arXiv subjects

Kaida Shi

Publications and source records attributed to Kaida Shi.

9 recordsLinked to original sources

arXiv2009

To Get Overall Shapes and New Data of the 120-Cell and the 600-Cell

This research will be helpful for people to display the 2-dimensiona projective models of 4-variable actual problems in many fields, in order to investigate deeply those actual problems. By using the theory of N-dimensional finite rotation group of the regular polytopes, the author established the 2-dimensional projective model of 4-dimensional rectangular coordinate system, and deduced a transformation matrix, and adopt it to display successfully the 2-dimensional overall shapes of two most complicated regular polytopes 120-Cell and 600-Cell. In the meantime, the author calculated all the vertex coordinates and determine the joint relationships between adjacent vertices of the regular polytopes 120-Cell and 600-Cell. Also, this provided a pattern for displaying the 2-dimensional projective model of 4-variable actual problem. (The tables of vertex coordinates of the 120-Cell and the 600-Cell and the table of joint relationship between adjacent vertices of the 120-Cell and the 600-Cell are listed below)

math.GM↗

arXiv2009

The n-dimensional Cube--A New Way to Prove the Fermat's Last Theorem

By studying the n-dimensional cube, the author finds a new way, and use it to proves that the indefinite equation $x^n+y^n=z^n(n=>3)$ has no any solutions of positive integers.

math.GM↗

arXiv2009

New results based on Riemann hypothesis is tenable

Starting from the Euler's identity, the author improved Riemann's results, discovered the relationship between the Riemann Zeta function and the prime function, and obtained two new corollaries based on Riemann hypothesis is tenable. From these corollaries, the author found the relationship between the p_m, its subscript m and the t_m, and obtains a complete table of primes (less than 5000).

math.GM↗

arXiv2009

Solving the Properties of Primes within Prime Series Based on the GRH is Tenable

Investigating Dirichlet L functional equation, the author found the relationship between Dirichlet L functional equation and the prime property function, two new corollaries based on GRH is tenable and the equation of the prime property function. By using the geometric method, the author obtained a formula for solving the properties of primes within the prime series.

math.GM↗

arXiv2003

A Proof that Euler's Constant Gamma is an Irrational Number

The attributes of Euler's constant Gamma have been a baffling problem to the world's mathematicians in the number theory field. In 1900, when German mathematician D. Hilbert addressed the 2nd International Congress of Mathematicians, he suggested twenty-three previously unsolved problems to the international mathematical field. The 7th of these problems pertained to Euler's constant Gamma. After investigating this problem for many years, the author has proved that Euler's constant Gamma is an irrational number.

math.GM↗

arXiv2003

The Proof of Goldbach Conjecture, Twin Primes Conjecture and Other Two Propositions

By creating a new method, the author proved the well-known world's baffling problems Goldbach conjecture, twin primes conjecture, the Proposition (C) and the Proposition $n^2+1$.

math.GM↗

arXiv2003

A Geometric Proof of the Hecke Conjecture

Beginning from the resolution of the Dirichlet L function, using the inner product formula between two infinite-dimensional vectors in the complex space, the author proved the baffling problem--Hecke conjecture.

math.GM↗

arXiv2003

A Geometric Proof of Generalized Riemann Hypothesis

Beginning from the resolution of Dirichlet L function, using the inner product formula of infinite-dimensional vectors in the complex space, the author proved the world's baffling problem--Generalized Riemann hypothesis.

math.GM↗

arXiv2003

A Geometric Proof of Riemann Hypothesis

Beginning from the formal resolution of Riemann Zeta function, by using the formula of inner product between two infinite-dimensional vectors in the complex space, the author proved the world's baffling problem -- Riemann hypothesis raised by German mathematician B. Riemann in 1859.

math.GM↗