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1 ```
2 % pandoc -f latex -t native
3 \newtheorem{theorem}{Theorem}
4 \newtheorem{corollary}[theorem]{Corollary}
5 \newtheorem{lemma}[theorem]{Lemma}
6 \theoremstyle{definition}
7 \newtheorem{definition}[theorem]{Definition}
8 \theoremstyle{remark}
9 \newtheorem{remark}{Remark}
10
11 \begin{definition}[right-angled triangles] \label{def:tri}
12 A \emph{right-angled triangle} is a triangle whose sides of length~\(a\), \(b\) and~\(c\), in some permutation of order, satisfies \(a^2+b^2=c^2\).
13 \end{definition}
14
15 \begin{lemma}
16 The triangle with sides of length~\(3\), \(4\) and~\(5\) is right-angled.
17 \end{lemma}
18
19 \begin{proof}
20 This lemma follows from \cref{def:tri} since \(3^2+4^2=9+16=25=5^2\).
21 \end{proof}
22
23 \begin{theorem}[Pythagorean triplets] \label{thm:py}
24 Triangles with sides of length \(a=p^2-q^2\), \(b=2pq\) and \(c=p^2+q^2\) are right-angled triangles.
25 \end{theorem}
26
27 \begin{remark}
28 These are all pretty interesting facts.
29 \end{remark}
30 ^D
31 [ Div
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57 , Str "length\160"
58 , Math InlineMath "a"
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63 , Str "and\160"
64 , Math InlineMath "c"
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135 )
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137 ( "#def:tri" , "" )
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142 , Str "."
143 , Str "\160\9723"
144 ]
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146 , Div
147 ( "thm:py" , [ "theorem" ] , [] )
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149 [ Strong [ Str "Theorem" , Space , Str "3" ]
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152 , Space
153 , Str "triplets)."
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155 , Space
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158 , Space
159 , Str "with"
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161 , Str "sides"
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202 ]
203 ]
204 ]
205 ```