what is the equation of pi?

Hi - there are any number of them, but they're all infinite series: if you go to Wikipedia and look up "pi", you'll find at least fifteen of them in the "Computation in the Computer Age" section of that entry.

If you are looking to calculate π numerically, there are many series that will eventually converge to π, none of which will yield the exact value with a finite number of terms.

For example, the famous Gregory-Leibniz series will converge rather slowly (requires 10n terms for n accurate digits):
π/4 = 1-1/3+1/5-1/7+1/9-...

The Borweins and Dilcher have improved on the convergence of the above series, giving 136 digits with 100 terms:
http://mathpath.net/leibniz.htm

One of my favourites is the one from T.J.Bromwich(1926):
π/2=1+(2/3)/2+(2*4/(3*5))/2²+(2*4*6/(3*5*7))/2³+....
because it converges relatively rapidly, and each term can be derived from the previous.

The value of pi (π) is a mathematical constant that represents the ratio of a circle's circumference to its diameter. It is an irrational number, meaning it cannot be expressed as a simple fraction or a finite decimal.

The most common way to approximate the value of pi is to use the formula:

π = 3.14159...

However, this is only an approximation, as the decimal representation of pi goes on infinitely without repeating.

To calculate the value of pi with more precision, one can use various mathematical methods, such as the Leibniz formula or the Monte Carlo method. These methods involve complex algorithms and are typically executed using computer programs or specialized mathematical software.

It's important to note that for most everyday calculations, the approximation of pi as 3.14 or 22/7 is sufficient. But if you require a higher level of precision, you would need to use more digits of pi, either by looking them up or by using a specific algorithm to compute them.