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}
9\newtheorem{remark}{Remark}
11\begin{definition}[right-angled triangles] \label{def:tri}
12A \emph{right-angled triangle} is a triangle whose sides of length~\(a\), \(b\) and~\(c\), in some permutation of order, satisfies \(a^2+b^2=c^2\).
16The triangle with sides of length~\(3\), \(4\) and~\(5\) is right-angled.
20This lemma follows from \cref{def:tri} since \(3^2+4^2=9+16=25=5^2\).
23\begin{theorem}[Pythagorean triplets] \label{thm:py}
24Triangles with sides of length \(a=p^2-q^2\), \(b=2pq\) and \(c=p^2+q^2\) are right-angled triangles.
28These are all pretty interesting facts.
31[Div ("def:tri",["definition"],[])
32 [Para [Strong [Str "Definition",Space,Str "1"],Space,Str "(right-angled",Space,Str "triangles).",Space,Space,Str "A",Space,Emph [Str "right-angled",Space,Str "triangle"],Space,Str "is",Space,Str "a",Space,Str "triangle",Space,Str "whose",Space,Str "sides",Space,Str "of",Space,Str "length\160",Math InlineMath "a",Str ",",Space,Math InlineMath "b",Space,Str "and\160",Math InlineMath "c",Str ",",Space,Str "in",Space,Str "some",Space,Str "permutation",Space,Str "of",Space,Str "order,",Space,Str "satisfies",Space,Math InlineMath "a^2+b^2=c^2",Str "."]]
34 [Para [Strong [Str "Lemma",Space,Str "2"],Str ".",Space,Space,Emph [Str "The",Space,Str "triangle",Space,Str "with",Space,Str "sides",Space,Str "of",Space,Str "length\160",Math InlineMath "3",Str ",",Space,Math InlineMath "4",Space,Str "and\160",Math InlineMath "5",Space,Str "is",Space,Str "right-angled."]]]
36 [Para [Emph [Str "Proof."],Space,Str "This",Space,Str "lemma",Space,Str "follows",Space,Str "from",Space,Link ("",[],[("reference-type","ref"),("reference","def:tri")]) [Str "Definition\160\&1"] ("#def:tri",""),Space,Str "since",Space,Math InlineMath "3^2+4^2=9+16=25=5^2",Str ".",Str "\160\9723"]]
37,Div ("thm:py",["theorem"],[])
38 [Para [Strong [Str "Theorem",Space,Str "3"],Space,Str "(Pythagorean",Space,Str "triplets).",Space,Space,Emph [Str "Triangles",Space,Str "with",Space,Str "sides",Space,Str "of",Space,Str "length",Space,Math InlineMath "a=p^2-q^2",Str ",",Space,Math InlineMath "b=2pq",Space,Str "and",Space,Math InlineMath "c=p^2+q^2",Space,Str "are",Space,Str "right-angled",Space,Str "triangles."]]]
39,Div ("",["remark"],[])
40 [Para [Emph [Str "Remark",Space,Str "1"],Str ".",Space,Space,Str "These",Space,Str "are",Space,Str "all",Space,Str "pretty",Space,Str "interesting",Space,Str "facts."]]]
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