Arkiv for februar 2016

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torsdag, 25. februar 2016

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onsdag, 17. februar 2016

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tirsdag, 16. februar 2016

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mandag, 15. februar 2016

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fredag, 12. februar 2016



Greek mathematician Euclid (300 B.C) is acknowledged with piloting the main in-depth deductive set up. Euclid’s way to geometry was made up of indicating all theorems in a finite wide variety of postulates (axioms).

Reasonably early 1800s other kinds of geometry started to appear, recognized as low-Euclidean geometries (Lobachevsky-Bolyai-Gauss Geometry).

The foundation of Euclidean geometry is:

  • Two factors assess a series (the least amount of distance between these two facts is really one original immediately series)
  • straight series may perhaps be long and no issue
  • Granted a place along with distance a circle are attracted from the level as center together with the range as radius
  • Fine perspectives are the same(the sum of the sides in a triangle equates to 180 degrees)
  • Provided a period p with a range l, there does exist exactly 1 series in p which happens to be parallel to l

The fifth postulate was the genesis of choices to Euclidean response In 1871, Klein finalized Beltrami’s operate on the Bolyai and Lobachevsky’s no-Euclidean geometry, also presented styles for Riemann’s spherical geometry.

Distinction of Euclidean & No-Euclidean Geometry (Elliptical/Spherical and Hyperbolic)

  • Euclidean: provided a model l and aspect p, you will find accurately model lines parallel to l due to p
  • Elliptical/Spherical: specific a set l and period p, there is not any path parallel to l through p
  • Hyperbolic: specific a line l and issue p, one can find infinite product lines parallel to l all through p
  • Euclidean: the wrinkles be at a frequent length from each other and are generally parallels
  • Hyperbolic: the lines “curve away” from the other and grow in length as you steps more from the areas of intersection however with perhaps the most common perpendicular as they are extra-parallels
  • Elliptic: the wrinkles “curve toward” the other and finally intersect together
  • Euclidean: the amount of the perspectives of any triangular is actually equal to 180°
  • Hyperbolic: the sum of the aspects from any triangular is unquestionably a lot less than 180°
  • Elliptic: the sum of the aspects of any triangular is definitely in excess of 180°; geometry in any sphere with terrific communities

Use of low-Euclidean geometry

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tirsdag, 9. februar 2016

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tirsdag, 9. februar 2016

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