where s is a complex number, and the function also returns a complex number.
A complex number is really just two coordinates in the complex plane: s=x+iy. So you can plot a complex number on a two-dimensional axis, as in the app.
So the app just shows, for whatever set of complex coordinates you draw on the input plane, what the Riemann Zeta function's output coordinates are in the output plane.
In other words, it transforms your drawing (a set of input points) into another drawing (a set of output points)
It just has a really weird, circular and stretched transformation.
It also has deep connections to number theory and prime numbers, which is why mathematicians obsess over this function. A lot of mathematical theorems rely on the Riemann hypotheis being true, but no one has proved it.
The function is formally defined as:
where s is a complex number, and the function also returns a complex number.
A complex number is really just two coordinates in the complex plane: s=x+iy. So you can plot a complex number on a two-dimensional axis, as in the app.
So the app just shows, for whatever set of complex coordinates you draw on the input plane, what the Riemann Zeta function's output coordinates are in the output plane.
In other words, it transforms your drawing (a set of input points) into another drawing (a set of output points)
It just has a really weird, circular and stretched transformation.
It also has deep connections to number theory and prime numbers, which is why mathematicians obsess over this function. A lot of mathematical theorems rely on the Riemann hypotheis being true, but no one has proved it.