micromass said:It took me 5 seconds to google your answer: http://en.wikipedia.org/wiki/Approximations_of_π
mesa said:Are you suggesting all of those approximations are better than Archimedes?
mesa said:Are you suggesting all of those approximations are better than Archimedes?
micromass said:Obviously, yes.
mesa said:A wonderfully surprising answer! Which is best and why?
micromass said:Read the wiki page I linked. It covers all that and more.
mesa said:I don't see it, explain your reasoning.
micromass said:Explain what? That the wiki page covers the most efficient and fastest formulas and algorithms to approximate ##\pi##? Did you even look at the wiki page?
mesa said:No doubt about the power of some of those identities such as Ramanujan's 1/Pi (a personal favorite!) however it is difficult to 'see', even the newbies on PF can agree to that. Providing a simple link to wikipedia and claiming victory is not being scientific.
mesa said:If we all here to just copy and paste wikipedia links then what is the point of PF?
Archimedes was a Greek mathematician, physicist, engineer, inventor, and astronomer who lived in the 3rd century BC. He is credited with discovering the mathematical constant Pi, which represents the ratio of a circle's circumference to its diameter.
Archimedes used a method called the "method of exhaustion" to approximate the value of Pi. He inscribed and circumscribed polygons inside and outside of a circle, respectively, and calculated their perimeters to get closer and closer approximations of Pi.
While Archimedes' method is still taught in mathematics, it is not used in modern calculations of Pi. With the advancement of technology, we now have more precise and efficient methods for calculating Pi, such as using infinite series or computer algorithms.
Archimedes' approximation of Pi was remarkably accurate for his time, with his final calculation being between 3.1408 and 3.1429. This is impressive considering he did not have the use of calculus or modern technology.
Today, we have various methods for calculating Pi that are more efficient and accurate than Archimedes' method. These include infinite series, continued fractions, and computer algorithms. We also have advanced technology, such as supercomputers, that can calculate Pi to trillions of digits.