How to write mathematical formulas in HTML?

Some simple mathematical formulas can be written using HTML tags, such as formula 1:

$\left( x^{2}+y^{2}-1\right) ^{3}-x^{2}y^{3}=0$

Using the ^{tag of HTML:}

(x<sup>2</sup> + y<sup>2</sup>1)<sup>3</sup> - x<sup>2</sup>y<sup>3</sup> = 0
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But HTML can’t handle more complex formulas, like this one:

$f\left( t\right) =\lim _{n\rightarrow \infty }\dfrac{n! n^{t}}{t\left( t+1\right) \ldots \left( t+n\right) }=\dfrac{1}{t}\prod ^{\infty }_{n=1}\dfrac{\left( 1+\dfrac{1}{n}\right) ^{t}}{1+\dfrac{t}{n}}=\dfrac{e^{-rt}}{t}\prod ^{\infty }_{n=1}\left( 1+\dfrac{t}{n}\right) ^{-1}e^{\dfrac{t}{n}}$

We can use MathML to describe complex mathematical formulas like this.

Mathematical Markup Language (MathML) is an XML-based standard for describing Mathematical symbols and formulas. Its goal is to integrate mathematical formulas into the World Wide Web and other documents. Since 2015, MathML has become part of HTML5 and an ISO standard. —- Wikipedia

Formula 2 is described in MathML like this:

<math>
  <mi> f </mi>
  <mrow>
    <mo> ( </mo>
    <mi> t </mi>
    <mo> ) </mo>
  </mrow>
  <mo> = </mo>
  <munder>
    <mrow>
      <mi> lim </mi>
    </mrow>
    <mrow>
      <mi> n </mi>
      <mo> &#x2192;
        <! -- rightwards arrow -->
      </mo>
      <mi> &#x221E;
        <! -- infinity -->
      </mi>
    </mrow>
  </munder>
  <mfrac>
    <mrow>
      <mi> n </mi>
      <mo> ! </mo>
      <msup>
        <mrow>
          <mi> n
            <! -- greek capital letter lambda -->
          </mi>
        </mrow>
        <mrow>
          <mi> t </mi>
        </mrow>
      </msup>
    </mrow>
    <mrow>
      <mi> t </mi>
      <mrow>
        <mo> ( </mo>
        <mi> t </mi>
        <mo> + </mo>
        <mn> 1 </mn>
        <mo> ) </mo>
      </mrow>
      <mo> &#x2026;
        <! -- horizontal ellipsis -->
      </mo>
      <mrow>
        <mo> ( </mo>
        <mi> t </mi>
        <mo> + </mo>
        <mi> n </mi>
        <mo> ) </mo>
      </mrow>
    </mrow>
  </mfrac>
  <mo> = </mo>
  <mfrac>
    <mrow>
      <mn> 1 </mn>
    </mrow>
    <mrow>
      <mi> t </mi>
    </mrow>
  </mfrac>
  <munderover>
    <mrow>
      <mo> &#x220F;
        <! -- n-ary product -->
      </mo>
    </mrow>
    <mrow>
      <mi> n </mi>
      <mo> = </mo>
      <mn> 1 </mn>
    </mrow>
    <mrow>
      <mi> &#x221E;
        <! -- infinity -->
      </mi>
    </mrow>
  </munderover>
  <mfrac>
    <mrow>
      <msup>
        <mrow>
          <mrow>
            <mo> ( </mo>
            <mn> 1 </mn>
            <mo> + </mo>
            <mfrac>
              <mrow>
                <mn> 1 </mn>
              </mrow>
              <mrow>
                <mi> n </mi>
              </mrow>
            </mfrac>
            <mo> ) </mo>
          </mrow>
        </mrow>
        <mrow>
          <mi> t </mi>
        </mrow>
      </msup>
    </mrow>
    <mrow>
      <mn> 1 </mn>
      <mo> + </mo>
      <mfrac>
        <mrow>
          <mi> t </mi>
        </mrow>
        <mrow>
          <mi> n </mi>
        </mrow>
      </mfrac>
    </mrow>
  </mfrac>
  <mo> = </mo>
  <mfrac>
    <mrow>
      <msup>
        <mrow>
          <mi> e </mi>
        </mrow>
        <mrow>
          <mo> - </mo>
          <mi> r </mi>
          <mi> t </mi>
        </mrow>
      </msup>
    </mrow>
    <mrow>
      <mi> t </mi>
    </mrow>
  </mfrac>
  <munderover>
    <mrow>
      <mo> &#x220F;
        <! -- n-ary product -->
      </mo>
    </mrow>
    <mrow>
      <mi> n </mi>
      <mo> = </mo>
      <mn> 1 </mn>
    </mrow>
    <mrow>
      <mi> &#x221E;
        <! -- infinity -->
      </mi>
    </mrow>
  </munderover>
  <msup>
    <mrow>
      <mrow>
        <mo> ( </mo>
        <mn> 1 </mn>
        <mo> + </mo>
        <mfrac>
          <mrow>
            <mi> t </mi>
          </mrow>
          <mrow>
            <mi> n </mi>
          </mrow>
        </mfrac>
        <mo> ) </mo>
      </mrow>
    </mrow>
    <mrow>
      <mo> - </mo>
      <mn> 1 </mn>
    </mrow>
  </msup>
  <msup>
    <mrow>
      <mi> e </mi>
    </mrow>
    <mrow>
      <mfrac>
        <mrow>
          <mi> t </mi>
        </mrow>
        <mrow>
          <mi> n </mi>
        </mrow>
      </mfrac>
    </mrow>
  </msup>
</math>
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Copy the above code to a local HTML file and open it in FireFox or Safari to see the effect. You can also set different CSS styles for each tag.

