Data commit

Task/Heronian-triangles/Mathematica/heronian-triangles.math

@@ -0,0 +1,23 @@
+ClearAll[Heron]
+Heron[a_, b_, c_] := With[{s = (a + b + c)/2}, Sqrt[s (s - a) (s - b) (s - c)]]
+PrintTemporary[Dynamic[{a, b, c}]];
+results = Reap[
+    Do[
+     If[a < b + c \[And] b < c + a \[And] c < a + b,
+      If[GCD[a, b, c] == 1,
+       If[IntegerQ[Heron[a, b, c]],
+        Sow[<|"Sides" -> {a, b, c}, "Area" -> Heron[a, b, c],
+          "Perimeter" -> a + b + c, "MaximumSide" -> Max[a, b, c]|>]
+        ]
+       ]
+      ]
+     ,
+     {a, 1, 200},
+     {b, a, 200},
+     {c, b, 200}
+     ]
+    ][[2, 1]];
+results = SortBy[results, {#["Area"] &, #["Perimeter"] &, #["MaximumSide"] &}];
+results // Length
+Take[results, 10] // Dataset
+Select[results, #["Area"] == 210 &] // Dataset