New Interesting Property and Application of the Rectangular Hyperbola
Xingbo Wang *
Department of Mechatronics, Foshan University, Guangdong, China.
*Author to whom correspondence should be addressed.
Abstract
This paper derives an interesting property of the rectangular hyperbola. On the branch of the first quadrant, the slope of a chord starting from the vertex of the hyperbola has an opposite sign with the slope of the line segment from the coordinate origin to the peak of the chord. An arbitrary another chord starting from the ending-point of the former one continues owning the stated property. With this property, hyperbola xy = N can be subdivided into a series of hyperbolic arcs to factorize N or to estimate the divisor-ratio q/p if N=pq with 2 <p<q is a semiprime. It is proven that a semiprime is easier to be factorized if it has a small divisor-ratio. The paper presents detail mathematical reasoning as well as an approach to realize the factorization or estimation.
Keywords: Rectangular hyperbola, subdivision, integer factorization, divisor-ratio