MathML code generation

As you can see from the example above, MathML is so complex that this single formula can take a day to write. But we can use itTools (click to visit)Automatically generate MathML code.

MathML element

The top element<math>

The top-level elements of MathML. Similar to in HTML.

<math>.</math>
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Character/symbol element

• The
  
  element indicates that content should be rendered as an identifier, such as a function name, variable, or symbolic constant. You can also use any text in it to tag terms.
  

  <math>
    <mi> x </mi> <! -- x -->
    <mi> &pi; </mi>  <! - PI - >
  </math>
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• The
  
  element represents a numeric literal, which is usually a string of numbers with possible separators (dots or commas). However, it also allows you to include arbitrary text in it, which is actually a numeric quantity, such as “11”.
  

  <math>
    <mn> 1 </mn>
    <mn> 2e10 </mn>
  </math>
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• The
  
  element represents operations, including “operators” such as parentheses and separators such as commas and semicolons.
  

    <math>
      <mn> 5 </mn>
      <mo> + </mo>
      <mn> 5 </mn>
    </math>
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• The
  
  element represents string literals to be interpreted by programming languages and computer algebra systems. By default, string literals are enclosed in double quotation marks (“); Using the lQUOTE and rQUOTE properties, you can set custom characters to display. Note that quotation marks should not be specified unless they are part of the string literal. The content of the
  
  element itself is not an ASCII string, but a series of characters along with the
  
  and
  
  elements.
  
  
  
  

  <math>
    <ms lquote="„" rquote="" "> abc </ms> <! - „ ABC "-- >
  </math>
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• The
  
  element is used to represent a blank space, the size of which is determined by its attributes (width,height,depth).
  

  <math>
    <! -- depth: blank height below the baseline -->
    <! -- height: the blank height above the baseline
    <mspace depth="40px" height="20px" />
    <! --> < span style = "max-width: 100%; clear: both;
    <mspace width="100px" />
  </math>
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• The
  
  element is used to render arbitrary text without symbolic meaning, such as comments or annotations. To display symbolic text, use
  
  and
  
  .
  
