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I am reading about the basic properties of the Pythagorean triples, and according to the Wikipedia the only real life application of them is on cryptography, but it does not specify very much apart from providing that reference.

For instance, talking about something more simple, it is possible to simplify the calculation of the area of a right triangle if we know that the sides of the triangle are a Pythagorean triple which is the multiple of a primitive Pythagorean triple, but that does not seem really useful as a shortcut because it implies first knowing that indeed the triple is a multiple of another triple.

So my question is: Are there real life applications of the Pythagorean triples apart from cryptography?

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    $\begingroup$ Teachers demonstrating arithmetically easy examples. $\endgroup$ – Trademark Jun 21 '15 at 5:51
  • $\begingroup$ @Trademark true! that is an application! but the focus of the examples I am looking for on my question is slightly different :) Have a nice Sunday! $\endgroup$ – iadvd Jun 21 '15 at 6:00
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    $\begingroup$ When I worked in landscaping, $21,20,29$ was just perfect for laying out a sidewalk with a $30$' tape and making sure it was perpendicular to the house. $\endgroup$ – poetasis Jun 22 at 11:39
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I'd say the following is one of the oldest and real-lifiest applicatios: In old Egypt, it was necessary after each Nile flood to reestablish land measurements. For this a quick construction of right angles was needed. You can construct a right angle by partitioning a rope into twelve equal parts and then spanning a triangle with side lengths 3parts, 4 parts, 5 parts.

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    $\begingroup$ I read long time ago about that, but I did not remember that exactly the parts were 3,4,5, thank you! $\endgroup$ – iadvd Jun 21 '15 at 6:21
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    $\begingroup$ Wikipedia: rope stretcher. $\endgroup$ – Martin Sleziak Jun 21 '15 at 8:04

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