Abstract
A Pythagorean triple is a triple of positive integers $(a,b,c)$ such that $a^2+b^2=c^2$. If $a,b$ are coprime, then it is called a primitive Pythagorean triple. It is known that every primitive Pythagorean triple can be generated from the triple $(3,4,5)$ using multiplication by unique number and order of three specific $3\times3$ matrices, which yields a ternary tree of triplets. Two such trees were described by Berggren and Price, respectively. A different approach is to view the primitive Pythagorean triples as points in the three-dimensional Euclidean space. In this paper, we prove that the triple of descendants of any primitive Pythagorean triple in Berggren's or Price's tree forms a triangle (and therefore defines a plane), and we present our results related to these triangles (and these planes).
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
