Specifying Special Characters and Mathematical Symbols Because HTML files are in ASCII, you cannot introduce special characters and mathematical symbols into your documents simply by typing them in. Also some characters (such as the < sign) are interpreted as markup. Instead, you need to instruct the browser to look up a string (called an entity) as it renders a document and replace it with equivalent characters from a character table. This is done by starting the string with with an ampersand (&) and ending it with a semicolon (;). The browser uses the characters enclosed by these signs to lookup and display the requested character or symbol. Note that HTML is case-sensitive when producing special characters from a string. This means that   renders a different character than &NBSP. Mathematical expressions are created using the MATH tag in conjunction with entities. HTML provides the following types of entities and tags to specifying special characters and mathematical symbols: * (Draw Symbol Above) draws an arrow, line, or symbol above the enclosed text. * (Draw Array) draws an array in a mathematical expression. * (Bold Text) indicates that the enclosed text be displayed in a boldface. * (Draw Bar) draws a bar over the enclosed text. * (Draw Symbol Below) draws an arrow, line, or symbol below the enclosed text. * (Draw Box) draws a box around the enclosed text. * (Bold Upright Text) indicates that the enclosed text be displayed in a boldface upright text. * (Draw Double Dot) draws a double dot over the enclosed text. * (Draw Dot) draws a dot over the enclosed text. * Graphic Entities (Markup and Other Characters) represents characters that are used to indicate markup and other special symbols or spacing. * (Draw Hat) draws a hat over the enclosed text. * ISO Latin 1 Character Entities (Special Characters) creates special diacritical marks for non-English languages. * (Mathematical Expression) defines the enclosed text as a mathematical expression. * Math and Spacing Entities (Mathematical Symbols and Special Spacing) specifies symbols and spacing used in mathematical expressions and notation. * Numerical Entities (Special Symbols) reproduces higher order ASCII characters (codes higher than 127), non-ASCII charater types, and special diacritical marks for non-English languages. * (Draw Root) draws a root symbol around the enclosed text. * (Draw Square Root) draws a square root symbol around the enclosed text. * (Subscript Text) creates text that is shown as a subscript. * (Superscript Text) creates text that is shown as a superscript. * (Upright Text) indicates that the enclosed text be displayed in an upright text. * (Include Text) includes a short piece of text within a math expression. * (Draw Tilde) draws a tilde symbol around the enclosed text. * (Draw Vector) draws a vector around the enclosed text. --------------------------------------------------------------------------- (Draw Symbol Above) To draw an arrow, line, or symbol above a mathematical expression, use the ABOVE tag. You should place the ABOVE tag within the MATH tag. Syntax ... Proposed for inclusion in a future version of the HTML standard. --------------------------------------------------------------------------- (Draw Array) Use the ARRAY tag to draw an array in a mathematical expression. You should place the ARRAY tag within the MATH tag. Syntax ... Proposed for inclusion in a future version of the HTML standard. --------------------------------------------------------------------------- (Bold Text) The B tag displays enclosed text in a boldface font. You should place the B tag within the MATH tag. Syntax ... Proposed for inclusion in a future version of the HTML standard. --------------------------------------------------------------------------- (Draw BAR) To draw an bar above a mathematical expression, use the BAR tag. You should place the BAR tag within the MATH tag. Syntax ... Proposed for inclusion in a future version of the HTML standard. --------------------------------------------------------------------------- (Draw Symbol Below) To draw an arrow, line, or symbol below a mathematical expression, use the BELOW tag. Use the BELOW tag only within the MATH tag. Syntax ... Proposed for inclusion in a future