How can pi be estimated

It appears everywhere in mathematics and also has countless uses in Engineering and Science. For example if an engineer wants to calculate the volume of a water pipe they will use the following formula for a cylinder:. Where is the radius of the pipe and is the height of the pipe. This is what ancient civilisations would have done and it is how they would have first realised that there is a constant ratio hidden within every circle.

Archimedes began by inscribing a regular hexagon inside a circle and then circumscribing another regular hexagon outside the same circle. Archimedes then found a way to double the number of sides of his hexagons.

Back to the new record, though. Because the last several records have all used the same algorithm, any changes in speed represent something in the programming or computing power on display. And for what it's worth, simply having an algorithm to use is one thing, but how you "implement" that algorithm in code can vary a great deal. This is a really important point to make, because these records are set as the result of careful mathematical thinking, as well as the practical concerns of programming a computer to do what we want.

The wrong programming can absolutely sink a project in terms of increasing computation time. It took him 15 years to do so! At the time, Shanks was the fastest "computer" around. In January , Timothy Mullican—a cybersecurity analyst and entrepreneur living in Huntsville, Alabama—broke the previous world record for the "most accurate value of pi," a title that he will continue to hold until the Guinness Book of World Records certifies Keller's attempt.

Mullican calculated the value down to 50 trillion digits, upsetting the prior record holders from Google. As for Keller and company? They're keeping their full calculation for the number pi under lock until Guinness certifies their record. If you remember, there is a relationship between period and length for a pendulum with a small oscillation amplitude :. Put in 1 meter for the length and 2 seconds for the period and boom there is your connection. Here is a more detailed explanation.

If you don't think that equation is crazy and awesome, then you aren't paying attention. It makes a relationship between these five numbers:. But why does this equation work? That's not such a simple answer. Of course, you could use Euler's formula for exponentials:. However, that is sort of like explaining magic with more magic.

For me, the problem is that we like to think of numbers as real countable things. But you can't count an imaginary number. You can say that 3 2 is like 3 groups of 3, but what about 3 1. Or what about 3 Those are pretty tough to picture. If you still want to grok this Euler Identity, check out this site. Imagine a large sphere. If you know the diameter of this large sphere, you can also find the circumference using the value of Pi.

Now replace the sphere with the diameter of the observable universe at 93 billion light years yes, I know this is bigger than 13 billion light yearsit's complicated. If we don't know the exact value of Pi, but one digits then we don't know the exact circumference.

However, the uncertainty in the circumference is less than the Planck lengththe smallest unit of distance measurement that has any meaning. Active Oldest Votes. Matt E Matt E k 10 10 gold badges silver badges bronze badges. I considered adding a discussion of these, AGM, etc. And it didn't seem too misleading to discuss these formulas based on the arctan series, since they were the key methods at one time and polygonal methods had already been mentioned.

In the end, I just wanted to record an answer with some connection to actual practice, as a counterweight to some of the Buffon's needle type answers that were already here. It is extremely hard to make a nearly perfect circle out of thread, and even if you can good luck obtaining a sufficiently precise measuring instrument.

In fact, probably lots of people have. Petite Etincelle Petite Etincelle Shuchang Shuchang 9, 4 4 gold badges 23 23 silver badges 43 43 bronze badges. Stefan Stefan I cannot see why you should call this an easy method, even with quotes. Neither do I see what is "robust" about the initial geometric method; what kind of perturbations is this robust against?

And the "easy" means that although it seems like a straight ahead method, it's quite difficult to achieve it in practise. NoBugs NoBugs 5 5 bronze badges. Asif Iqubal Asif Iqubal 1 1 1 bronze badge. Upcoming Events.