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Why is the parallel axiom in Euclid's geometry false in non-Euclidian geometry?
Wiki User
∙ 13y ago
Euclid's parallel axiom is false in non-Euclidean geometry because non-Euclidean geometry occurs within a different theory of space. There may be one absolute occurrence in non-Euclidean space where Euclid's parallel axiom is valid. Possibly as some form of infinity.
Wiki User
∙ 13y ago
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Are two lines that are parallel to the same line parallel to each other?
Yes they are. It is delineated in something called the parallel postulate, and the axiom is also called Euclid's fifth postulate. This is boilerplate Euclidean geometry, and a link can be found below if you'd like to review the particulars.
Through a given point not on a given line there is exactly one line parallel to the given line?
The Playfair Axiom (or "Parallel Postulate")
A statement we accept as true without proof is a?
it is called an axiom
Who restated Euclid's 5th postulate?
Probably the best known equivalent of Euclid's parallel postulate, contingent on his other postulates, is Playfair's axiom, named after the Scottish mathematician John Playfair, which states:In a plane, given a line and a point not on it, at most one line parallel to the given line can be drawn through the point.
What is a statement that is accepted as truw without proof?
axiom
What statement is accepted without proof geometry?
An axiom.
Do parrallel lines meet?
Not in Euclidean Geometry. Euclid's 5th axiom is that parallel lines never meet. However, unlike the first 4 axiom, it is impossible to prove the 5th axiom; depending upon the situation, you can either assume that parallel lines meet or don't; when they do meet, there are some very interesting consequences (for example, the possibility of a hyperbolic space). To my knowledge, if they meet, they are intersecting/perpendicular lines.
What is two point form of a line?
An axiom of Euclidean geometry.
Are two lines that are parallel to the same line parallel to each other?
Yes they are. It is delineated in something called the parallel postulate, and the axiom is also called Euclid's fifth postulate. This is boilerplate Euclidean geometry, and a link can be found below if you'd like to review the particulars.
What is a sentence for the word axiom?
"A geometry rule that we accept to be true without any proof is called an axiom." "The axiom 'might makes right' is often true in the governments of the world.
What is another name for the parallel postulate?
Playfair Axiom
Another name for the Playfair Axiom?
parallel postulate
What is another name for the Playfair Axiom?
Parallel Postulate
How does parallels lines meet?
It is an axiom that parallel lines never meet in Euclidean geometry. Never.However in another kind of geometry (can't remember name) it states that parallel lines will eventually meet.Take a look at this picture in the related link, below.Technically the lines are parallel (in theory, they have imperfections), but due to our perspective parallel lines appear to meet. Note: If they really do meet, then you could drive down the road and eventually there would not be a road, anymore.
Is axiom a fundamental truth?
An axiom, in Geometry, is a statement that we assume is true. Whether it is actually true or not is irrelevant. For the purpse of solving the problem, it is considered to be true.
Through a given point not on a given line there is exactly one line parallel to the given line?
The Playfair Axiom (or "Parallel Postulate")
Why is the postulate 5 in the Euclid axiom considered to be universal truth?
It is NOT considered a universal truth. It used to be, because mathematicians considered it to be "self-evident", but more recently, mathematical systems both with and without the parallel axiom have been developed. It turns out the "non-euclidian geometries" are very useful. In the real world, the euclidian geometry does NOT apply - although in many cases it is a good approximation.
