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In geometry, how are lines defined in terms of dimension?
In geometry, how are lines defined in terms of dimension?
- Spaces of dimension three, which may be embedded in spaces of dimension one or two
- Spaces of dimension one, which may be embedded in spaces of dimension two, three, or higher (correct)
- Spaces of dimension two, which may be embedded in spaces of dimension one or three
- Spaces of dimension one, which cannot be embedded in any other dimension
What is the definition of a straight line in Euclid's Elements?
What is the definition of a straight line in Euclid's Elements?
- A 'breadthless length' that 'lies evenly with respect to the points on itself' (correct)
- A line segment delimited by two points
- An infinitely long object with no width, depth, or curvature
- A curve that is 'breadthless length'
What does the term 'Euclidean line' refer to?
What does the term 'Euclidean line' refer to?
- A curved line in non-Euclidean geometry
- A line in Euclidean geometry introduced to avoid confusion with generalizations (correct)
- A line segment in projective geometry
- An infinitely long object with no width, depth, or curvature
What is a line segment?
What is a line segment?
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How did Euclid define a general line in his Elements?
How did Euclid define a general line in his Elements?
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