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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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.
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 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 .
Happy Pi Day