Euclidean Geometry Geometry was thoroughly organized in about 300 BC‚ when the Greek mathematician Euclid gathered what was known at the time‚ added original work of his own‚ and arranged 465 propositions into 13 books‚ called ’Elements’. The books covered not only plane and solid geometry but also much of what is now known as algebra‚ trigonometry‚ and advanced arithmetic. Through the ages‚ the propositions have been rearranged‚ and many of the proofs are different‚ but the basic idea presented
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Euclid “Father of Geometry” Euclid is a Greek mathematician. He was also known as Euclid of Alexandria‚ “The Father of Geometry”. Little is known of his life other than the fact that he taught at Alexandria‚ being associated with the school that grew up there in the late 4th century B.C. It is believed that he taught at Plato’s academy in Athens‚ Greece. Most history states that he was a kind‚ patient‚ and fair man. One story that exposes something of his personality‚ involves
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Geometry is simply the study of space. There are Euclidean and Non-Euclidean Geometries. Euclidean geometry is the most common and is the basis for other Non-Euclidean types of geometry. Euclidean geometry is based on five main rules‚ or postulates. Differences in these rules are what make new kinds of geometries. There is Euclidean‚ Elliptic‚ and Hyperbolic Geometry. Euclidean geometry is the study of flat space and was invented by Euclid‚ a mathematician from Alexandria‚ in 330 B.C. Euclid described
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Non-Euclidean geometry is any form of geometry that is based on axioms‚ or postulates‚ different from those of Euclidean geometry. These geometries were developed by mathematicians to find a way to prove Euclid’s fifth postulate as a theorem using his other four postulates. They were not accepted until around the nineteenth century. These geometries are based on a curved plane‚ whether it is elliptic or hyperbolic. There are no parallel lines in non-Euclidean geometry‚ and the angles of triangles
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segment PQ: In Euclidean geometry the perpendicular distance between the rays remains equal to the distance from P to Q as we move to the right. However‚ in the early nineteenth century two alternative geometries were proposed. In hyperbolic geometry (from the Greek hyperballein‚ "to exceed") the distance between the rays increases. In elliptic geometry (from the Greek elleipein‚ "to fall short") the distance decreases and the rays eventually meet. These non-Euclidean geometries were later incorporated
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When it comes to Euclidean Geometry‚ Spherical Geometry and Hyperbolic Geometry there are many similarities and differences among them. For example‚ what may be true for Euclidean Geometry may not be true for Spherical or Hyperbolic Geometry. Many instances exist where something is true for one or two geometries but not the other geometry. However‚ sometimes a property is true for all three geometries. These points bring us to the purpose of this paper. This paper is an opportunity for me to
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Geometry III 1st Grading Period I. Undefined Terms 1. Point- though we represent a point with a dot‚ the point has no length‚ width‚ or thickness. A point is usually named with a capital letter. In the coordinate plane‚ a point is named by an ordered pair‚ (point A) . A 2. LINE –In geometry‚ a line has no thickness but its length extends in one dimension and goes on forever in both directions. A line is depicted to be a straight line with two arrowheads indicating that the line extends
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Module one- Lesson 01.01 The terms point‚ line‚ and plane are referred to as undefined. When you write the definition of these terms‚ you have to rely on other terms that need defining. Point- In general‚ a point is a location. Because points have no size‚ you can say they have no dimension. Line- a "stream" of points that has no width or depth. You can also think of a line as points lined up next to each other that go on forever in opposite directions. Because you can measure the distance
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Analytic geometry‚ or analytical geometry‚ has two different meanings in mathematics. The modern and advanced meaning refers to the geometry of analytic varieties. This article focuses on the classical and elementary meaning. In classical mathematics‚ analytic geometry‚ also known as coordinate geometry‚ or Cartesian geometry‚ is the study of geometry using a coordinate system and the principles of algebra and analysis. This contrasts with the synthetic approach of Euclidean geometry‚ which treats
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We use Euclidean and Non-Euclidean geometry in our everyday use. In many ways they are similar and different. There are similarities and differences in Euclidean geometry and spherical geometry‚ Euclid’s fifth postulate applies to both forms‚ and it is used every day in astronomy. Euclidean geometry is the study of flat space‚ and can be easily drawn on a piece of paper. Non-Euclidean geometry is any form of geometry that uses a postulate that is equivalent to the negation of Euclidean parallel postulate
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