9 дек. 2020 г. · Pi cannot be transcendental because pi is defined as the ratio a circle's circumference divided by a circle's diameter and the derivation is an ...

2 мая 2019 г. · An "easy" way to do this is by assossiating each algebraic number with the English sentence "It's the Nth smallest root of the polinomial p(x)." ...

23 июн. 2018 г. · The one-page proof of pi's irrationality (expanded into a 20 minute video of course) has potential, I think. It does require competence in ...

22 авг. 2021 г. · Answer: yes. Proof: if some A = π p/q were algebraic, then A q/p would be algebraic, but A q/p = π. Just let p/q=0.

1 апр. 2014 г. · All proofs of transcendence I know of are proofs by contradiction. You assume the number may be written as the root of a polynomial, and derive ...

9 янв. 2024 г. · The proof of this theorem relies on special features of the exponential function that don't generalize to arbitrary exponential bases. Upvote

Okay, today was the day I finally understood why pi is transcendental. Feels good.

5 дек. 2022 г. · The phrasing of the post suggests that for any transcendental T, the number T(pi) is algebraic. This is false, no?

13 февр. 2014 г. · Yeah I've seen part of that before. Simply expand (x-pi)(x-e), and get coefficients of e + pi and e*pi, so at least one of them is irrational ...

25 мая 2024 г. · A rational number a/b is the solution to the polynomial bx - a = 0. This means that, by contrapositive, if a number is transcendental, it is irrational.