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# 5 parallelism

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# 5 parallelism

a cura della classe IE scientifico a.s. 2011-12 con la guida della prof.ssa M. Montanarelli

a cura della classe IE scientifico a.s. 2011-12 con la guida della prof.ssa M. Montanarelli

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### 5 parallelism

1. 1. Parallelism is a term in geometry that refers to a propiety in Euclidean space of two or more lines or planes, or a combination of these. The assumed existence and properties of parallel lines are the basis of euclid’s parallel postulate. Two lines in a plane that do not intersect or tuch at a point are called parallel lines.
2. 2. Eucliden Parallelism • Given straight lines / and m, the following description of line m equivalently define it as parallel to line / in Euclidean space: • Lines m and / are both intersected by a third straight line ( a trasversal ) in the same plane, and corresponding angles of intersection whit the trasversal are equal. ( this is equivalent to euclid’s parallel postulate).
3. 3. Ellictical geometry In the spherical plane, all geodesics are great circles. Great circles divide the sphere in two equal hemispheres and all great circles intersect each other. Equidistant line on the sphere are called parallels of latitude in analog to latitude lines on a globe.
4. 4. Hyperbolic geometry • The Poincare disc model, also know as the conformal disc model, also employs the interior of a circle, but lines are rapresented by arcs of a circles that are orthogonal to the boundary circle, plus diameters of the boundary circle.
5. 5. Perpendicular • In geometry, two lines or planes ( or a lines and a plane ) are considered perpendicular ( or orthogonal ) to each other if they form congruent adjacent angles.
6. 6. REALIZZATO DA ABBONDANZA MARCO BORRACINO SIMONE LOZITO ALESSANDRO MALLARDI SABINO PARADISO LORENZO