Theory of spiral angles, spirals and trigonometric partitions

by José Mauricio Orellana Díaz

Overview

This mathematical work is a new theory, which complements the existing theories of the Theodorus, Archimedean, Logarithmic and Hyperbolic spirals. Starting from assumptions that a radius, an apothem, an arrow, a chord, a circular sector, are growing or decreasing, in the space of a plane of two or three dimensions in a spiral or exponential or other form. Just as a circle is having partitions to generate its wave function and wavelets. Applying the graphical and mathematical methodology, to draw triangles where all the basic trigonometric identities can be defined. With this new methodology, new trigonometric identities were found for the mean angles as well as two new mathematical equations for the circular sector. Also, laws governing trigonometric spirals were discovered. These laws define trigonometric spirals, thus distinguishing them from the current spirals.

It is also shown how the radius is inversely proportional to the sine or cosine of its angle. These equations indicate which of the two ways can be taken, to analyze, or to make the graphs of the trigonometric spirals. This theory leads us to analyze at infinity each of the properties of a circle, in order to observe how its calculations and graphs are.

Product Details

BN ID:	2940160955162
Publisher:	BARKER & JULES, LLC
Publication date:	07/28/2023
Sold by:	Barnes & Noble
Format:	eBook
File size:	11 MB
Note:	This product may take a few minutes to download.

About the Author

José Mauricio Orellana Díaz (1975) is an Industrial Mechanical Engineer from the National Autonomous University of Honduras of Valle de Sula and has a Master's Degree in Financial Management from the Technological University of Honduras. It has been developed in multiple areas of the agricultural, food, construction and energy industries at a national and international level.

He has been a professor in different institutions at the secondary and higher education level in his native country. Likewise, it has developed theoretical and technological tools, such as software and mathematical theories that have had a positive impact on the field of academic and applied engineering.