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This article is about the centroid of any real number. In mathematics, real numbers are the basic
of the concept of measure. Real numbers are contributed a lot to the history of Humanity and
pioneered the structure of technological developments. Real numbers are enabled the concept
of numbers to be unified in the process and this expansion of numbers is achieved by adding
new operations to it. Many studies are carried out on the resulting number system. Some of
these studies are logarithmic calculations, functional operations, logic and base studies. Binary
logic allowed for communication and digital structure. This situation is contributed to every
part of life. Therefore, due to the contribution of numbers to life, there is a significant need for
a change in number systems and bases. The topic base of numbers is gained importance in 2023.
The definition of centroid, which is related to the base, is given in 2024. The connection of
numbers with the centroid is examined in this study. New situations related to numbers are
investigated. The common aspect of sets and centralizers is discussed. The new perspective on
numbers is gained with this aspect. In particular, different expressions of numbers are obtained.
This situation is drew attention to the idea of numbers intertwined with logic. Centroids of
positive integers are written. This centroid relation of real numbers is given. The course of
numbers is analyzed. The foundation of logic with the centered is built. New developments of
the centrist in itself are observed. The subject is researched in depth in order to pioneer further
studies.

This study is about division in matrices and eigenvalues-eigenvectors. The concept of eigenvalues-eigenvectors in the literature is discussed. The status of division operation on these concepts is analyzed. The eigenvalues and eigenvectors of the elements forming the division are compared with the result. The matrix resulting and the resulting difference are investigated. The eigenvalues-eigenvectors of the constituent matrices the division and the eigenvalueseigenvectors obtained from the result matrix are examined. The brief literature review of the study is written and the summary history of this study is added in the first section. The theorems related to the subject are listed. Some applications related to this topic are given. The preliminary information that will form the second part is given. The new developments and findings are investigated in the next section. The changes of known definitions, theorems and lemmas are observed. If there are unprotected cases, examples are given for these situations. The new contributions on the parallel cases of matrix product and scalar product in the eigenvalue definition are investigated. The important hints that will contribute to transformations are obtained. The concept of rotation in the planes in the studies is concluded carried to higher dimensions with this contribution. The rotation in the plane is realized only in two directions. There is no direction limit in dimension 3. This situation covers matrices larger than order 3rd. The computation of parallel states corresponding to the same eigenvalue is expected to be of new interest. In short, the study marks the beginning of innovations between multiplication-division and eigenvalue-eigenvector.

Konik kesitlerinin çiziminde döndürme yok edilmeden açı kullanılmadan çizilebilirliğine dair 2014 yılında tescil edilen yöntemdir.