Friday, June 18, 2021

Pythagoras's Constant

 Pythagoras's constant


Introduction:

Pythagoras's constant:
 
   The square root of 2 , i.e., √2 is known as the Pythagoras's constant.


Pythagoras's constant


Geometrical interpretation:

   Pythagoras's constant geometrically represents the length of  diagonal of a square with unit lengh.

Pythagoras's constant


  Pythagoras's constant is also the length of the  hypotenuse of a right isosceles triangle of unit base and unit perpendicular.

Pythagoras's constant



Properties:

 Pythagoras's constant √2 is an irrational number. More interesting fact is that, it is the first irrational number.


Decimal expansion:


The decimal expansion of pythagoras's constant is: 

   √2= 1.414213562373...

Pythagoras's constant

Simple continued fraction of Pythagoras's constant:


The simple continued fraction of Pythagoras's constant is:

Pythagoras's constant



If you find any incorrect information or know more about this topic, please mention in the comment section!!!

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