  The main result of the paper is a definition of possible ways of the
confirmation of the Riemann hypothesis based on the properties of the vector
system of the second approximate equation of the Riemann Zeta function. The
paper uses a feature of calculating the Riemann Zeta function in the critical
strip, where its approximate value is determined by partial sums of the
Dirichlet series, which it is given. These expressions are called the first and
second approximate equation of the Riemann Zeta function. The representation of
the terms of the Dirichlet series by vectors allows us when analyzing the
polyline formed by these vectors: 1) explain the geometric meaning of the
generalized summation of the Dirichlet series in the critical strip; 2) obtain
formula for calculating the Riemann Zeta function; 3) obtain the functional
equation of the Riemann Zeta function based on the geometric properties of
vectors forming the polyline; 4) explain the geometric meaning of the second
approximate equation of the Riemann Zeta function; 5) obtain the vector
equation of non-trivial zeros of the Riemann Zeta function; 6) determine why
the Riemann Zeta function has non-trivial zeros on the critical line; 7)
understand why the Riemann Zeta function cannot have non-trivial zeros in the
critical strip other than the critical line.