version of the HTML standard. --------------------------------------------------------------------------- (Draw Box) To draw box around a mathematical expression, use the BOX tag. Place the BOX tag within the MATH tag. Syntax ... Proposed for inclusion in a future version of the HTML standard. --------------------------------------------------------------------------- (Bold Upright Text) To display text in a bold, upright font, use the BT tag. You should place the BT tag within the MATH tag. Syntax ... Proposed for inclusion in a future version of the HTML standard. --------------------------------------------------------------------------- (Draw Double Dot) Use the DDOT tag to draw a double dot in a mathematical expression. You should place the DDOT tag within the MATH tag. Syntax ... Proposed for inclusion in a future version of the HTML standard. --------------------------------------------------------------------------- (Draw Dot) To draw dot above a mathematical expression, use the DOT tag. Nest the DOT tag within the MATH tag. Syntax ... Proposed for inclusion in a future version of the HTML standard. --------------------------------------------------------------------------- Graphic Entities (Markup and Other Characters) To display characters in your document that are used to indicate markup, or to create other characters or spacing, use the following entities. NameSyntax Description lt < Less than sign gt > Greater than sign amp & Ampersand quot" Double quote sign em   em space (equivalent to two space characters) en   en space (equivalent to a single character space) nbsp  non-breaking space reg ® registered trademark copy© copyright Implementation Implemented under HTML 2.0. The  ,  , ®, and © entities are proposed for inclusion in a future version of the HTML standard, and implemented in Netscape Navigator 2.0 and above. --------------------------------------------------------------------------- (Draw Hat) To draw hat above a mathematical expression, use the HAT tag. You should place the HAT tag within the MATH tag. Syntax ... Proposed for inclusion in a future version of the HTML standard. --------------------------------------------------------------------------- ISO Latin 1 Character Entities (Special Characters) Use the following entities to create special diacritical marks for non-English languages. Name Syntax Description AacuteÁ Capital A, acute accent AgraveÀ Capital A, grave accent Acirc  Capital A, circumflex accent Atildeà Capital A, tilde Aring Å Capital A, ring Auml Ä Capital A, dieresis or umlaut mark AElig Æ Capital AE dipthong (ligature) CcedilÇ Capital C, cedilla EacuteÉ Capital E, acute accent EgraveÈ Capital E, grave accent Ecirc Ê Capital E, circumflex accent Euml Ë Capital E, dieresis or umlaut mark IacuteÍ Capital I, acute accent IgraveÌ Capital I, grave accent Icirc Î Capital I, circumflex accent Iuml Ï Capital I, dieresis or umlaut mark ETH Ð Capital Eth, Icelandic NtildeÑ Capital N, tilde OacuteÓ Capital O, acute accent OgraveÒ Capital O, grave accent Ocirc Ô Capital O, circumflex accent OtildeÕ Capital O, tilde Ouml Ö Capital O, dieresis or umlaut mark OslashØ Capital O, slash UacuteÚ Capital U, acute accent UgraveÙ Capital U, grave accent Ucirc Û Capital U, circumflex accent Uuml Ü Capital U, dieresis or umlaut mark YacuteÝ Capital Y, acute accent THORN Þ Capital THORN, Icelandic szlig ß Small sharp s, German (sz ligature) aacuteá Small a, acute accent agraveà Small a, grave accent acirc â Small a, circumflex accent atildeã Small a, tilde atildeã Small a, tilde auml ä Small a, dieresis or umlaut mark aelig æ Small ae dipthong (ligature) ccedilç Small c, cedilla eacuteé Small e, acute accent egraveè Small e, grave accent ecirc ê Small e, circumflex accent euml ë Small e, dieresis or umlaut mark iacuteí Small i, acute accent igraveì Small i, grave accent icirc î Small i, circumflex accent iuml ï Small i, dieresis or umlaut mark eth ð Small eth, Icelandic ntildeñ Small n, tilde oacuteó Small o, acute accent ograveò Small o, grave accent ocirc ô Small o, circumflex accent otildeõ Small o, tilde ouml ö Small o, dieresis or umlaut mark oslashø Small o, slash uacuteú Small u, acute accent ugraveù Small u, grave accent ucirc û Small u, circumflex accent uuml ü