Do-you-know-a-geometrical-proof-of-the-irrationality-of-number-2-

Question Number 54909 by Hassen_Timol last updated on 14/Feb/19

D o y o u k n o w a g e o m e t r i c a l p r o o f

o f t h e i r r a t i o n a l i t y o f n u m b e r \sqrt{2} ?

Commented by kaivan.ahmadi last updated on 14/Feb/19

https://jeremykun.com/2011/08/14/the-square-root-of-2-is-irrational-geometric-proof/

Commented by kaivan.ahmadi last updated on 14/Feb/19

you can see in above page

Commented by Hassen_Timol last updated on 14/Feb/19

T h a n k y o u s i r!

Commented by maxmathsup by imad last updated on 14/Feb/19

i f \sqrt{2} i s r a t i o n a l w e g e t \sqrt{2} = \frac{p}{q} w i t h p a n d q f r o m Q^{+ ★} w e c a n t a k e

Δ (p, q) = 1 \Rightarrow 2 q^{2} = p^{2} \Rightarrow p^{2} i s e v e n \Rightarrow p e v e n \Rightarrow \exists m \in N / p = 2 m \Rightarrow

2 q^{2} = 4 m^{2} \Rightarrow q^{2} = 2 m^{2} \Rightarrow q^{2} i s e v e n \Rightarrow q i s e v e n \Rightarrow \exists m^{^{'}} / q = 2 m^{^{'}} \Rightarrow

2 d i v i d e p a n d d i v i d e q b u t t h i s i s i m p o s s i b l e b e c a u s e Δ (p, q) = 1 .

Commented by maxmathsup by imad last updated on 14/Feb/19

t h i s p r o o f i s a l g e b r i c .