Abstract:
We investigate the arithmetic properties of the value $\mathrm{arctg}\, \frac {1}{3}$. We elaborate special integral construction with the property of symmetry for evaluating irrationality measure of this number. We research linear form, generated by this integral, and prove a new result for extent of the irrationality of $\mathrm{arctg}\, \frac {1}{3}$, which improves the previous one.