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

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. 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. 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. 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. 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. REALIZZATO DA
ABBONDANZA MARCO
BORRACINO SIMONE
LOZITO ALESSANDRO
MALLARDI SABINO
PARADISO LORENZO