Law of cosines - triples: Difference between revisions
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There are 18394 solutions for gamma = 60 degrees in the range 1 to 10000 where the sides are not all of the same length.
</pre>
=={{header|C sharp}}==
<lang csharp>using System;
using System.Collections.Generic;
using static System.Linq.Enumerable;
public static class LawOfCosinesTriples
{
public static void Main2() {
PrintTriples(60, 13);
PrintTriples(90, 13);
PrintTriples(120, 13);
PrintTriples(60, 10_000, true, false);
}
private static void PrintTriples(int degrees, int maxSideLength, bool notAllTheSameLength = false, bool print = true) {
string s = $"{degrees} degree triangles in range 1..{maxSideLength}";
if (notAllTheSameLength) s += " where not all sides are the same";
Console.WriteLine(s);
int count = 0;
var triples = FindTriples(degrees, maxSideLength);
if (notAllTheSameLength) triples = triples.Where(NotAllTheSameLength);
foreach (var triple in triples) {
count++;
if (print) Console.WriteLine(triple);
}
Console.WriteLine($"{count} solutions");
}
private static IEnumerable<(int a, int b, int c)> FindTriples(int degrees, int maxSideLength) {
double radians = degrees * Math.PI / 180;
int coefficient = (int)Math.Round(Math.Cos(radians) * -2, MidpointRounding.AwayFromZero);
int maxSideLengthSquared = maxSideLength * maxSideLength;
return
from a in Range(1, maxSideLength)
from b in Range(1, a)
let cc = a * a + b * b + a * b * coefficient
where cc <= maxSideLengthSquared
let c = (int)Math.Sqrt(cc)
where c * c == cc
select (a, b, c);
}
private static bool NotAllTheSameLength((int a, int b, int c) triple) => triple.a != triple.b || triple.a != triple.c;
}</lang>
{{out}}
<pre>
60 degree triangles in range 1..13
(1, 1, 1)
(2, 2, 2)
(3, 3, 3)
(4, 4, 4)
(5, 5, 5)
(6, 6, 6)
(7, 7, 7)
(8, 3, 7)
(8, 5, 7)
(8, 8, 8)
(9, 9, 9)
(10, 10, 10)
(11, 11, 11)
(12, 12, 12)
(13, 13, 13)
15 solutions
90 degree triangles in range 1..13
(4, 3, 5)
(8, 6, 10)
(12, 5, 13)
3 solutions
120 degree triangles in range 1..13
(5, 3, 7)
(8, 7, 13)
2 solutions
60 degree triangles in range 1..10000 where not all sides are the same
18394 solutions</pre>
=={{header|Factor}}==
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