18 Questions
What is the term used to describe a set of points incident with a line?
Pencil of points
What is the center of perspectivity?
The point where the lines intersect
What is the term used to describe a set of lines incident with a point?
Pencil of lines
What is the definition of an elementary correspondence?
A one-to-one mapping between a pencil of points and a pencil of lines
What is the term used to describe the line containing the points of intersection?
Axis of the perspectivity
What is the main difference between projective and Euclidean geometry?
Euclidean geometry deals with parallel lines, while projective geometry deals with intersecting lines
What is the primary characteristic of projective geometry that distinguishes it from Euclidean geometry?
Any two distinct lines intersect in at least one point
In the context of projective geometry, what is a perspectivity?
A relationship between two pencils of points
What is the term used to describe a one-to-one mapping between two pencils of points?
Elementary correspondence
What is the result of projecting a figure through a pin hole?
The image is inverted
What is the term for a set of lines that intersect at a point?
Pencil of lines
What is the term used to describe the line containing the points of intersection of the corresponding lines of two pencils of lines?
Axis of perspectivity
What is a quadrangle in the context of projective geometry?
A set of four points, no three of which are collinear
What is the condition for two distinct lines to be incident with exactly one point?
They exist in Projective geometry
What is the result of extending the sides of a 2D drawing of a tetrahedron?
Each pair of opposite sides intersect at a point
What is a one-to-one mapping between two pencils of lines called?
Perspectivity
What is the center of perspectivity?
The point where the lines intersect
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?
Projectivity
Learn about the properties of triangles in perspective, including concurrent lines and pencils of points and lines. Test your understanding of geometric concepts and their applications.
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