Perspective in Triangles
18 Questions
0 Views

Choose a study mode

Play Quiz
Study Flashcards
Spaced Repetition
Chat to lesson

Podcast

Play an AI-generated podcast conversation about this lesson

Questions and Answers

What is the term used to describe a set of points incident with a line?

  • Pencil of lines
  • Range of points
  • Pencil of points (correct)
  • Perspectivity

    • What is the center of perspectivity?

  • The line containing the points of intersection
  • The axis of the perspectivity
  • The axis of the perspective
  • The point where the lines intersect (correct)

    • What is the term used to describe a set of lines incident with a point?

  • Pencil of points
  • Projectivity
  • Perspectivity
  • Pencil of lines (correct)

    • What is the definition of an elementary correspondence?

    <p>A one-to-one mapping between a pencil of points and a pencil of lines</p> Signup and view all the answers

    What is the term used to describe the line containing the points of intersection?

    <p>Axis of the perspectivity</p> Signup and view all the answers

    What is the main difference between projective and Euclidean geometry?

    <p>Euclidean geometry deals with parallel lines, while projective geometry deals with intersecting lines</p> Signup and view all the answers

    What is the primary characteristic of projective geometry that distinguishes it from Euclidean geometry?

    <p>Any two distinct lines intersect in at least one point</p> Signup and view all the answers

    In the context of projective geometry, what is a perspectivity?

    <p>A relationship between two pencils of points</p> Signup and view all the answers

    What is the term used to describe a one-to-one mapping between two pencils of points?

    <p>Elementary correspondence</p> Signup and view all the answers

    What is the result of projecting a figure through a pin hole?

    <p>The image is inverted</p> Signup and view all the answers

    What is the term for a set of lines that intersect at a point?

    <p>Pencil of lines</p> Signup and view all the answers

    What is the term used to describe the line containing the points of intersection of the corresponding lines of two pencils of lines?

    <p>Axis of perspectivity</p> Signup and view all the answers

    What is a quadrangle in the context of projective geometry?

    <p>A set of four points, no three of which are collinear</p> Signup and view all the answers

    What is the condition for two distinct lines to be incident with exactly one point?

    <p>They exist in Projective geometry</p> Signup and view all the answers

    What is the result of extending the sides of a 2D drawing of a tetrahedron?

    <p>Each pair of opposite sides intersect at a point</p> Signup and view all the answers

    What is a one-to-one mapping between two pencils of lines called?

    <p>Perspectivity</p> Signup and view all the answers

    What is the center of perspectivity?

    <p>The point where the lines intersect</p> Signup and view all the answers

    What is a one-to-one mapping between two pencils of points called, if it is a composition of finitely many elementary correspondences or perspectivities?

    <p>Projectivity</p> Signup and view all the answers

    More Like This

    Use Quizgecko on...
    Browser
    Open
    Browser
    Browser