Geometry: Lines and Line Segments
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Questions and Answers

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?

  • 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?

  • 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?

    <p>A part of a line delimited by two points (its endpoints)</p> Signup and view all the answers

    How did Euclid define a general line in his Elements?

    <p>'Breadthless length'</p> Signup and view all the answers

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