Editing Pythagorean triple (section)

===Interpretation of parameters in Euclid's formula===

Suppose the sides of a Pythagorean triangle have lengths {{math|''m''{{sup|2}} − ''n''{{sup|2}}}}, {{math|2''mn''}}, and {{math|''m''{{sup|2}} + ''n''{{sup|2}}}}, and suppose the angle between the leg of length {{math|''m''{{sup|2}} − ''n''{{sup|2}}}} and the [[hypotenuse]] of length {{math|''m''{{sup|2}} + ''n''{{sup|2}}}} is denoted as {{math|''β''}}. Then <math>\tan{\tfrac{\beta}{2}}=\tfrac{n}{m}</math> and the full-angle trigonometric values are <math>\sin{\beta}=\tfrac{2mn}{m^2+n^2}</math>, <math>\cos{\beta}=\tfrac{m^2-n^2}{m^2+n^2}</math>, and {{tmath|1=\tan{\beta}=\tfrac{2mn}{m^2-n^2} }}.<ref>{{citation |editor-first=Roger B. |editor-last=Nelsen |title=Proofs Without Words: Exercises in Visual Thinking |chapter-url=https://books.google.com/books?id=cyyhZr-SffcC |year=1993 |publisher=Mathematical Association of America |isbn=978-0-88385-700-7 |oclc=29664480 |last=Houston |first=David |chapter=Pythagorean triples via double-angle formulas |page=141}}</ref>