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Happy Pythagorean Day 3^2 + 4^2 = 5^2

Posted 4 hours ago

Happy Pythagorean Day  3^2 + 4^2 = 5^2

9/16/25
$3^2 / 4^2 / 5^2$
$3^2 + 4^2 = 5^2$
Today's date is a Pythagorean triple, a very rare event.

We have many Pythagorean Demonstrations.

Below is a standard image ... as a puzzle, divide it into 56 identical triangles.

s = {{3, 4, 5}, {6, 8, 10}, {5, 12, 13}, {9, 12, 15}, {8, 15, 
    17}, {12, 16, 20}, {7, 24, 25}, {15, 20, 25}, {10, 24, 26}, {20, 
    21, 29}};
makeSquares[{xval_, yval_}, col_, bound_] := {Thickness[.001], col, 
   EdgeForm[{Thickness[.001], Black}], 
   Rectangle[{0, 0} + {xval, yval}, {bound, bound} + {xval, yval}], 
   Black, Table[
    Line[{{i, 0} + {xval, yval}, {i, bound} + {xval, yval}}], {i, 1, 
     bound - 1}], 
   Table[Line[{{0, i} + {xval, yval}, {bound, i} + {xval, yval}}], {i,
      1, bound - 1}]};

Manipulate[
 Graphics[{Blend[{RGBColor[.12, .61, .78], RGBColor[.67, .75, .15]}], 
   Polygon[{{0, 0}, {s[[a, 2]], 0}, {s[[a, 2]], s[[a, 1]]}, {0, 0}}], 
   makeSquares[{0, -s[[a, 2]]}, RGBColor[.67, .75, .15], s[[a, 2]]], 
   makeSquares[{s[[a, 2]], 0}, RGBColor[.12, .61, .78], s[[a, 1]]], 
   Rotate[{Thickness[.001], EdgeForm[{Thickness[.001], Black}], 
     makeSquares[{0, 0}, RGBColor[.67, .75, .15], s[[a, 3]]], 
     makeSquares[{0, 0}, RGBColor[.12, .61, .78], s[[a, 1]]]}, 
    ArcTan[s[[a, 1]]/s[[a, 2]]], {0, 0}]}, ImageSize -> {400, 400}, 
  PlotLabel -> 
   Grid[{{""}, {Style[
       Row[{Superscript[s[[a, 1]], 2], " + ", 
         Superscript[s[[a, 2]], 2], " = ", Superscript[s[[a, 3]], 2]}],
        Bold]}}]], {{a, 1, "triple"}, 1, Length[s], 1}, 
 SaveDefinitions -> True]

enter image description here

POSTED BY: Ed Pegg

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POSTED BY: EDITORIAL BOARD
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