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    Contributing to BookOfProofs is easy - thanks to cool open source software!

    Easy Posts With a Simple Text Markup

    This site deploys a simple text markup found and used under conditions stated at https://raw.githubusercontent.com/netcarver/textile/2.5/classTextile.php,where you can also find exhaustive examples of syntax and usage. Here, we provide only some demo examples:

    Close

    Use h[1-6]. to create headers.

    h1. My Header¶
    h2. My Header¶
    h3. My Header¶

    Result:

    My Header

    My Header

    My Header

    Close

    Creation of tables is very simple using | to indicate columns.

    |_. heading one|_. heading two|
    |<. left|>. right|
    |^. top|<>{width:250px}. This is a 250px cell with a justified text inside.|
    |~. bottom|=. This text will be centered. |
    
    heading one heading two
    left right
    top This is a 250px cell with a justified text inside.
    bottom This text will be centered.

    It is also possible to span across columns and rows like this (shown in a table with border):

    Markdown:

    |\2=. this cell spans two columns|
    |=. first column|=. second column|
    |/3=. this row spans 3 rows|=. a|
    |=. b|
    |=. c|
    

    Result:

    this cell spans two columns
    first column second column
    this row spans 3 rows a
    b
    c
    Close

    Create external links in your text using quotation marks ".

    Markdown:

    "This is my external link":http://en.wikipedia.org/
    

    Result:

    This is my external link

    Close

    To create footnotes use [1-100], to actually type them use fn1. Footnote..., separated by empty lines, for instance:

    Markdown:

    p. This is a text with a footnote reference[1].
    An this will create another reference[2].
    
    p. Here comes another paragraph.
    
    fn1. This is the first footnote
       ← empty line
    fn2. This is the second footnoted.

    This is a text with a footnote reference1.
    An this will create another reference2.

    Here comes another paragraph.

    1 This is the first footnote

    2 This is the second footnoted.

    Close

    Using exclamation marks !, you can include scaled images in your text and link to them:

    Markdown:

    !{width:250px}https://www.bookofproofs.org/graphics/examples/digraph1.gif!
    

    Result:

    Markdown:

    !{width:350px}https://www.bookofproofs.org/graphics/examples/digraph1.gif!
    

    Result:

    Close

    Create internal links in your text using quotation marks and the "dd"-notation ("drill-down" open book notation) ".

    Markdown:

    My internal link to "natural numbers":https://www.bookofproofs.org/branches/?dd=103
    

    Result:

    My internal link to natural numbers

    Markdown:

    My internal link to "Niels Henrik Abel":https://www.bookofproofs.org/history/?dd=3576
    

    Result:

    My internal link to Niels Henrik Abel

    Close

    Create internal links in your text using quotation marks and the "dd"-notation ("drill-down" open book notation) ".

    My internal link to "natural numbers":https://www.bookofproofs.org/branches/natural-numbers/
    

    Result:

    My internal link to natural numbers

    My internal link to "Niels Henrik Abel":https://www.bookofproofs.org/history/niels-henrik-abel/
    

    Result:

    My internal link to Niels Henrik Abel

    Close

    Use p. Text to create paragraphs.

    p. This is a paragraph¶
    p. And here begins a new pararagraph...¶

    Result:

    This is a paragraph.

    And here begins a new pararagraph. Lorem ipsum dolor sit amet, ea dolore vivendum nec, sit at facer suscipit, sea affert vivendo maluisset no.

    Close

    Use bq. Text to quote.

    p. This is a quotation:¶

    bq. "Veni, vidi, vici"¶
    Julius Caesar (100–44 BC).¶

    Result:

    This is a quotation:

    “Veni, vidi, vici”
    Julius Caesar (100–44 BC).

    Close

    Create lists using # for enumerations, * for itemizations, and - =: := for Redcloth-style definition lists.

    Markdown:

    # First Level
    ## Second Level
    ### Third Level

    Result:

    1. First Level
      1. Second Level
        1. Third Level

    Markdown:

    * First Level
    ** Second Level
    *** Third Level

    Result:

    • First Level
      • Second Level
        • Third Level

    Markdown:

    - Term1 := Definition1
    - Term2 := Extended
    definition =:

    Result:

    Term1
    Definition1
    Term2
    Extended
    definition
    Close

    You can use inline modifiers to change the appearance of your text.

