A Non-Existence Property of Pythagorean Triangles with a 3-D Application

Details A Non-Existence Property of Pythagorean Triangles with a 3-D Application A Non-Existence Property of Pythagorean Triangles with a 3-D Application

2009-03-06

arxiv.org/abs/0903.1280v1

Mathematics

General Mathematics

10 Pages

Scientific paper

After the introduction, in section 2 we state the well known parametric formulas that describe the entire family of Pythagorean triples. In section 3, we list four well known results from number theory, used later in the paper. in section 2, we prove two propositions. Proposition 1 says that the diophantine equation z^2=x^4+4y^4, has no solutions in positive integers x,y, and z. We then use Proposition 1, to prove the insolvability of a certain four-variable diophantine system, which is Proposition 2. In Section 5, we present some examplesof pairs of Pythagorean triangles with a common hypotenuse. In Section 6, we use Proposition 2 to prove Theorem 1: There exists no pair of Pythagorean triangles such that the leg of largest length in the first triangle is the hypotenuse of the second triangle; and in addition, with the leg of smallest length in the first triangle; having the same length as a leg in the second triangle. in Section 7, we present information on Pythagorean boxes, and we describe how to generate infinitely many Pythagorean boxes with a face diagonal of integral length. Finally, in Section 8, we apply Proposition 2 to prove Theorem 2: There exists no Pythagorean box with a pair of congruent (or opposite) faces being squares. And with the four diagonals of equal length in another pair of opposite faces, also having integral length.

Affiliated with

Also associated with

No associations

Rating

A Non-Existence Property of Pythagorean Triangles with a 3-D Application does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with A Non-Existence Property of Pythagorean Triangles with a 3-D Application, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and A Non-Existence Property of Pythagorean Triangles with a 3-D Application will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-136471