  
  

  <math> 
    <mtext> Theorem of Pythagoras </mtext>  
    <mtext> /* comment here */ </mtext>
  </math>
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Common layout elements

• <menclosed>The element renders its content in a closed notation specified by the notation attribute. Support 17 different closed symbols, detailed viewThe document.

  <! -- Factorial -->
  <math> 
    <menclose notation="madruwb">
      <msup><mi>a</mi><mn>2</mn></msup>
      <mo>+</mo>
      <msup><mi>b</mi><mn>2</mn></msup>
    </menclose>
  </math>
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• <merror>The element is used to display content as an error message. In Firefox, this error message is rendered like a typical XML error message. Note that this error is not thrown when the MathML tag is incorrect or not well-formed XML. You still get an XML parsing error (in the case of MathML’s XHTML notation), which is associated with<merror>Has nothing to do.

  <math>
    <merror>
      <mrow>
        <mtext>Divide by zero:</mtext>
        <mfrac>
          <mn> 1 </mn>
          <mn> 0 </mn>
        </mfrac>
      </mrow>
    </merror>
  </math>
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• <mfrac>The element is used to display the score.

  <math>
    <mfrac> <! -- a / b -->
      <mi> a </mi>
      <mi> b </mi>
    </mfrac>
  </math>
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• <mphantom>Elements are rendered invisible, but dimensions (such as height, width, and baseline position) remain the same. Similar to CSSvisibility: hidden.

  <math>
    <mrow>
      <mi> x </mi>
      <mo> + </mo> 
      <mphantom> <! -- elements inside mphantom tag are not visible -->
        <mi> y </mi>
        <mo> + </mo>
      </mphantom>
      <mi> z </mi>
    </mrow>
  </math>
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• <mroot>The element is used to represent a radical with an explicit radical exponent. It takes two arguments, with the following syntax:<mroot> base index </mroot>.

  <math>
    <mroot>
      <mi>x</mi>
      <mn>3</mn>
     </mroot>
  </math>
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• <mrow>The element is used to group different subexpressions of consecutive multi-line expressions. A sliver expression usually counts as a single line and contains at least one or more operators and their operands (e.g<mi> 和 <mn>).
• <msqrt>The element is used to represent a square root (without showing the root exponent). It takes only one argument, with the syntax:<msqrt> base </msqrt>.

  <math>
    <msqrt>
      <mi>x</mi>
    </msqrt>
  </math>
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• <mstyle>Element changes the style of its child elements.

<math> 
  <mstyle displaystyle="true" mathcolor="teal">
    <mrow>
      <munderover>
        <mo stretchy="true" form="prefix">&sum;</mo>
        <mrow>
          <mi>i</mi>
          <mo form="infix">=</mo>
          <mn>1</mn>
        </mrow>
        <mi>n</mi>
      </munderover>
      <mstyle displaystyle="true">
        <mfrac>
          <mn>1</mn>          
          <mi>n</mi>
        </mfrac>
      </mstyle>
   </mrow>
  </mstyle>
</math>
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Edge and corner elements

• <msub>The element is used to append the index to an expression as follows:<msub> base subscript </msub>.

  <math>
    <msub>
      <mi>X</mi>
      <mn>1</mn>
    </msub>
  </math>
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• <msubsup>The element is used to append both upper and lower subscripts to an expression. Its syntax is as follows:<msubsup> base subscript superscript </msubsup>

  <math displaystyle="true">   
    <msubsup>
      <mo> &#x222B;<! -- Integral symbol --> </mo>
      <mn> 0 </mn>
      <mn> 1 </mn>
    </msubsup>
  </math>
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• <msup>The element is used to label an expression.

  <math>
    <msup>
      <mi>X</mi>
      <mn>2</mn>
  </msup> 
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Form mathematics

< mtable >, < MTR >, < MTD > element is similar to HTML in the < table >, < tr > < td >.

