Archimedes and his solution for Pi, what do we have that is better?

In summary, the conversation discusses the topic of methods for deriving pi and whether or not there are any current methods better than Archimedes' method of exhaustion. One person suggests that all of the approximations listed on a Wikipedia page are better, while another argues that the page only covers the most efficient and fastest formulas and algorithms, making it difficult for beginners to understand. The conversation ends with a question about the purpose of Physics Forums and a link to a blog post discussing the issue.
  • #1
mesa
Gold Member
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The title pretty much says it all, what do we have today that is better than Archimedes 'method of exhaustion' (although I would argue it is quite beautiful) for deriving Pi?
 
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  • #3
  • #4
mesa said:
Are you suggesting all of those approximations are better than Archimedes?

Obviously, yes.
 
  • #5
mesa said:
Are you suggesting all of those approximations are better than Archimedes?
micromass said:
Obviously, yes.

A wonderfully surprising answer! Which is best and why?
 
  • #6
mesa said:
A wonderfully surprising answer! Which is best and why?

Read the wiki page I linked. It covers all that and more.
 
  • #7
micromass said:
Read the wiki page I linked. It covers all that and more.

I don't see it, explain your reasoning.
***EDIT***
If we all here to just copy and paste wikipedia links then what is the point of PF?
 
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  • #8
mesa said:
I don't see it, explain your reasoning.

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?
 
  • #9
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?

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.
 
  • #10
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?

The point of PF is certainly not so you can ask questions that can be googled in 5 seconds.

https://www.physicsforums.com/blog.php?b=3588

I think we're done here.
 
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FAQ: Archimedes and his solution for Pi, what do we have that is better?

1. Who was Archimedes and why is he associated with the solution for Pi?

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.

2. What is Archimedes' solution for Pi?

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.

3. Is Archimedes' solution for Pi still used today?

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.

4. How accurate was Archimedes' approximation of Pi?

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.

5. What do we have today that is better than Archimedes' solution for Pi?

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.

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