
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]