Home U+2980 to U+29FF Miscellaneous Mathematical Symbols-B

# U+29E0Square with Contoured Outline

U+29E0 was added to Unicode in version 3.2 (2002). It belongs to the block U+2980 to U+29FF Miscellaneous Mathematical Symbols-B in the U+0000 to U+FFFF Basic Multilingual Plane.

This character is a Math Symbol and is commonly used, that is, in no specific script. The character is also known as D'Alembertian.

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+29E0 behaves as Alphabetic regarding line breaks. It has type Other for sentence and Other for word breaks. The Grapheme Cluster Break is Any.

In special relativity, electromagnetism and wave theory, the d'Alembert operator (denoted by a box: ◻ {displaystyle Box } ), also called the d'Alembertian, wave operator, box operator or sometimes quabla operator (cf. nabla symbol) is the Laplace operator of Minkowski space. The operator is named after French mathematician and physicist Jean le Rond d'Alembert.

In Minkowski space, in standard coordinates (t, x, y, z), it has the form

◻ = ∂ μ ∂ μ = η μ ν ∂ ν ∂ μ = 1 c 2 ∂ 2 ∂ t 2 − ∂ 2 ∂ x 2 − ∂ 2 ∂ y 2 − ∂ 2 ∂ z 2 = 1 c 2 ∂ 2 ∂ t 2 − ∇ 2 = 1 c 2 ∂ 2 ∂ t 2 − Δ     . {displaystyle {egin{aligned}Box &=partial ^{mu }partial _{mu }=eta ^{mu u }partial _{ u }partial _{mu }={frac {1}{c^{2}}}{frac {partial ^{2}}{partial t^{2}}}-{frac {partial ^{2}}{partial x^{2}}}-{frac {partial ^{2}}{partial y^{2}}}-{frac {partial ^{2}}{partial z^{2}}}\&={frac {1}{c^{2}}}{partial ^{2} over partial t^{2}}- abla ^{2}={frac {1}{c^{2}}}{partial ^{2} over partial t^{2}}-Delta ~~.end{aligned}}}

Here ∇ 2 := Δ {displaystyle abla ^{2}:=Delta } is the 3-dimensional Laplacian and ημν is the inverse Minkowski metric with

η 00 = 1 {displaystyle eta _{00}=1} , η 11 = η 22 = η 33 = − 1 {displaystyle eta _{11}=eta _{22}=eta _{33}=-1} , η μ ν = 0 {displaystyle eta _{mu u }=0} for μ ≠ ν {displaystyle mu eq u } .

Note that the μ and ν summation indices range from 0 to 3: see Einstein notation. We have assumed units such that the speed of light c = 1.

(Some authors alternatively use the negative metric signature of (− + + +), with η 00 = − 1 , η 11 = η 22 = η 33 = 1 {displaystyle eta _{00}=-1,;eta _{11}=eta _{22}=eta _{33}=1} .)

Lorentz transformations leave the Minkowski metric invariant, so the d'Alembertian yields a Lorentz scalar. The above coordinate expressions remain valid for the standard coordinates in every inertial frame.

## Representations

System Representation
10720
UTF-8 E2 A7 A0
UTF-16 29 E0
UTF-32 00 00 29 E0
URL-Quoted %E2%A7%A0
HTML hex reference &#x29E0;
Wrong windows-1252 Mojibake â§
alias D'Alembertian

## Complete Record

Property Value
Age 3.2 (2002)
Unicode Name SQUARE WITH CONTOURED OUTLINE
Unicode 1 Name
Block Miscellaneous Symbols
General Category Math Symbol
Script Common
Bidirectional Category Other Neutral
Combining Class Not Reordered
Decomposition Type None
Decomposition Mapping Square with Contoured Outline
Lowercase
Simple Lowercase Mapping Square with Contoured Outline
Lowercase Mapping Square with Contoured Outline
Uppercase
Simple Uppercase Mapping Square with Contoured Outline
Uppercase Mapping Square with Contoured Outline
Simple Titlecase Mapping Square with Contoured Outline
Titlecase Mapping Square with Contoured Outline
Case Folding Square with Contoured Outline
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 Square with Contoured Outline
Grapheme Cluster Break Any
Grapheme Base
Grapheme Extend
Hex Digit
Hyphen
ID Continue
ID Start
IDS Binary Operator
IDS Trinary Operator and
Ideographic
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 Square with Contoured Outline
NFKC Quick Check Yes
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
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 Square with Contoured Outline
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 Square with Contoured Outline
Script Extension
Vertical Orientation R