About: Euclid's Postulates   Sponge Permalink

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Euclid's postulates are a set of five postulates that describe Euclidian geometry. 1. * There exists a line that contains two points 2. * There exists a ray that contains two points 3. * One can draw a circle by picking a center point, and a distance 4. * All right angles (π∕2 radians) are congruent 5. * Given a straight line and a point, there exists one parallel line that passes through the point Some geometries, like hyperbolic geometry do not follow some, or all of these postulates.

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  • Euclid's Postulates
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  • Euclid's postulates are a set of five postulates that describe Euclidian geometry. 1. * There exists a line that contains two points 2. * There exists a ray that contains two points 3. * One can draw a circle by picking a center point, and a distance 4. * All right angles (π∕2 radians) are congruent 5. * Given a straight line and a point, there exists one parallel line that passes through the point Some geometries, like hyperbolic geometry do not follow some, or all of these postulates.
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  • Euclid's postulates are a set of five postulates that describe Euclidian geometry. 1. * There exists a line that contains two points 2. * There exists a ray that contains two points 3. * One can draw a circle by picking a center point, and a distance 4. * All right angles (π∕2 radians) are congruent 5. * Given a straight line and a point, there exists one parallel line that passes through the point Some geometries, like hyperbolic geometry do not follow some, or all of these postulates. Removing the parallel postulate (Axiom 5) gives a geometry called absolute geometry, of which hyperbolic geometry is an example. Removing the notions of distance and angle (Axioms 3 and 4) gives affine geometry. Removing distance, angle and parallel lines (Axioms 3, 4 and 5) gives ordered geometry.
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