CONSIDERATION OF MANUAL ESTIMATION OF THE VALUES OF PI (π): IMPROVEMENT OF TAN150 OVER TAN300

OLADEMO Johnson O. Ani, OLAGUNJU Samuel Oluand LAWAL Matthew Oluwafemi

Department of Mathematics

Adeyemi College of Education, Ondo.

 

Abstract

Mathematicians eventually discovered that there are numerous exact formulas for calculating Pi (π). The only catch is that each formula requires you to do something an infinite number of times (which makes sense given that the digits of Pi (π) go on forever). One of the amazing things which interests people about Pi (π) is that there is not just one formula, but a large number of different ones for people to study. In 2004, the world record was that a computer has calculated Pi (π) correct to 13,300,000,000,000 decimal places.  The purpose of this study is to improve on the manual computation and to develop a new formula that will bring this improvement. In some ways, Pi (π) is a really straight forward number. calculating Pi (π) simply involves taking any circle and dividing its circumference by its diameter. On the other hand Pi (π) is the first number we learn about at school where we cannot write it as an exact decimal. It is a mysterious number which has digits which go on forever and has fascinating people for thousands of years.

 

Key Words: π, convergence rate, algebraic numerical method, trigonometric, significant figures.