    Markdown:

    This text is _emphasized_.
    This text is __italic__.
    This text is *strong*.
    This text is **bold**.
    This text is ??cited??
    This text is -deleted-.
    This text is +inserted+.
    This text is in ^superscript^.
    This text is in ~subscript~.
    This text is in @computer system script@.
    %(red)This text is red.%
    %(blue)This text is blue.%
    %(green)This text is green.%
    %(gray)This text is gray.%
    %(w3-amber)This text is in one of the many w3-colors (see w3schools w3.css)%
    ==This text is not formated at all.==

    Result:

    This text is emphasized.
    This text is italic.
    This text is strong.
    This text is bold.
    This text is cited
    This text is deleted.
    This text is inserted.
    This text is in superscript.
    This text is in subscript.
    This text is in computer system script.
    This text is red.
    This text is blue.
    This text is green.
    This text is gray.
    This text is in one of the many w3-colors (see w3schools w3.css)
    This text is not formated at all.


    Beautiful Maths with MathJax

    Mathjax is a powerful, open-source display engine for mathematics using client-side javascript in your browser.You can find more information at the MathJax homepage.If you are looking for an exhaustive list of MathJax syntax and the corresponding typesetting in action, you might visit http://www.onemathematicalcat.org/MathJaxDocumentation/TeXSyntax.htm.Here, we provide only some formatting examples.

    Close

    Type mathematic formulae using \[...\] or type them inline using \(...\).

    Mathjax:

    p. The Cauchy-Schwarz Inequality states that
    \[
    \left( \sum_{k=1}^n a_k b_k \right)^{2} \leq
     \left( \sum_{k=1}^n a_k^2 \right) \left( \sum_{k=1}^n b_k^2 \right)
    \]
    
    p. Einstein's famous equation is \(E=mc^2\).
    

    Result:

    The Cauchy-Schwarz Inequality states that
    \[
    \left( \sum_{k=1}^n a_k b_k \right)^{2} \leq \left( \sum_{k=1}^n a_k^2 \right) \left( \sum_{k=1}^n b_k^2 \right)
    \]

    Einstein’s famous equation is \(E=mc^2\).

    Close

    Superscripting and Subscripting

    \(x^{2y}\)

    Mathjax:

    \(x^{2y}\)

    Result:

    \(x^{2y}\)

    Mathjax:

    \(x^{y^{2}}\)

    Result:

    \(x^{y^{2}}\)

    Mathjax:

    \(x_{1}^{a_{2}}\)

    Result:

    \(x_{1}^{a_{2}}\)

    Fractions and Squares

    Multiplying with \(\sqrt[n]{2}\) results in \( (m+n)/n\).

    Mathjax:

    Multiplying with
     \(\sqrt[n]{2}\)
     results in \( (m+n)/n\).

    Result:

    Result:

    Multiplying with \(\sqrt[n]{2}\) results in \( (m+n)/n\).

    Mathjax:

    \frac{-b\pm
    \sqrt{b^2-4ac}}{2a}

    Result:

    \(\frac{-b\pm
    \sqrt{b^2-4ac}}{2a}\)

    Mathjax:

    \frac{x+y}
    {1+\frac{y}{z+1}}

    Result:

    \(\frac{x+y}
    {1+\frac{y}{z+1}}\)

    Matrix and Ellipsis

    \(x_{1},\ldots,x_{n}\)

    Mathjax:

    x_{1},\ldots,x_{n}

    Result:

    \(x_{1},\ldots,x_{n}\)

    Mathjax:

    x_{1},\cdots,x_{n}

    Result:

    \(x_{1},\cdots,x_{n}\)

    Mathjax:

    \left(\begin{array}{ccc}
    x_{11}&\cdots&x_{1n}\\
    \vdots&\ddots&\vdots\\
    x_{n1}&\cdots&x_{nn}
    \end{array}\right)

    Result:

    \(\left(\begin{array}{ccc}
    x_{11}&\cdots&x_{1n}\\
    \vdots&\ddots&\vdots\\
    x_{n1}&\cdots&x_{nn}
    \end{array}\right)\)

