outer boundary of the given line Line with an infinite number of parallel lines can be drawn. Later in 1860, German mathematician Georg Friedrich Bernhart Rimon showed that it is possible to create another geometric arrangement where such parallel lines can not be drawn.

The details of the two types of non-Euclidean geometry are quite complex, but it is possible to show them both through simple models. A geometric arrangement is discussed in the Bolian-Lobachevski geometry (often called hyperbolic gametes), all of which are limited to a circle, and whose all possible lines are the chords of the circle. Since the definition of two parallel lines stretches as much as possible, it never matches, and since hyperbolic geometry is not possible to stretch beyond the horizontal geometry, it is possible to draw an infinite number of lines parallel to any line with the outer points of the line.

Likewise, the geometric "world" or "world" in the remnant or elliptical non-euclidean geometry is the surface of a huge sphere where all the straight lines are the largest circles. It is impossible to draw a pair parallel line in this geometry.

For lesser distances, that is, in our daily experience, there is no difference between Euclidean and non-Euclidean geometry. However, non-Euclidean geometry can give a more accurate and accurate explanation of the observed events than Euclidean geometry to solve problems of cosmic distance and modern physics such as relativity problems. For example, Albert Einstein's theory of relativity is based on a rectangular geometry based on the crutch.

• Projection geometry

In the 17th century, another branch of geometry began to be discussed when discussing the relations between different geometrical objects and their projection. For example, conics can be transformed into projection through one projection. When you place a flashlight in a perpendicular fashion with a wall, it is a circular light;

Despite the projection of the projection, some of the geometrical images remain unchanged. What are these irreversible religions, so the theories of projection geometry are discussed.

• Geometry of four or more dimensions

Development of projection and analytical geometry encourages mathematicians to study geometry of the world of more than three dimensions. Many think that it is very difficult to think about such a multidimensional world. But mathematicians actually imagine them in a more easy way.

It is possible to place the position of any point in the physical world relative to three axes (commonly known as x, y, and z axis). Geometry of physical world space is therefore three dimensional.

If every point in this three-dimensional world is replaced with a sphere in imagination, then it becomes a four dimensional world. Because to indicate the location of each sphere, then there are four indicators: the x, y, and z coordinates of the spheres, and the radius length of the sphere.

Similarly, it is possible to present a three-dimensional world with a two-dimensional world. In this case, each point of two-dimensional world is replaced with a circle, and three dimensions of the three-dimensional world are the two coordinates of the center of the circle and its radius.

Geometrical concepts of more than three dimensional worlds play an important role in the development of physical science, especially the theory of relativity.

Analytical geometry is also applied in the study of balanced geometrical objects in the world of four or more dimensions. This geometry is called structural geometry. A simple example of organizational geometry is the definition of zero, one, two, three, four or more dimensional geometric objects in the universe, which can be defined by the least number of tops, lows and surfaces. Among them, the objects for the zero, one, two, and three dimensions are our known point, line, triangle and quadrilateral. For the world of four dimensions, it is shown that the topmost geometrical object has five tops, 10 bows and 10 surfaces.

History of Geometry

Ancient geometrists used to think about the problem of right angle diagnosis during the field of land zones and construction of houses. In ancient Egypt, the borders of the fields of the Nile dam were damaged every year and geometry help were restored for these borders. Such experimental geometry develops in ancient Egypt, Sumer, and Babylonia, and later sophisticated and systematic in the hands of the Greeks.

• Ancient geometry

The name of which is known as the first important geomatologist in history is Thalas of Miletus. Thales lived in Greece on 600 BC. Thales is regarded as the father of many simple but important theorems; One of them is the proof of the right angle at the right angle, which is the right angle.

Thalaysi first showed how to establish a geometrical truth by proceeding rationally from the publicly accepted statement (self-evident). Thales and his subsequent Greek geometrists considered these autocomputations to be self-proven. But in modern mathematical thought, these are considered as convenient but arbitrary estimates. The concept of Thales's ascending system is dominated by all geometrical studies, even in the whole of mathematical research till the present tense.

Pythagoras was a famous Thales student. Pythagoras and his associates prove many new theorems for triangles, circles, ratios, and some solid objects. Pythagoras' most famous theorem is now named after him and says that the sum of the sum of the square of the square of the ultraviolet of the right triangle is the sum of the sum of the bahubede.

