Definitions for projective geometrypro·jec·tive geom·e·t·ry

Princeton's WordNetRate this definition:0.0 / 0 votes

1. projective geometry, descriptive geometrynoun

the geometry of properties that remain invariant under projection

WiktionaryRate this definition:0.0 / 0 votes

1. projective geometrynoun

a branch of mathematics that investigates those properties of figures that are invariant when projected from a point to a line or plane

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1. projective geometry

Projective geometry is a branch of non-Euclidean geometry that focuses on properties that remain invariant under projective transformations, a set of transformations also known as perspective transformations or the projections of a space onto another space. It deals with the properties and relationships of geometric objects that do not change under projective transformations, such as lines, points, and conics. It emphasizes the concepts of perspective and projection, and it includes both real and complex geometric elements and operations. It extends the concepts of traditional geometry and allows for the representation of points at infinity.

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1. Projective geometry

In mathematics, projective geometry is the study of geometric properties that are invariant under projective transformations. This means that, compared to elementary geometry, projective geometry has a different setting, projective space, and a selective set of basic geometric concepts. The basic intuitions are that projective space has more points than Euclidean space, in a given dimension, and that geometric transformations are permitted that move the extra points to traditional points, and vice versa. Properties meaningful in projective geometry are respected by this new idea of transformation, which is more radical in its effects than expressible by a transformation matrix and translations. The first issue for geometers is what kind of geometric language is adequate to the novel situation? It is not possible to talk about angles in projective geometry as it is in Euclidean geometry, because angle is an example of a concept not invariant under projective transformations, as is seen clearly in perspective drawing. One source for projective geometry was indeed the theory of perspective. Another difference from elementary geometry is the way in which parallel lines can be said to meet in a point at infinity, once the concept is translated into projective geometry's terms. Again this notion has an intuitive basis, such as railway tracks meeting at the horizon in a perspective drawing. See projective plane for the basics of projective geometry in two dimensions.

Numerology

1. Chaldean Numerology

The numerical value of projective geometry in Chaldean Numerology is: 1

2. Pythagorean Numerology

The numerical value of projective geometry in Pythagorean Numerology is: 6

Translations for projective geometry

From our Multilingual Translation Dictionary

• geometria proiettiva
• проективна геометрија
• проекти́вная геоме́трия
• projektivna geometrija

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"projective geometry." Definitions.net. STANDS4 LLC, 2024. Web. 21 Jun 2024. <https://www.definitions.net/definition/projective+geometry>.

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