    Close

    Greek letters

    \(\) \(\) \(\) \(\)
     \alpha 
    \( \alpha \)
     \beta 
    \( \beta \)
     \gamma,\Gamma 
    \( \gamma,\Gamma \)
     \delta,\Delta 
    \( \delta,\Delta \)
     \epsilon 
    \( \epsilon \)
     \varepsilon 
    \( \varepsilon \)
     \zeta 
    \( \zeta \)
     ta 
    \( ta \)
     \theta,\Theta 
    \( \theta,\Theta \)
     \vartheta 
    \( \vartheta \)
     \iota 
    \( \iota \)
     \kappa 
    \( \kappa \)
     \lambda,\Lambda 
    \( \lambda,\Lambda \)
     \mu 
    \( \mu \)
     \nu 
    \( \nu \)
     \xi,\Xi 
    \( \xi,\Xi \)
     o 
    \( o \)
     \pi,\Pi 
    \( \pi,\Pi \)
     \varpi 
    \( \varpi \)
     \rho 
    \( \rho \)
     \varrho 
    \( \varrho \)
     \sigma,\Sigma 
    \( \sigma,\Sigma \)
     \varsigma 
    \( \varsigma \)
     \tau 
    \( \tau \)
     \upsilon,\Upsilon 
    \( \upsilon,\Upsilon \)
     \phi,\Phi 
    \( \phi,\Phi \)
     \varphi 
    \( \varphi \)
     \chi 
    \( \chi \)
     \psi,\Psi 
    \( \psi,\Psi \)
     \omega,\Omega\ 
    \( \omega,\Omega\ \)
    Close

    Relations

     < 
    ('space > space') \( < \)
     > 
    ('space > space') \( > \)
    \le
    \(\le\)
    \geq
    \(\geq\)
    \in
    \(\in\)
    \notin
    \(\notin\)
    \ni
    \(\ni\)
    \propto
    \(\propto\)
    =
    \(=\)
    \neq
    \(\neq\)
    \simeq
    \(\simeq\)
    \sim
    \(\sim\)
    \subset
    \(\subset\)
    \subseteq
    \(\subseteq\)
    \supset
    \(\supset\)
    \supseteq
    \(\supseteq\)
    \ll
    \(\ll\)
    \gg
    \(\gg\)
    \prec
    \(\prec\)
    \succ
    \(\succ\)
    \vdash
    \(\vdash\)
    \dashv
    \(\dashv\)
    \perp
    \(\perp\)
    \mid
    \(\mid\)
    \parallel
    \(\parallel\)
    \equiv
    \(\equiv\)
    \asymp
    \(\asymp\)
    \cong
    \(\cong\)
    \sqsubseteq
    \(\sqsubseteq\)
    \sqsupseteq
    \(\sqsupseteq\)
    \doteq
    \(\doteq\)
    \models
    \(\models\)
    \preceq
    \(\preceq\)
    \succeq
    \(\succeq\)
    \smile
    \(\smile\)
    \frown
    \(\frown\)
    Close

    Arrows

     \leftarrow 
    \( \leftarrow \)
     \rightarrow 
    \( \rightarrow \)
     \longleftarrow 
    \( \longleftarrow \)
     \longrightarrow 
    \( \longrightarrow \)
     \Leftarrow 
    \( \Leftarrow \)
     \Rightarrow 
    \( \Rightarrow \)
     \Longleftarrow 
    \( \Longleftarrow \)
     \Longrightarrow 
    \( \Longrightarrow \)
     \Leftrightarrow 
    \( \Leftrightarrow \)
     \leftrightarrow 
    \( \leftrightarrow \)
     \Longleftrightarrow 
    \( \Longleftrightarrow \)
     \longleftrightarrow 
    \( \longleftrightarrow \)
     \uparrow 
    \( \uparrow \)
     \Uparrow 
    \( \Uparrow \)
     \downarrow 
    \( \downarrow \)
     \Downarrow 
    \( \Downarrow \)
     \nearrow 
    \( \nearrow \)
     \searrow 
    \( \searrow \)
     \nwarrow 
    \( \nwarrow \)
     \swarrow 
    \( \swarrow \)
     \mapsto 
    \( \mapsto \)
     \longmapsto 
    \( \longmapsto \)
     \leadsto 
    \( \leadsto \)
     \rightleftharpoons 
    \( \rightleftharpoons \)
     \leftharpoonup 
    \( \leftharpoonup \)
     \rightharpoonup 
    \( \rightharpoonup \)
     \leftharpoondown 
    \( \leftharpoondown \)
     \rightharpoondown 
    \( \rightharpoondown \)
     \hookleftarrow 
    \( \hookleftarrow \)
     \hookrightarrow 
    \( \hookrightarrow \)
     \updownarrow 
    \( \updownarrow \)
     \Updownarrow 
    \( \Updownarrow \)
    Close

