2020-07-23 20:11:28 +02:00
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```
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% pandoc -f latex -t native
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\newtheorem{theorem}{Theorem}
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\newtheorem{corollary}[theorem]{Corollary}
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\newtheorem{lemma}[theorem]{Lemma}
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\theoremstyle{definition}
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\newtheorem{definition}[theorem]{Definition}
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\theoremstyle{remark}
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\newtheorem{remark}{Remark}
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\begin{definition}[right-angled triangles] \label{def:tri}
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A \emph{right-angled triangle} is a triangle whose sides of length~\(a\), \(b\) and~\(c\), in some permutation of order, satisfies \(a^2+b^2=c^2\).
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\end{definition}
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\begin{lemma}
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The triangle with sides of length~\(3\), \(4\) and~\(5\) is right-angled.
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\end{lemma}
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\begin{proof}
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This lemma follows from \cref{def:tri} since \(3^2+4^2=9+16=25=5^2\).
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\end{proof}
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\begin{theorem}[Pythagorean triplets] \label{thm:py}
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Triangles with sides of length \(a=p^2-q^2\), \(b=2pq\) and \(c=p^2+q^2\) are right-angled triangles.
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\end{theorem}
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\begin{remark}
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These are all pretty interesting facts.
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\end{remark}
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^D
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2021-09-19 21:09:51 +02:00
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[ Div
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( "def:tri", [ "definition" ], [] )
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[ Para
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[ Strong
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[ Str "Definition", Space, Str "1" ]
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, Space
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, Str "(right-angled"
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, Space
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, Str "triangles)."
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, Space
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, Space
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, Str "A"
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, Space
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, Emph
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[ Str "right-angled", Space, Str "triangle" ]
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, Space
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, Str "is"
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, Space
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, Str "a"
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, Space
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, Str "triangle"
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, Space
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, Str "whose"
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, Space
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, Str "sides"
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, Space
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, Str "of"
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, Space
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, Str "length\160"
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, Math InlineMath "a"
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, Str ","
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, Space
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, Math InlineMath "b"
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, Space
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, Str "and\160"
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, Math InlineMath "c"
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, Str ","
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, Space
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, Str "in"
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, Space
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, Str "some"
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, Space
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, Str "permutation"
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, Space
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, Str "of"
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, Space
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, Str "order,"
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, Space
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, Str "satisfies"
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, Space
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, Math InlineMath "a^2+b^2=c^2"
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, Str "."
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]
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]
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, Div
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( "", [ "lemma" ], [] )
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[ Para
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[ Strong
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[ Str "Lemma", Space, Str "2" ]
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, Str "."
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, Space
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, Space
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, Emph
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[ Str "The"
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, Space
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, Str "triangle"
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, Space
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, Str "with"
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, Space
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, Str "sides"
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, Space
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, Str "of"
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, Space
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, Str "length\160"
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, Math InlineMath "3"
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, Str ","
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, Space
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, Math InlineMath "4"
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, Space
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, Str "and\160"
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, Math InlineMath "5"
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, Space
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, Str "is"
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, Space
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, Str "right-angled."
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]
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]
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]
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, Div
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( "", [ "proof" ], [] )
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[ Para
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[ Emph
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[ Str "Proof." ]
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, Space
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, Str "This"
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, Space
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, Str "lemma"
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, Space
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, Str "follows"
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, Space
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, Str "from"
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, Space
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, Link
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( ""
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, []
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,
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[ ( "reference-type", "ref" ), ( "reference", "def:tri" ) ]
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)
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[ Str "Definition\160\&1" ]
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( "#def:tri", "" )
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, Space
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, Str "since"
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, Space
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, Math InlineMath "3^2+4^2=9+16=25=5^2"
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, Str "."
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, Str "\160\9723"
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]
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]
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, Div
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( "thm:py", [ "theorem" ], [] )
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[ Para
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[ Strong
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[ Str "Theorem", Space, Str "3" ]
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, Space
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, Str "(Pythagorean"
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, Space
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, Str "triplets)."
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, Space
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, Space
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, Emph
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[ Str "Triangles"
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, Space
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, Str "with"
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, Space
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, Str "sides"
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, Space
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, Str "of"
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, Space
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, Str "length"
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, Space
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, Math InlineMath "a=p^2-q^2"
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, Str ","
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, Space
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, Math InlineMath "b=2pq"
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, Space
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, Str "and"
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, Space
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, Math InlineMath "c=p^2+q^2"
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, Space
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, Str "are"
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, Space
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, Str "right-angled"
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, Space
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, Str "triangles."
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]
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]
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]
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, Div
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( "", [ "remark" ], [] )
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[ Para
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[ Emph
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[ Str "Remark", Space, Str "1" ]
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, Str "."
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, Space
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, Space
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, Str "These"
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, Space
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, Str "are"
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, Space
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, Str "all"
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, Space
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, Str "pretty"
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, Space
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, Str "interesting"
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, Space
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, Str "facts."
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]
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]
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]
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2020-07-23 20:11:28 +02:00
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```
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