How did we get 22/7 as approximate value for pi?
How did we get 22/7 as approximate value for pi?
Pi is a Transcendental Number in that it transcends our ability to define it in terms of roots of rationals. In other words, it cannot be defined as the root of any rational number. According to Archimides approximation of pi, 223⁄71 < π < 22⁄7 and 3.14 would be a good approximation of Pi for all practical purposes.
If you were a numberphile fan like me, you would know that there are even better approximations than 22/7. For instance, π ≈ 62832/20000 is a correct up to 5 decimal places. In fact a whole pi approximations page at Mathworld.Wolfram is dedicated to this very topic.
Now I can find my inner peace to answer your previous question as to what is Pi. The original definition for Pi was as the ratio of the Circumference of any circle to it’s Diameter. But it proved to be less useful mathematical in this form. So now we have several newer, more complex definitions of Pi (one in terms of an Infinite Series). But the root of it all was the fact that no matter how large a circle you make, it’s circumference to diameter ratio was a constant called Pi
Pi is a Transcendental Number in that it transcends our ability to define it in terms of roots of rationals. In other words, it cannot be defined as the root of any rational number. According to Archimides approximation of pi, 223⁄71 < π < 22⁄7 and 3.14 would be a good approximation of Pi for all practical purposes.
If you were a numberphile fan like me, you would know that there are even better approximations than 22/7. For instance, π ≈ 62832/20000 is a correct up to 5 decimal places. In fact a whole pi approximations page at Mathworld.Wolfram is dedicated to this very topic.
Now I can find my inner peace to answer your previous question as to what is Pi. The original definition for Pi was as the ratio of the Circumference of any circle to it’s Diameter. But it proved to be less useful mathematical in this form. So now we have several newer, more complex definitions of Pi (one in terms of an Infinite Series). But the root of it all was the fact that no matter how large a circle you make, it’s circumference to diameter ratio was a constant called Pi