<math>
  <mtable>
    <mtr>
      <mtd><mi>A</mi></mtd>
      <mtd><mi>B</mi></mtd>
      <mtd><mi>C</mi></mtd>
    </mtr>
  </mtable>
</math>
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Mathematical symbols

Algebraic symbols

symbol	HTML character entity	Hex code
+	+	+	A plus sign
–	−	−	A minus sign
x	×	×	Multiplication sign
present	÷	÷	devide
indicates	≠	≠	Sign of inequality
material	≈	≈	Approximately equal to the
<	&lt;	&#x003c;	Less than
Or less	&le;	&#x2264;	Less than or equal to
>	&gt;	&#x003e;	Is greater than
p	&ge;	&#x2265;	Greater than or equal to
Plus or minus	&plusmn;	&#x00b1;	Plus or minus
∝	&prop;	&#x221d;	Is proportional to
∑	&sum;	&#x2211;	Summation operator
∏	&prod;	&#x220f;	Quadrature or direct product
⌊	&lfloor;	&#x230a;	Round down the left parenthesis
⌋	&rfloor;	&#x230b;	Round down the close parenthesis
⌈	&lceil;	&#x2308;	Round up the left parenthesis
⌉	&rceil;	&#x2309;	Round up the closing parenthesis

Calculus symbol

symbol	HTML character entity	Hex code
‘	′	′	Single quotation mark (first derivative)
“	″	″	Double quotation marks (second derivative)
‴	‴	‴	Triple quotation marks (third derivative)
partial	∂	∂	Partial derivative
Delta t.	δ	Δ	variational
∇	∇	∇	Gradient operator
∫	∫	∫	integral
∬	∬	∬	Double integral
∭	∭	∭	Triple integral
⨌	⨌	⨌	Four integrals
30	∮	∮	Curvilinear integral
∲	∲	∲	Clockwise curve integral
∳	∳	∳	Counterclockwise integral
∯	∯	∯	Surface integral
∰	∰	∰	Volume integral
up	∞	∞	infinity

apostrophes

symbol	HTML character entity	Hex code
…	…	…	Horizontal ellipsis
⋮	⋮	⋮	Vertical ellipsis
…	⋯	⋯	Center line horizontal ellipsis
⋰	⋰	⋰	Diagonal ellipsis
⋱	⋱	⋱	Diagonal ellipsis

Function of symbols

symbol	HTML character entity	Hex code
⋅	⋅	⋅	The dot product
⨯	⨯	⨯	Cross product
lots	‖	‖
⟨	⟨	⟨	The left Angle brackets
⟩	⟩	⟩	Right Angle brackets
∘	∘	∘	Composite function
–	→	→	Function mapping
↦	↦	↦	Concrete function mapping
ı	ı	ı	The letter I with no dots
ȷ	ȷ	ȷ	The letter J without a dot

Geometric symbols

symbol	HTML character entity	Hex code
°	°	°	degree
<	&ang;	&#x2220;	The Angle
∡	&angmsd;	&#x2221;	Measuring Angle
∟	&angrt;	&#x221f;	Right Angle
⦜	&vangrt;	&#x299c;	Right Angle
⊿	&lrtri;	&#x22bf;	Right triangle
a.	&cir;	&#x25cb;	round
delta	&xutri;	&#x25b3;	triangle
–	&squ;	&#x25a1;	square
▱	&fltns;	&#x25b1;	parallelogram
∥	&spar;	&#x2225;	parallel
∦	&npar;	&#x2226;	Not parallel
an	&perp;	&#x22a5;	vertical
≅	&cong;	&#x2245;	Are congruent
–	&rarr;	&#x2192;	ray
↔	&harr;	&#x2194;	A straight line
–	(n/a)	&#x002d;	Line segment

