Heru Search Method—Unique in the World that Uses Unprecedented Mathematical Formulas and Replaces the Binary Tree Breaking Various Paradigms Like 0(log&amp;lt;i&amp;gt;n&amp;lt;/i&amp;gt;)

Carlos Roberto França

doi:10.4236/ajcm.2017.71003

Abstract

This paper deals with the efficiency of the search, with a method of organization and storage of the information that allows better results than the research trees or binary trees. No one ever dared to present better results than 0(log n) complexity, and when they wish to improve, they use balanced trees, but they continue to use principles that do not impact the pre-semantic information treatment. The Heru search method has as main characteristic the total or partial substitution of the use of the binary trees, enabling the elimination of the approximate results and informing the user the desired information instead of occurrences by sampling outside the desired information. The breakdown of the 0(log n) paradigm and the refinement of the searches are achieved with the use of a set of unpublished mathematical formulas and concepts called Infinite Series with Multiple Ratios.

Highlights

Sir Isaac Newton initiated the research involving Infinite Series with Multiple Ratios (SMRs), but he didn’t conclude or published
Some citations in documentaries about the incomplete work of the brilliant physicist were the source of inspiration for two Brazilian researchers, and what served as an auxiliary at the beginning of the 90s, followed the search for practical applications to the set of 16 formulas
The conceptual exposition begins below from the general term of this new approach. They are concepts that identify the elements that make up the basic law of formation of the same, and that do not invalidate the traditional formulas of the fields mentioned above, because it is a conceptual extension and the conventional formulas become subset of the SMRs

Summary

Introduction

Sir Isaac Newton initiated the research involving Infinite Series with Multiple Ratios (SMRs), but he didn’t conclude or published. SMRs complement and extend centennial physical/mathematical concepts such as those involving arithmetic and geometric progressions, Newtonian kinematics, Torricelli’s equation, and others. They are all formulas that are based on singular events with a single ratio, or a speed or acceleration stipulated as a starting point to solve problems of the universes of physics and mathematics. The conceptual exposition begins below from the general term of this new approach They are concepts that identify the elements that make up the basic law of formation of the same, and that do not invalidate the traditional formulas of the fields mentioned above, because it is a conceptual extension and the conventional formulas become subset of the SMRs

Arithmetic Series in the Conceptual Approach of SMRs—General Terms

Replacing the Binary Tree Search Method

Heru Search Method

Results and Discussion