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What are the postulates that non-Euclidean geometry is based on?
Wiki User
∙ 14y ago
Non-Euclidean geometries are based on the negation of his parallel postulate (his fifth postulate). The other Euclidean postulates remain.
A rephrasing of Euclid's parallel postulate is as follows:
For any given line â„“ and a point A, which is not on â„“, there is exactly one line through A that does not intersect â„“. (The other postulates confirm the existence of â„“ and A.)
One set of alternative geometries (projective geometry, for example) is based on the postulate that there are no such lines. Another set of is based on the postulate of an infinite number of lines.
Wiki User
∙ 14y ago
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Euclids geometry has been questioned but never has a nonEuclidean geometry been accepted as a valid possibility?
false
In geometry what is postulates?
dkjdf
What is a statement accepted as true in geometry?
postulates
What are the properties of geometry?
logic postulates theorems
What is the name for an underlying assumption in geometry?
postulates
Why are postulates not proved in geometry?
postulates cannot be proved, they are the base of geometry and there isn't anything to prove it with. if the postulates were wrong then all of euclidian geometry would be wrong. that is like saying how do we know the English language is correct, it is the basis for communication and if it wasn't, then how would speaking the language work?
Do postulates need to be proven?
No. Postulates are the foundations of geometry. If you said they were wrong then it would be saying that Euclidean geometry is wrong. It is like if you asked how do we know that English is right. It is how the English language works. So no postulates do not need to be proven.
Do Postulates need to proven?
No. Postulates are the foundations of geometry. If you said they were wrong then it would be saying that Euclidean geometry is wrong. It is like if you asked how do we know that English is right. It is how the English language works. So no postulates do not need to be proven.
What is not a postulate euclidean geometry apex?
The axioms are not postulates.
What is the difference between a postulate and theorem in Geometry?
A postulate is assumed to be true while a theorem is proven to be true. The truth of a theorem will be based on postulates.
What is ruler placement postulates?
The ruler placement postulate is the third postulate in a set of principles (postulates, axioms) adapted for use in high schools concerning plane geometry (Euclidean Geometry).
Why is it necessary to use postulates in geometry?
Postulates are statements that prove a fact. An example would be that 2 points create a line segment. You usually use postulates in proofs.
