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Glyph for U+2305
Source: Noto Sans Symbols

U+2305 Projective

U+2305 was added to Unicode in version 1.1 (1993). It belongs to the block U+2300 to U+23FF Miscellaneous Technical in the U+0000 to U+FFFF Basic Multilingual Plane.

This character is a Other Symbol and is commonly used, that is, in no specific script.

The glyph is not a composition. It has a Neutral East Asian Width. In bidirectional context it acts as Other Neutral and is not mirrored. In text U+2305 behaves as Alphabetic regarding line breaks. It has type Other for sentence and Other for word breaks. The Grapheme Cluster Break is Any.

The Wikipedia has the following information about this codepoint:

In mathematics, the concept of a projective space originated from the visual effect of perspective, where parallel lines seem to meet at infinity. A projective space may thus be viewed as the extension of a Euclidean space, or, more generally, an affine space with points at infinity, in such a way that there is one point at infinity of each direction of parallel lines.

This definition of a projective space has the disadvantage of not being isotropic, having two different sorts of points, which must be considered separately in proofs. Therefore, other definitions are generally preferred. There are two classes of definitions. In synthetic geometry, point and line are primitive entities that are related by the incidence relation "a point is on a line" or "a line passes through a point", which is subject to the axioms of projective geometry. For some such set of axioms, the projective spaces that are defined have been shown to be equivalent to those resulting from the following definition, which is more often encountered in modern textbooks.

Using linear algebra, a projective space of dimension n is defined as the set of the vector lines (that is, vector subspaces of dimension one) in a vector space V of dimension n + 1. Equivalently, it is the quotient set of V {0} by the equivalence relation "being on the same vector line". As a vector line intersects the unit sphere of V in two antipodal points, projective spaces can be equivalently defined as spheres in which antipodal points are identified. A projective space of dimension 1 is a projective line, and a projective space of dimension 2 is a projective plane.

Projective spaces are widely used in geometry, as allowing simpler statements and simpler proofs. For example, in affine geometry, two distinct lines in a plane intersect in at most one point, while, in projective geometry, they intersect in exactly one point. Also, there is only one class of conic sections, which can be distinguished only by their intersections with the line at infinity: two intersection points for hyperbolas; one for the parabola, which is tangent to the line at infinity; and no real intersection point of ellipses.

In topology, and more specifically in manifold theory, projective spaces play a fundamental role, being typical examples of non-orientable manifolds.

Representations

System Representation
8965
UTF-8 E2 8C 85
UTF-16 23 05
UTF-32 00 00 23 05
URL-Quoted %E2%8C%85
HTML hex reference ⌅
Wrong windows-1252 Mojibake ⌅
HTML named entity ⌅
HTML named entity ⌅
LATEX \barwedge
Adobe Glyph List projective

Elsewhere

Complete Record

Property Value
Age 1.1 (1993)
Unicode Name PROJECTIVE
Unicode 1 Name
Block Miscellaneous Technical
General Category Other Symbol
Script Common
Bidirectional Category Other Neutral
Combining Class Not Reordered
Decomposition Type None
Decomposition Mapping Glyph for U+2305 Projective
Lowercase
Simple Lowercase Mapping Glyph for U+2305 Projective
Lowercase Mapping Glyph for U+2305 Projective
Uppercase
Simple Uppercase Mapping Glyph for U+2305 Projective
Uppercase Mapping Glyph for U+2305 Projective
Simple Titlecase Mapping Glyph for U+2305 Projective
Titlecase Mapping Glyph for U+2305 Projective
Case Folding Glyph for U+2305 Projective
ASCII Hex Digit
Alphabetic
Bidi Control
Bidi Mirrored
Composition Exclusion
Case Ignorable
Changes When Casefolded
Changes When Casemapped
Changes When NFKC Casefolded
Changes When Lowercased
Changes When Titlecased
Changes When Uppercased
Cased
Full Composition Exclusion
Default Ignorable Code Point
Dash
Deprecated
Diacritic
Emoji Modifier Base
Emoji Component
Emoji Modifier
Emoji Presentation
Emoji
Extender
Extended Pictographic
FC NFKC Closure Glyph for U+2305 Projective
Grapheme Cluster Break Any
Grapheme Base
Grapheme Extend
Grapheme Link
Hex Digit
Hyphen
ID Continue
ID Start
IDS Binary Operator
IDS Trinary Operator and
IDSU 0
ID_Compat_Math_Continue 0
ID_Compat_Math_Start 0
Ideographic
InCB None
Indic Mantra Category
Indic Positional Category NA
Indic Syllabic Category Other
Jamo Short Name
Join Control
Logical Order Exception
Math
Noncharacter Code Point
NFC Quick Check Yes
NFD Quick Check Yes
NFKC Casefold Glyph for U+2305 Projective
NFKC Quick Check Yes
NFKC_SCF Glyph for U+2305 Projective
NFKD Quick Check Yes
Other Alphabetic
Other Default Ignorable Code Point
Other Grapheme Extend
Other ID Continue
Other ID Start
Other Lowercase
Other Math
Other Uppercase
Prepended Concatenation Mark
Pattern Syntax
Pattern White Space
Quotation Mark
Regional Indicator
Radical
Sentence Break Other
Soft Dotted
Sentence Terminal
Terminal Punctuation
Unified Ideograph
Variation Selector
Word Break Other
White Space
XID Continue
XID Start
Expands On NFC
Expands On NFD
Expands On NFKC
Expands On NFKD
Bidi Paired Bracket Glyph for U+2305 Projective
Bidi Paired Bracket Type None
East Asian Width Neutral
Hangul Syllable Type Not Applicable
ISO 10646 Comment
Joining Group No_Joining_Group
Joining Type Non Joining
Line Break Alphabetic
Numeric Type None
Numeric Value not a number
Simple Case Folding Glyph for U+2305 Projective
Script Extension
Vertical Orientation U