Small u, dieresis or umlaut mark yacuteý Small y, acute accent thorn þ Small thorn, Icelandic yuml ÿ Small y, dieresis or umlaut mark Implementation Implemented under HTML 2.0. --------------------------------------------------------------------------- (Mathematical Expression) Use the MATH tag in your document to indicate mathematical expressions. Mathematical symbols are created by using mathematical entities. You can further define and specify an expression by using the following tags nested within : * ABOVE * ARRAY * B * BAR * BELOW * BOX * BT * DDOT * DOT * HAT * ROOT * SQRT * SUB * SUP * T * TEXT * TILDE * VEC You should place the MATH tag within the BODY tag. Syntax ... Use the following optional attributes for the tag: * BOX draws a rectangle around the mathematical expression. * CLASS="type" identifies and further specifies the characteristics of a mathematical expression, thereby allowing the extension of HTML tags for different purposes. This is especially useful in the construction of style sheets. You can specify multiple classes (i.e. subclasses) for a heading by separating class names with a period. * ID="location" designates a location in the mathematical expression as a destination for a link. This attribute replaces the tag . Proposed for inclusion in a future version of the HTML standard. --------------------------------------------------------------------------- Math and Spacing Entities (Mathematical Symbols and Special Spacing) The following entities display mathematical symbols and special spacing: Syntax Description &ldots; three dots on the baseline &cdots; three dots on same level as a minus sign &vdots; three vertical dots &ddots; diagonal dots (top left to bottom right) &dotfill; like cdots but fills column in an array   thin space &sp; medium space   thick space   thin space &quad; huge space   non-breaking space α alpha β beta γ gamma δ delta ε epsilon &vepsilon; var epsilon ζ zeta η eta θ theta &vtheta; var theta ι iota κ kappa λ lambda μ mu ν nu ξ xi ο omicron π pi ϖ var pi ρ rho ϱ var rho σ sigma &vsigma; var sigma τ tau υ upsilon φ phi ϕ var phi χ chi ψ psi ω omega Implementation Proposed for inclusion in a future version of the HTML standard. --------------------------------------------------------------------------- Numerical Entities (Special Symbols) Use the following entities to display higher order ASCII characters (with codes higher than 127), non-ASCII character types, and special diacritical marks for non-English languages. Name Description �-  Unused Horizontal tab Line feed - amp;#31; Unused &32; Space &33; Exclamation mark &34; Quotation mark &35; Number sign &36; Dollar sign &37; Percent sign &38; Ampersand &39; Apostrophe &40; Left parenthesis &41; Right parenthesis &42; Asterisk &43; Plus sign &44; Comma &45; Hyphen &46; Period (fullstop) &47; Solidus (slash) 0 - 9 Digits 0-9 &58; Colon &59; Semi-colon &60; Less than &61; Equals aign &62; Greater than &63; Question mark &64; Commercial at A- Z Letters A-Z &91; Left square bracket &92; Reverse solidus (backslash) &93; Right square bracket &95; Horizontal bar &96; Acute accent a- z Letters a-z &123; Left curly brace &124; Vertical bar &125; Right curly brace &126; Tilde -   Unused &161; Inverted exclamation &162; Cent sign &163; Pound sterling &164; General currency sign &165; Yen sign &166; Broken vertical bar &167; Section sign &168; Umlaut (dieresis) &169; Copyright &170; Feminine ordinal &171; Left angle quote, guillemotleft &172; Not sign &173; Soft hyphen &174; Registered trademark &175; Macron accent &176; Degree sign &177; Plus or minus &178; Superscript two &179; Superscript three &180; Acute accent &181; Micro sign &182; Paragraph sign &183; Middle dot &184; Cedilla &185; Superscript one &186; Masculine ordinal &187; Right angle quote, guillemotright &188; Fraction one-fourth &189; Fraction one-half &190; Fraction three-fourths &191; Inverted question mark &192; Capital A, acute accent &193; Capital A, grave accent &194; Capital A, circumflex accent &195; Capital A, tilde &196; Capital A, ring &197; Capital A, dieresis or umlaut mark &198; Capital AE dipthong (ligature) &199; Capital C, cedilla &200; Capital E, acute accent &201; Capital E, grave accent &202; Capital E, circumflex accent &203; Capital E, dieresis or umlaut mark &204; Capital I, acute accent &205; Capital I, grave accent &206; Capital I, circumflex accent &207; Capital I, dieresis or umlaut mark &208; Capital Eth, Icelandic &209; Capital N, tilde &210; Capital O, acute accent &211; Capital O, grave accent &212; Capital O, circumflex accent &213; Capital O, tilde &214; Capital O, dieresis or umlaut mark &215; Multiply sign &216; Capital O, slash &217; Capital U, acute accent &218; Capital U, grave accent &219; Capital U, circumflex accent &220; Capital U, dieresis or umlaut mark &221; Capital Y, acute accent &222; Capital THORN, Icelandic &223; Small sharp s, German (sz ligature) &224; Small a, acute accent &225; Small a, grave accent &226; Small a, circumflex accent &227; Small a, tilde &228; Small a, tilde &229; Small a, dieresis or umlaut mark &230; Small ae dipthong (ligature) &231; Small c, cedilla &232; Small e, acute accent &233; Small e, grave accent &234; Small e, circumflex accent &235; Small e, dieresis or umlaut mark &236; Small i, acute accent &237; Small i, grave accent &238; Small i, circumflex accent &239; Small i, dieresis or umlaut mark &240; Small eth, Icelandic &241; Small n, tilde &242; Small o, acute accent &243; Small o, grave accent &244; Small o, circumflex accent &245; Small o, tilde &246; Small o, dieresis or umlaut mark &247; Division sign &248; Small o, slash &249; Small u, acute accent &250; Small u, grave accent &251; Small u, circumflex accent &252; Small u, dieresis or umlaut mark &253; Small y, acute accent &254; Small thorn, Icelandic &255; Small y, dieresis or umlaut mark Implementation Implemented under HTML 2.0. --------------------------------------------------------------------------- (Draw Root) Use the ROOT tag to draw a root in a mathematical expression. You should place the ROOT tag within the MATH tag. Syntax ... Proposed for inclusion in a future version of the HTML standard. --------------------------------------------------------------------------- (Draw Square Root) If you want to include a square root in your mathematical equation, use the SQRT tag. You should place the SQRT tag within the MATH tag. Syntax ... Proposed for inclusion in a future version of the HTML standard. --------------------------------------------------------------------------- (Subscript Text) The SUB tag is used to specify text that is displayed as a subscript. A subscript appears slightly below the baseline (bottom edge) of surrounding text and may be in a smaller font. Subscripts are commonly used in mathematical and chemical notation. Place within the MATH tag. Syntax ... Implementation Proposed for inclusion in a future version of the HTML standard. --------------------------------------------------------------------------- (Superscript Text) Use to display text as a superscript. A superscript appears slightly above surrounding text and may be in a smaller font. Superscripts are commonly used in reference citations and in mathematical and technical notation. You should nest the SUP tag within the MATH tag. Syntax ... Implementation Proposed for inclusion in a future version of the HTML standard. --------------------------------------------------------------------------- (Upright Text) To display the enclosed text in an upright font, use the T tag. Nest the T tag within the MATH tag. Syntax ... Proposed for inclusion in a future version of the HTML standard. --------------------------------------------------------------------------- (Include Text) Use the TEXT tag to include a short piece of text within your mathematical expression You should place the TEXT tag within the MATH tag. Syntax ... Proposed for inclusion in a future version of the HTML standard. --------------------------------------------------------------------------- (Draw Tilde) If you want to draw a tilde in your mathematical equation, use the TILDE tag. Place the TILDE tag within the MATH tag. Syntax ... Proposed for inclusion in a future version of the HTML standard. --------------------------------------------------------------------------- (Draw Vector) To draw a vector, use the VEC tag. You should place the VECTOR tag within the MATH tag. Syntax ... Proposed for inclusion in a future version of the HTML standard.