Abstract
In geometrical computations it is often necessary to find two unit vectors such that they and a given vector form an orthogonal basis. Computationally simple forms for the two unit vectors are clearly useful. We show that they cannot always be chosen to have rational coordinates, but that in general the simplest possible vectors can be chosen to involve only one square root. We develop number-theoretic criteria for the existence of a rational vector and an effective algorithm for calculation of one if it exists. We also discuss storage and time requirements of the algorithm.
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.
