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In hyperbolic geometry how many lines are there parallel to a given line through a given point?
Wiki User
∙ 14y ago
infinitely many
Wiki User
∙ 14y ago
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What does it mean for a system to be consistent or inconsistent?
does it stay the same or not? Actually, a system is inconsistent if you can derive two (or more) statements within the system which are contradictory. Otherwise it is consistent. For example, Eucliadean geometry requires that given a line and a point not on that line, you can have one and only one line through the point which is parallel to the original line. However, you can have a consistent system of geometry if you assume that there is no such parallel line. This is known as the projective plane. You can assume that there will be an infinite number of parallel lines through a point not on the line. And again you can have a consistent system. Consistency or inconsistency has nothing whatsoever to do with time.
What is needed to determine a line?
Two points determine a line. Also there is one and only line perpendicular to given line through a given point on the line,. and There is one and only line parallel to given line through a given point not on the line.
A given line is always parallel to itself?
False.
To find a segment parallel to another segment and through a given point fold a piece of paper so that the fold goes through the point and the pieces of the segment on either side of the fold match?
The answer is FALSE i just did it on
Write an equation of the line containing the given point and parallel to the the given line6 and 7 3x plus y equals 8?
Given point: (6, 7) Equation: 3x+y = 8 Parallel equation: 3x+y = 25
What are the characteristics of hyperbolic geometry?
A.When represented on a Poincaré Disk, a line is an arc that has endpoints.B.There is an infinite number of lines parallel to a given line through a given point.C.It can be represented by a Poincaré Disk.Triangles have less than 180 degrees.
Why don't parallel lines exist in elliptical geometry?
Elliptical geometry is a non-Euclidean geometry. The parallel postulate of Euclidean geometry was replaced by the statement that through any point in the plane, there exist no lines parallel to a given line. A consistent geometry - of a space with positive curvature - was developed on that basis.It is, therefore, by definition that parallel lines do not exist in elliptical geometry.
What is eullidean geometry?
"Euclidean" geometry is the familiar "standard" geometry. Until the 19th century, it was simply "geometry". It features infinitely divisible space, up to three dimensions, and, most notably, the "parallel postulate": "Given a line, and a point not on the line, there is exactly one line that can be drawn through the point and parallel to the given line."
how to negate the hyperbolic parallel postulate?
The hyperbolic parallel postulate states that given a line L and a point P, not on the line, there are at least two distinct lines through P that do not intersect L.The negation is that given a line L and a point P, not on the line, there is at most one line through P that does not intersect L.The negation includes the case where there is exactly one such line - which is the Euclidean space.
What postulate is not of euclidean geometry?
Euclidean Geometry is based on the premise that through any point there is only one line that can be drawn parallel to another line. It is based on the geometry of the Plane. There are basically two answers to your question: (i) Through any point there are NO lines that can be drawn parallel to a given line (e.g. the geometry on the Earth's surface, where a line is defined as a great circle. (Elliptic Geometry) (ii) Through any point, there is an INFINITE number of lines that can be drawn parallel of a given line. (I think this is referred to as Riemannian Geometry, but someone else needs to advise us on this) Both of these are fascinating topics to study.
What is elliptical geometry and examples?
Elliptical geometry is like Euclidean geometry except that the "fifth postulate" is denied. Elliptical geometry postulates that no two lines are parallel.One example: define a point as any line through the origin. Define a line as any plane through the origin. In this system, the first four postulates of Euclidean geometry hold; through two points, there is exactly one line that contains them (i.e.: given two lines through the origin, there is one plane that contains them) and so on. However, it is nottrue that given a line and a point not on the line that there is a parallel line through the point (that is, given a plane through the origin, and a line through the origin, not on the plane, there is no other plane through the origin that is parallel to the given plane).
Which postulates led to the discovery of non-Euclidean geometry?
Adding to what Anand Mehta said, the negation of that statement has two interpretations. (i) there are zero lines through that point that are parallel to the given line (this is called Elliptic or Reimannian Geometry) (ii) there is an infinite number of lines that pass through the point and parallel to a given line (this is called Hyperbolic or Lobachevskian Geometry) I might add that the study of non-Euclidean Geometries are absolutely fascinating.
What is parallelogram in geometry?
It is a quadrilateral with parallel sides. This includes a square and rectangle, given that a side is parallel with another side.
What is Euclidean geometry mean in math?
Euclidean geometry is the traditional geometry: it is the geometry of a plane surface, as developed by Euclid. Among other things, it is based on Euclid's parallel postulate which said (in effect) that given a line and a point outside that line there could only be one line through that point that was parallel to the given line. It has since been discovered that both alternatives to that postulate - that there are many such lines possible and that there are none - give rise to consistent geometries. These are non-Euclidean geometries.
What are different ideas about geometry?
The main different ideas are based on Euclid's fifth postulates, more commonly known as the parallel postulate. Unlike his other postulates which are simple and self-evident, the parallel postulate is not.Along with the other postulates, the Fifth postulate is equivalent to the assertion that given a straight line and a point not on that line, there is exactly one line which goes through the given point and is parallel to the given line. A consistent geometry can be developed from these axioms.However, it is also possible to develop wholly consistent geometries with either of the two alternatives to the parallel postulate. One is that no such parallel lines exist and this gives rise to affine or projective geometries. The other is that there are more than one parallel lines and this gives rise to elliptic geometry.
How do you negate the euclidean parallel postulate?
Assume there are no lines through a given point that is parallel to a given line or assume that there are many lines through a given point that are parallel to a given line. There exist a line l and a point P not on l such that either there is no line m parallel to l through P or there are two distinct lines m and n parallel to l through P.
Through a point not on the line exactly one line can be drawn parallel to the?
... given line. This is one version of Euclid's fifth postulate, also known as the Parallel Postulate. It is quite possible to construct consistent systems of geometry where this postulate is negated - either many parallel lines or none.
