Heronian triangles: Difference between revisions

=={{header|Mathematica}} / {{header|Wolfram Language}}==

<lang Mathematica>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</lang>

{{out}}

<pre>517

Sides Area Perimeter MaximumSide

{3,4,5} 6 12 5

{5,5,6} 12 16 6

{5,5,8} 12 18 8

{4,13,15} 24 32 15

{5,12,13} 30 30 13

{9,10,17} 36 36 17

{3,25,26} 36 54 26

{7,15,20} 42 42 20

{10,13,13} 60 36 13

{8,15,17} 60 40 17

Sides Area Perimeter MaximumSide

{17,25,28} 210 70 28

{20,21,29} 210 70 29

{12,35,37} 210 84 37

{17,28,39} 210 84 39

{7,65,68} 210 140 68

{3,148,149} 210 300 149</pre>