# Can pi be written as an infinite series?

## Can pi be written as an infinite series?

A stunning solution of the mystery was discovered by Indian mathematicians about 1500 ce: π can be represented by the infinite, but amazingly simple, series π4 = 1 − 13 + 15 − 17 +⋯. They discovered this as a special case of the series for the inverse tangent function: tan−1 (x) = x − x33 + x55 − x77 +⋯.

## Why is Pi shown in infinite series?

Pi is irrational, and all irrational numbers, when calculated in decimal form, continue on forever in a string of digits which seem to lack any kind of pattern. Notice I mention that there is no pattern… 1/3 = . 33333333333 with the 3’s continuing on into infinity. This is NOT an irrational number.

How do you find PI in a series?

The circumference of a circle is found with the formula C= π*d = 2*π*r. Thus, pi equals a circle’s circumference divided by its diameter. Plug your numbers into a calculator: the result should be roughly 3.14. Repeat this process with several different circles, and then average the results.

What is a good pi %?

If the rate is 94% or less than it, the person needs to be treated quickly. Less than 90% of oxygen saturation is a clinical emergency. The normal perfusion index (PI) ranges from 0.02% to 20% showing weak to strong pulse strength.

### Did Archimedes calculate pi?

Around 250 B.C., the Greek mathematician Archimedes calculated the ratio of a circle’s circumference to its diameter. Archimedes’ value, however, was not only more accurate, it was the first theoretical, rather than measured, calculation of pi. …

### Is there a formula for pi?

The formula for the value of pi is the ratio of the circumference of a circle to its diameter. In the ratio form, it is π = Circumference/Diameter.

Is there an exact formula for pi?

Mathematicians eventually discovered that there are in fact exact formulas for calculating Pi (π). You need to add up more than 300 terms in order to produce Pi (π) accurate to two decimal places! Another series which converges more quickly is the Nilakantha Series which was developed in the 15th century.