A slight clarification in return: the constructible numbers are a strict subset of the algebraic (i.e. non-transcendental) real numbers.
(The constructible numbers are those numbers resulting from the closure of the rational numbers under square roots.)
This means that although the proof of pi’s transcendentality proved that squaring the circle is impossible, it could have been the case that pi was neither transcendental nor constructible. A simple example of such a number is the cube root of 2.
Thanks for the correction - misremembered that.
A slight clarification in return: the constructible numbers are a strict subset of the algebraic (i.e. non-transcendental) real numbers.
(The constructible numbers are those numbers resulting from the closure of the rational numbers under square roots.)
This means that although the proof of pi’s transcendentality proved that squaring the circle is impossible, it could have been the case that pi was neither transcendental nor constructible. A simple example of such a number is the cube root of 2.