Significance of Pi in various science formulae | Happy PI Day

There is no doubt that PI comes under one of the most used formula in mathematics , physics and chemistry . This characteristic of Pi to get fit into number of formulas make it very unique and useful .It actually make large range of formula significant enough to use them for driving complex theorems. On this special day i.e PI day , we are listing some of the many formulas that make use of Pi in them .

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Funny Pi Day posters

Significance of Pi

Let us start with one of the most used formula in Mathematics .This formula was given by famous European scholar of  18th century , Leonard Euler’s . This is often  described as ” the most beautiful formula in mathematics”.This is termed as  Euler’s Formula and it shows that   exponential growth and circular motion are equivalent.

euler _formula

 

Here we are going to give the list of various  formulae involving the  use of mathematical constant π ( PI symbol ) . These include formulae from Euclidean geometry , Physics , Integrals ,Infinite series and various other miscellaneous  formulae  .Let’s start with Euclidean geomtery .

Pi (π) in Euclidean geometry

  • Circumference of a circle  where C = circle circumference and d= circle diameter
  • Area of a circle where A= Circle area and r= radius of a circle
  • Sphere Volume where r = radius of  a sphere
  • Sphere Surface Area where r = radius

Pi (π) in Physic

There are lots and lots of more theorems and concepts that use this amazing constants .Let us check the basic formula of very complex theories such as cosmological constant , Einstein’s theory of relativity , certain formulae in electric science

  • The cosmological constant:
  • Einstein’s field equation of general relativity:

  • Coulomb’s law:  Electric force law where q1 , q2 are charges , r= radius of atom :

  • Buckling Formula :

          

  • Magnetic permeability of free space:

  • Time Period of a  pendulum ( used in case of  small amplitude )

Pi (π) in Certain Other formulas 

  • Integrals

Integrals in incomplete without Pi .While solving integral problems , the value of Pi is taken as 360 degrees (full round of a circle ) .

Gaussian Integral = 

Pi (π) in Efficient infinite series

  • Double Factorial

        

  • Basel problem and Reimann zeta function

       

  • Bernoulli Number

  • Stirling’s approximation

Apart from these , we have an unending list of formulas that use Pi in that such as Euler’s totient function ,Gamma function and son on . It is now quite clear why this special mathematical constant deserves a special day to celebrate its importance .If someone ever says that why Pi is so significant, do not mind sharing this bunch of formulas .

Honor this Pi Day by sharing some of the Pi formulas with your nerdy friends .

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A time to celebrate Irrational side .

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Happy Pi Day

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