Physical meaning of geometrical proposition

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  • Thread starter Thread starter Shubham Raj22
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Discussion Overview

The discussion revolves around the geometric proposition regarding the relationship between straight lines and points, specifically whether a straight line can be defined as passing through only two points. The scope includes conceptual clarification and foundational principles of Euclidean geometry.

Discussion Character

  • Conceptual clarification, Debate/contested

Main Points Raised

  • One participant questions whether a straight line goes through only two points, seeking clarification on the concept.
  • Another participant asserts that a straight line actually passes through infinitely many points.
  • A third participant adds that while there is only one straight line that can pass through a given pair of points in Euclidean geometry, the initial question may have been misunderstood due to language barriers.
  • A later reply notes that the idea of a single line through two points is an axiom of Euclidean geometry, emphasizing that it serves as a foundational starting point without requiring proof.

Areas of Agreement / Disagreement

Participants express differing views on the interpretation of the original question, with some agreeing on the axiom of Euclidean geometry while others focus on the broader implications of lines and points.

Contextual Notes

There is a potential misunderstanding regarding the phrasing of the initial question, which may have led to varied interpretations among participants.

Shubham Raj22
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Is it true that one straight line goes through only 2 points??
If no then how ?? If yes then why??
 
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No. A straight line goes through a lot of points. Infinitely many.
 
To add slightly to what @BvU said, it is true that there is only one straight line passing through a given pair of points. In Euclidean geometry, at least.
 
Yes, my reply was a bit corny. I understand english is not your native language and you meant something else than what the post litterally states. It shows that accurate communication isn't easy, to say the least.

In fact, this is one of the axioms (or postulates) of euclidean geometry. The first axiom, even. As such there is no proof or reason why - except that it's a reasonable thing to state. It is a starting point for a huge construct, namely geometry as we commonly know it (there are others, such as projective geometry).
 

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