    Operators and other Symbols

     + 
    \( + \)
     - 
    \( - \)
     \cdot 
    \( \cdot \)
     \div 
    \( \div \)
     \pm 
    \( \pm \)
     \mp 
    \( \mp \)
     \times 
    \( \times \)
     \odot 
    \( \odot \)
     \oplus 
    \( \oplus \)
     \ominus 
    \( \ominus \)
     \otimes 
    \( \otimes \)
     \oslash 
    \( \oslash \)
     \bullet 
    \( \bullet \)
     \lfloor x \rfloor 
    \( \lfloor x \rfloor \)
     \lceil x \rceil 
    \( \lceil x \rceil \)
     \ast 
    \( \ast \)
     \diamond 
    \( \diamond \)
     \circ 
    \( \circ \)
     \dagger 
    \( \dagger \)
     \ddagger 
    \( \ddagger \)
     \cap 
    \( \cap \)
     \cup 
    \( \cup \)
     \sqcap 
    \( \sqcap \)
     \sqcup 
    \( \sqcup \)
     \vee 
    \( \vee \)
     \wedge 
    \( \wedge \)
     \bigtriangleup 
    \( \bigtriangleup \)
     \bigtriangledown 
    \( \bigtriangledown \)
     \triangleleft 
    \( \triangleleft \)
     \triangleright 
    \( \triangleright \)
     \triangle
    \( \triangle\)
     \Box 
    \( \Box \)
     \lhd 
    \( \lhd \)
     \rhd 
    \( \rhd \)
     \wr 
    \( \wr \)
     \amalg 
    \( \amalg \)
     \uplus 
    \( \uplus \)
     \nabla 
    \( \nabla \)
     \| 
    \( \| \)
     \surd 
    \( \surd \)
     \setminus 
    \( \setminus \)
     \emptyset 
    \( \emptyset \)
     \top 
    \( \top \)
     \bot 
    \( \bot \)
     \prime 
    \( \prime \)
     \partial 
    \( \partial \)
     \forall 
    \( \forall \)
     \exists 
    \( \exists \)
     \neg 
    \( \neg \)
     \backslash 
    \( \backslash \)
     \angle 
    \( \angle \)
     \infty 
    \( \infty \)
     \flat 
    \( \flat \)
     \natural 
    \( \natural \)
     \sharp 
    \( \sharp \)
     \star 
    \( \star \)
     \clubsuit 
    \( \clubsuit \)
     \diamondsuit 
    \( \diamondsuit \)
     \heartsuit 
    \( \heartsuit \)
     \spadesuit 
    \( \spadesuit \)
     \aleph 
    \( \aleph \)
     \hbar 
    \( \hbar \)
     \imath 
    \( \imath \)
     \jmath 
    \( \jmath \)
     ll 
    \( ll \)
     \wp 
    \( \wp \)
     \Re 
    \( \Re \)
     \Im 
    \( \Im \)
     \mho 
    \( \mho \)
     \unlhd 
    \( \unlhd \)
     \unrhd 
    \( \unrhd \)
     \Join 
    \( \Join \)
    Close

    Big Operators and Symbols

     \sum 
    \( \sum \)
     \prod 
    \( \prod \)
     \coprod 
    \( \coprod \)
     \bigsqcup 
    \( \bigsqcup \)
     \int 
    \( \int \)
     \iint 
    \( \iint \)
     \iiint 
    \( \iiint \)
     \iiiint 
    \( \iiiint \)
     \oint 
    \( \oint \)
     \oint\oint 
    \( \oint\oint \)
     \bigcap 
    \( \bigcap \)
     \bigcup 
    \( \bigcup \)
     \bigoplus 
    \( \bigoplus \)
     \biguplus 
    \( \biguplus \)
     \bigodot 
    \( \bigodot \)
     \bigotimes 
    \( \bigotimes \)
     \bigvee 
    \( \bigvee \)
     \bigwedge 
    \( \bigwedge \)
     \Diamond 
    \( \Diamond \)
     \bigcirc 
    \( \bigcirc \)

    Other Acknowledgements

    To improve the user experience, the site uses the great open-source libraries of jquery mobile, smarty, JSXGraph,and Sagecell. We also thank Pixabay and its artists for beautiful pictures used on our site.


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