Pie how many numbers

While treating pi as equal to 3. Archimedes, the greatest mathematician of antiquity , got as far as 3. Archimedes approached his calculation of pi geometrically, by sandwiching a circle between two straight-edged regular polygons. Using the new technique of integration , mathematicians like Gottfried Leibniz, one of the fathers of calculus, could prove such elegant equations for pi as:.

The right-hand side, just like pi, continues forever. But more efficient formulas were discovered. Take this one, from Leonhard Euler, probably the greatest mathematician ever, in the 18th century:. And Srinivasa Ramanujan, a self-taught mathematical genius from India, discovered the totally surprising and bizarre equation below in the early s.

Each additional term in this sum adds eight correct digits to an estimate of pi:. Much like with the search for large prime numbers , computers blasted this pi-digit search out of Earth orbit and into deep space starting in the mids. That means, for any circle, you can divide the circumference the distance around the circle by the diameter and always get exactly the same number.

It doesn't matter how big or small the circle is, Pi remains the same. Pi is often written using the symbol and is pronounced "pie", just like the dessert. History Pi web sites Do it yourself Pi The Digits Formulas A Brief History of Pi Ancient civilizations knew that there was a fixed ratio of circumference to diameter that was approximately equal to three.

The Greeks refined the process and Archimedes is credited with the first theoretical calculation of Pi. In Lambert proved that Pi was irrational, that is, that it can't be written as a ratio of integer numbers. In Lindeman proved that Pi was transcendental, that is, that Pi is not the root of any algebraic equation with rational coefficients. This discovery proved that you can't "square a circle", which was a problem that occupied many mathematicians up to that time.

More information on squaring the circle. How many digits are there? View Iframe URL. See, that's not so difficult for a computer. However, you can see that even after 10, terms the calculated value is still different than the accepted value. This isn't the best series to calculate Pibut I said that earlier. This is my favorite Pi activity. Here is the idea. Generate pairs of random numbers between 0 and 1 to create random x,y coordinates. Plot these points on a 1 by 1 grid and calculate their distance to the origin.

Some of these will have a origin distance less than 1 and some will be greater than 1. The points with a distance of less than one are "inside a circle"actually it's a quarter of a circle. You really should play around with this because it's fun. Try changing the number of points or something like that. I included a "rate " statement so you can see the points being added. Oh, run it more than onceeach time you get a different result because of the random part.

Get out your calculator. Use 9. Now try this:. That's pretty close to the accepted value of Piand it's not a coincidence. It comes from the original version of the meter as a unit of length. One way to define a meter is to create a pendulum that takes 1 second to make one swing or 2 seconds for the period. 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?