lazypast said:Hi
Can someone show me from step one how to show that 22/7 is greater than pi. I don't really know how much I am asking here, but thanks in advance
The purpose of proving 22/7 > pi is to show that the rational number 22/7 is a closer approximation to the irrational number pi than the commonly used approximation of 3.14. This can be useful in various fields of science and mathematics where precise calculations involving pi are needed.
The proof involves using a geometric approach known as the inscribed polygon method. This method involves inscribing a regular polygon inside a circle and calculating its perimeter, which can then be compared to the circumference of the circle. By increasing the number of sides of the polygon, the approximation of pi becomes more accurate.
The steps involved in the proof include drawing a circle, inscribing a regular polygon with n sides inside the circle, calculating the perimeter of the polygon, and then comparing it to the circumference of the circle. This process is repeated with increasing values of n, leading to a more accurate approximation of pi. The final step is to show that the perimeter of the polygon with n sides is always greater than the circumference of the circle.
The significance of this proof lies in its practical applications. In fields such as engineering, physics, and astronomy, precise calculations involving pi are crucial. By using the more accurate approximation of 22/7, these calculations can be made more accurate, leading to better results and designs.
Yes, this proof is universally accepted as it is based on mathematical principles and has been verified by numerous mathematicians and scientists. It is a well-established fact that the rational number 22/7 is a closer approximation to pi than 3.14, and this proof provides a clear and logical explanation for this phenomenon.