Euclidean Geometry
Published on Nov 19, 2015
Euclidean geometry vs. Non-Euclidean Geometry
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PRESENTATION OUTLINE
Euclidean geometry is the type of geometry that concerns flat space.
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Euclidean geometry was created when Euclid wrote The Elements of Geometry in 300BC.
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The Elements was the the first textbook to systematically prove theories in geometry completely.
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It used a system where axioms and postulates, ideas that are so basic that they cannot be defined or explained, to draw more conclusions.
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Because of this, the Elements became the most popular math textbook. In order to be educated, you had to have understood the book.
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It was the second most printed book ever, second only to the *meaningful pause* Bible.
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Any two points can determine a straight line.
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Any finite straight line can be extended in a straight line.
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A circle can be determined from any center and any radius.
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All right angles are equal.
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If two straight lines in a plane are crossed by a transversal, and sum the interior
angle on the same side of the transversal is less than two right angles, then the two
lines extended will intersect.
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Things which equal the same thing also equal one another.
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If equals are subtracted from equals, then the remainders are equal.
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The whole is greater than the part.
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Every concept of geometry can be deduced from these.
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The fifth postulate has another form called the Parallel Postulate.
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Given a line and a
point not on the line, there is one and only one line that passes through the given point
that is parallel to the given line.
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However, this was the only postulate that hadn't been completely proven.
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This beckoned the thought, "What if any of these postulates are incorrect or incomplete?"
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1826, Nikolai Lobachevsky created a type of geometry in which the parallel postulate was untrue.
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Spherical geometry is a type of geometry where the plane is a sphere.
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This theory was developed by Bernhard Riemann in 1889.
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So any thing on a flat surface is Euclidean, while curved surfaces are not.
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Personally, I think each type of geometry has it's own place, however,
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It is also the easiest to understand, and the best starting point for geometry, and so the most relevant.
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