Pi is a very important constant in mathematics as well as in science which is widely in use. On the other hand, we may say that Pi is a really straightforward number. It is represented with symbol Π. The calculation can be done in many ways. It is used and hence can be computed with a variety of methods. In this topic, the student will learn the Pi formula. Let us learn it!
Pi Formula
Concept of Pi
Pi refers to the ratio of the circumference to the diameter of a circle. So its approximate value is 3.14159 and often shortened to 3.14. The decimal in Pi never ends because the numbers never repeat themselves in a permanent pattern. Due to this fact, the number repeats it is not possible to find a circle’s true circumference or area. The record for calculating Pi is with 5 trillion digits! The closest fraction to represent Pi is found to be \(\frac {22}{7}\). But even this is not completely accurate.
The first calculations of Pi were done in the Babylonians in 2000 BC who determined it as 3.125. Further, the Ancient Egyptians came to the conclusion that it was 3.143. Then Plato determined it to be 3.146. Later on, Isaac Newton, who is considered to be calculus’ father, was able to calculate Pi to 16 decimal points.
Facts about Pi
- Rhind Papyrus made the first attempt to try and calculate pi. He built a square inside a circle to calculate the diameter.
- The symbol for Pi was introduced by William Jones in the year 1706.
- The first 36 digits of Pi are the Ludolphine Number. This number was named after Rudolph Van Ceulen who spent the majority of his life calculating the first 36 numbers.
- We celebrate Pi Day on 14th of March every year. Thus, we represent this date numerically by \(\frac {3} {14}.\)
- There are no zeros in the first 31 digits of Pi.
- Some mathematicians believe that it is better to say that circles have an infinite number of corners than to say that they have zero corners
Therefore, Pi i.e. \(\pi\) is the first number we learn as an irrational number. It is a mysterious number which has digits which go on forever and has fascinated people for many years. We learn that we can start to write down it as 3.141592653589….. but that we can never finish it.
Pi is also a really useful number. It appears everywhere in mathematics and also almost countless times in Engineering and Science.
Some Formulas in Mathematics that includes Pi
We define the number \(\pi\) mathematically as follows:
\(\pi = \frac {c}{d}\)
Where,
| \pi | Constant |
| d | diameter |
| c | circumference |
Other formulas are:
- The circumference of a circle with radius r is \(2 \pi r.\)
- We denote the area of a circle with radius r as \(\pi r^2.\)
- The volume of a sphere with radius r is \(\frac {4}{3} \pi r^3.\)
- The surface area of a sphere with radius r is\( 4 \pi r^2.\)
Solved Examples for Pi Formula
Q.1: Compute the value of \(\pi\), if a circle has a radius as 7 cm and circumference as 44 cm.
Solution: Given here:
c = 44 cm
d = \(2 \times 7 = 14 cm\)
Also, formula is,
\(\pi = \frac {c}{d} = \frac {44}{14}\)
= 3.142857142…..
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