any genious here please answer this question
Why we use 22/7 or 3.14 as a value of π ?
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Succinctly, pi—which is written as the Greek letter for p, or π—is the ratio of the circumference of any circle to the diameter of that circle. Regardless of the circle's size, this ratio will always equal pi. In decimal form, the value of pi is approximately 3.14. But pi is an irrational number, meaning that its decimal form neither ends (like 1/4 = 0.25) nor becomes repetitive (like 1/6 = 0.166666...). (To only 18 decimal places, pi is 3.141592653589793238.) Hence, it is useful to have shorthand for this ratio of circumference to diameter. According to Petr Beckmann's A History of Pi, the Greek letter π was first used for this purpose by William Jones in 1706, probably as an abbreviation of periphery, and became standard mathematical notation roughly 30 years later.
Succinctly, pi—which is written as the Greek letter for p, or π—is the ratio of the circumference of any circle to the diameter of that circle. Regardless of the circle's size, this ratio will always equal pi. In decimal form, the value of pi is approximately 3.14. But pi is an irrational number, meaning that its decimal form neither ends (like 1/4 = 0.25) nor becomes repetitive (like 1/6 = 0.166666...). (To only 18 decimal places, pi is 3.141592653589793238.) Hence, it is useful to have shorthand for this ratio of circumference to diameter. According to Petr Beckmann's A History of Pi, the Greek letter π was first used for this purpose by William Jones in 1706, probably as an abbreviation of periphery, and became standard mathematical notation roughly 30 years later.
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Well , π this beautiful , weird and interesting constant of mathematics !!
Well this constant is actually geometrically derived by taking the ratio of circumference to diameter of a perfect two dimensional circle.
So, interestingly this ratio that we denote as π
it's value actually comes out to be
π = 3.14159265368979...... so it goes on forever
That is yes ! it's irrational ! never gonna have a repeating or terminal decimal expansion
So, you see if want to make calculations for computing the circumference or area or many more things of a particular circle we will have to use this big number 3.14159265358979...
So obviously it's gonna be very difficult
so for mid and high school students it would be very difficult since even the use of calculators isn't allowed.
So for our satisfaction , we take the value of π = 3.14 obviously this is incorrect but our hands are tied to obey to make our work easier
And also, 3.14 can be expressed as 22/7
Since the value of 22/7 = 3.142857 so very nearly 22/7 is a good fractional approximation of the value of π , however still it's incorrect to use if we want to be precise.
So yeah , hope it's clear now !!
Fun fact is that we now know about a trillion decimal places of π from quantum super computers !!
Well this constant is actually geometrically derived by taking the ratio of circumference to diameter of a perfect two dimensional circle.
So, interestingly this ratio that we denote as π
it's value actually comes out to be
π = 3.14159265368979...... so it goes on forever
That is yes ! it's irrational ! never gonna have a repeating or terminal decimal expansion
So, you see if want to make calculations for computing the circumference or area or many more things of a particular circle we will have to use this big number 3.14159265358979...
So obviously it's gonna be very difficult
so for mid and high school students it would be very difficult since even the use of calculators isn't allowed.
So for our satisfaction , we take the value of π = 3.14 obviously this is incorrect but our hands are tied to obey to make our work easier
And also, 3.14 can be expressed as 22/7
Since the value of 22/7 = 3.142857 so very nearly 22/7 is a good fractional approximation of the value of π , however still it's incorrect to use if we want to be precise.
So yeah , hope it's clear now !!
Fun fact is that we now know about a trillion decimal places of π from quantum super computers !!
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