The Greeks' proposed and accepted anecdotes were such as: "The smallest path between the two points is straightforward." From such axioms, logical lines, lines, corners, curves, and floors could have been reasonably reached in various sub-texts. However, in the 3rd century BC, Euclidy first published the various theoremic theorems and autobiographies under an integrated system and published it in his Elements. This book, written in 13 parchment rolls or book, is a sign of human dignity. About a thousand years of publication, mathematicians were able to add some significant development to them. In the twentieth century, Euclid's book was used as an early text of geometry. The importance of Euclid's work is not in his results, but in his way. Most of his proven theorem was known many years ago, but no one before him could show that they are all closely related and it is possible to reach them from a few initial initially. Euclid thus established the importance of ascending system through his work.

The Greeks simply invented geometrical image painting (anecdote) using the ruler and thorn-compass. Simple problems include drawing a line length of a given segment, dividing an angle, etc. The three famous problems of the Greeks have not been solved by mathematicians for many years: drawing a double cube of given cube, drawing a square of the area of ​​the given area of ​​the given circle, and converging an angle. None of these can be drawn with the help of rulers and thorns. The disparity in the classification of the circle was not proved before 1882.

Greek mathematician Pergar researched the connotation of the Apollunus cone and discovered many of these basic religions around 300 BC. Conics are useful in many fields of physical science. For example, any b-orbit orbit, such as the planets or the comet's direction, which are rotating around the sun, always stand on a type of conical. Critical satellites also circulate the elliptical direction of the Earth.

The great Greek scientist Archimedes contributed many geometry in the 3rd century BC. He used to find out the area of ​​several curved shapes and the circumference of the curved cubes, such as the area and size of the cylinder surface. It also introduced a method to evaluate Pi's imminent value and said that this value is between 3 10/70 and 3 10/71

• Geometry in the Middle Ages

Geometry in the 15th century

After the fall of the Roman Empire in the 5th century, geometry has not improved much in Europe until the 15th century. Europe has entered into the Dark Age and most of North Africa and Middle East Muslims and India's Hindus improved most of geometry. Most of the mathematical calculations are spread or broken. But some of them, such as Euclid's Elements, translate and study Muslims and Hindus. 6th century Indian mathematician Aryabhata Samdibhuju reiterated the sources of the triangle. He also donates a formula to the very best quality of Pi; He calculated the value of Pi 6282/20000, or 3.1416, which is the correct value of pi for four cells after the decimal. In the middle of the 4th and the 13th centuries, the theory of geometry was improved by utilizing the theory of trigonometry.

In the 12th and 13th centuries, Euclid's Elements were translated from Greek and Arabic into Latin and Modern European languages, and geometry education was added to religious education.

17th and 18th century geometry

French philosopher and mathematician Ron Descarte gave geometry forward. His influential compose Discourse on Method was published in 1637, where he presented the method of expression of geometrical shape with the help of coordinates. His work is connected between geometry and algebra. This link is the basis of analytical geometry and modern geometry.

Another important event in the 17th century geometry was the evolution of projection geometry. If projection geometry projection of a geometrical object from one floor to another, then it is studied about what changed its religion. Jarra Dajarg, a French engineer, invented projection geometry while studying the perspective. In the 18th century, a mathematical professor named Gaspar Moja invented another branch of geometry called descriptive geometry. How to represent 3D objects with a two-dimensional image in descriptive geometry, and how it can solve various problems of 3D geometry are discussed. This descriptive geometry is the foundation of drawing on engineering and architecture.

• Modern Geometry
  Analytical, projectional, and descriptive geometry arise within the framework of Euclidean geometry. For many centuries, mathematicians believed that the fifth parallel line of Euclid's unique parallel line can be proved from the remaining four unmatched, but all attempts to find this evidence have failed. But in the 19th century, the new geometric system was invented, where Euclid's fifth axiom was replaced with something else. These new types of non-Euclidean geometry led to the development of Karl Friedrich Gauss, Yanosh Bolyai, Niklai Labachevsky and Georg Friedrich Bernhart Rimon.

In 1872, German mathematician Félix Klein used a relatively new group group theory of mathematics to bring all the geometric systems of his time under one system. In 1899 another German mathematician David Hilbert released his book Foundations of Geometry, in order to provide a systematic arrangement of self-evacuations for Euclidean geometry, and it has a profound impact on other branches of mathematics.

According to Einstein's relativity theory in 1916, it is possible that many physical phenomena can be derived from geometric principles. The success of this theory brings about the inherent geometry and topology research.

British mathematician Arthur Kelly of the 19th century introduced four or more dimensional geometry. In the 19th century, the discussion of fractal levels began. In the 1970s, fractal geometry originated with the idea of ​​fractal, the new branch of geometry.

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Reference

1. Different kinds of Geometry, Web Document.
2. The History of Geometry, Web Document.
3. Geometry, Web Document.

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