Wolfram Function Repository

Instant-use add-on functions for the Wolfram Language

Function Repository Resource:

 PythagoreanTripleQ

Source Notebook

Determine whether a triple of integers constitutes a Pythagorean triple

Contributed by: Jordan Hasler, Wolfram|Alpha Math Team

ResourceFunction["PythagoreanTripleQ"][{a,b,c}]

determines whether the triple of integers {a,b,c} satisfies a2+b2=c2.

Details

The option "UnorderedTriple" determines whether to treat the input as ordered and defaults to False. When set to True, ResourceFunction["PythagoreanTripleQ"] returns True if any ordering of the triples satisfies a2+b2=c2.

Examples

Basic Examples (2) 

The ordered triple {3,4,5} is a Pythagorean triple:

In[1]:=
ResourceFunction[ "PythagoreanTripleQ", ResourceSystemBase -> "https://www.wolframcloud.com/obj/resourcesystem/api/1.0"][{3, 4, 5}]
Out[1]=

{2,3,4} is not a Pythagorean triple:

In[2]:=
ResourceFunction[ "PythagoreanTripleQ", ResourceSystemBase -> "https://www.wolframcloud.com/obj/resourcesystem/api/1.0"][{2, 3, 4}]
Out[2]=

Options (2) 

{5,4,3} is not a Pythagorean triple:

In[3]:=
ResourceFunction[ "PythagoreanTripleQ", ResourceSystemBase -> "https://www.wolframcloud.com/obj/resourcesystem/api/1.0"][{5, 4, 3}]
Out[3]=

Specify that the triple is unordered to determine if any ordering of the numbers is a Pythagorean triple:

In[4]:=
ResourceFunction[ "PythagoreanTripleQ", ResourceSystemBase -> "https://www.wolframcloud.com/obj/resourcesystem/api/1.0"][{5, 4, 3}, "UnorderedTriple" -> True]
Out[4]=

Properties and Relations (2) 

To determine whether any ordering of potentially noninteger side lengths forms a right triangle, use RightTriangleQ:

In[5]:=
ResourceFunction["RightTriangleQ"] {5, 4, 3}]
Out[5]=
In[6]:=
ResourceFunction["RightTriangleQ"][{Sqrt[2], Sqrt[3], Sqrt[5]}]
Out[6]=

The integers {5,4,3} can form a right triangle when considered as edge lengths, but do not form a Pythagorean triple due to their ordering:

In[7]:=
ResourceFunction["RightTriangleQ"][{5, 4, 3}]
Out[7]=
In[8]:=
(* Evaluate this cell to get the example input *) CloudGet["https://www.wolframcloud.com/obj/721b003b-f461-4bac-a737-4d65a7b855c4"]
Out[8]=

Publisher

Wolfram|Alpha Math Team

Version History

  • 2.0.0 – 23 March 2023
  • 1.0.1 – 29 March 2021
  • 1.0.0 – 18 September 2020

Related Resources

Author Notes

To view the full source code for PythagoreanTripleQ, run the following code:

In[1]:=
FileNameJoin[ ReplacePart[ FileNameSplit[FindFile["ResourceFunctionHelpers`"]], -1 -> "PythagoreanTripleQ.wl"]] // SystemOpen

License Information