The Greek letter

symbol	HTML character entity	Hex code
Alpha / Α	α/Α	α/Α
Beta / Β	β/Β	β/Β
Gamma / Γ	γ/Γ	γ/Γ
The delta / Δ	δ/Δ	δ/Δ
Epsilon / Ε	ε/Ε	ε/Ε
Zeta / Ζ	ζ/Ζ	ζ/Ζ
Eta / Η	η/Η	η/Η
Theta / Θ	θ/Θ	θ/Θ
ι / Ι	ι/Ι	ι/Ι
Kappa / Κ predominate	κ/Κ	κ/Κ
Lambda / Λ	λ/Λ	λ/Λ
Mu / Μ	μ/Μ	μ/Μ
The argument / Ν	ν/Ν	ν/Ν
Factor / Ξ	ξ/Ξ	ξ/Ξ
&western / Ο	ο/Ο	ο/Ο
PI / Π	π/Π	π/Π
Rho / Ρ	ρ/Ρ	ρ/Ρ
Sigma / Σ	σ/Σ	σ/Σ
Tau / Τ	τ/Τ	τ/Τ
Nu / Υ	υ/Υ	υ/Υ
Phi / Φ	φ/Φ	φ/Φ
χ / Χ	χ/Χ	χ/Χ
Bits / Ψ	ψ/Ψ	ψ/Ψ
Omega / Ω	ω/Ω	ω/Ω

Invisible operator

symbol	HTML character entity	Hex code
⁡	⁡	⁡	Used to specify functional applications
⁢	⁢	⁢	Used to specify multiplication that is not visible
⁣	⁣	⁣	Use to specify invisible delimiters
⁤	(n/a)	⁤	Used to specify additions that are not visible

Logic symbol

symbol	HTML character entity	Hex code
such	¬	¬	non
Sunday afternoon	∧	∧	with
∨	∨	∨	or
⊻	⊻	⊻	Exclusive or
∀	∀	∀	Universal quantifier
∃	∃	∃	Existential quantifier
⇒	⇒	⇒	Material implication
As indicated by	⇔	⇔	Substantial equivalence
◻	◻	◻	necessary
◊	◊	◊	may
⊢	⊢	⊢	inference
⊩	⊩	⊨	contains
∵	∵	∵	because
∴	∴	∴	so

A collection of symbols

symbol	HTML character entity	Hex code
∅	∅	∅	An empty set
∈	∈	∈	Belong to
∉	∉	∉	Do not belong to
⊆	⊆	⊆	Included in the
⊈	⊈	⊈	Not included in
⊂	⊂	⊂	Proper subset
⊄	⊄	⊄	The proper subset
⊇	⊇	⊇	superset
⊉	⊉	⊉	A superset
⊃	⊃	⊃	True superset
⊅	⊅	⊅	Not really a superset
studying	∩	∩	intersection
∪	∪	∪	And set
∖	∖	∖	complement

Browser compatibility

Compatibility Solution

1. MathJax.js

Mathjax.js is a mathematical formula rendering tool that converts MathML tags into HTML tags and adds specific CSS styles to them.

Add a line of code to the header of the page:

<html>
  <head>.<script src="http://fred-wang.github.io/mathjax.js/mpadded-min.js"></script>.</head>.</html>
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What this js file does is determine if MathML is used in the document after the page is loaded. If it is used and the current browser is not compatible, load mathJax.js into the page and download the specific font file. The rendering is similar to FireFox’s native MathML-enabled browser, with the disadvantage of having to load a lot of files (9 files, or about 400KB) and being slow.

2. mathml.css

Mathml. CSS provides a simple adaptation. Again, if you are using MathML and the current browser is not compatible, you will load a simple CSS style sheet that does a simple simulation of the layout of the mathematical formula.

<html>
  <head>.<script src="http://fred-wang.github.io/mathml.css/mspace.js"></script>.</head>.</html>
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The formula²Different effects of: