, for example, which evidently has algebraic values for all rational arguments
, will on the other hand always take transcendental values for irrational algebraic values of the argument
. We can also give this statement a geometrical form, as follows:
If, in an isosceles triangle, the ratio of the base angle to the angle at the vertex be algebraic but not rational, the ratio between base and side is always transcendental.
In spite of the simplicity of this statement and of its similarity to the problems solved by Hermite and Lindemann, I consider the proof of this theorem very difficult; as also the proof that
The expression
