# Is the Euler–Mascheroni constant an algebraic number or a transcendental number?

Valid Assumption (Convergence): $1. \gamma = \frac{\sqrt{z^{2} - 1}}{2}$.

Remark: We tentatively assume $z$ is an algebraic number (rational number) where $1.52 < z < 1.53$.

We can apply Newton’s Method to equation one and study its convergence with regards to $\gamma$.

Warning: This may be a difficult problem…

Dave.