The discussion revolves around the comparison of Archimedes' method of exhaustion for deriving Pi with modern approximations and algorithms. Participants explore the beauty and effectiveness of Archimedes' approach while questioning the value of simply referencing online sources for more efficient methods.
Participants do not reach a consensus on whether modern methods are definitively better than Archimedes' approach. There are competing views regarding the value of linking to external sources versus providing original reasoning.
Some participants express frustration with the reliance on quick online searches, indicating a desire for more substantive discussion. The complexity of modern formulas for Pi is noted, but there is no resolution on their comparative effectiveness.
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?