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.

Geometrical interpretation:

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

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

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...

Simple continued fraction of Pythagoras's constant:

The simple continued fraction of Pythagoras's constant is:

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