Q&A for How to Calculate Pi

It is not precisely equal to pi. While it does look like pi at first (3.14285...), pi is 3.14159... It cannot be equal to pi because 3.14285 ends up repeating. Pi is an irrational number, meaning it goes on forever and does not repeat. Remember that irrational numbers are defined as "not being able to be written as a ratio between two numbers." 22/7 is a ratio of two numbers, so it cannot be exactly equal to pi.

You can't. Pi cannot be a fraction because it is irrational. This means that it cannot be expressed as a ratio of two rational numbers. Pi is sometimes expressed as the fraction 22/7, but that is just an approximation.

An irrational number is a number that cannot be expressed as a ratio of whole numbers (i.e., as a fraction). The root of the word 'irrational' is 'ratio', and the prefix 'ir' means 'not'. The word can have different meanings outside of math.

A rational number is a number that can be expressed as a fraction of two integers. There are no two integers you can plug into C and D that will give pi. Either the circumference or the diameter of the circle (if not both) is always irrational (though, like pi, we would normally round them when doing math to simplify things).

3.14159265358979.... (the numbers never end!)

The formula you are looking for is ∞*sin(180/∞).

2π = 2*π = 2*3.14.... = 6.28.... Sometimes, people call this value τ (tau).

The world record was set by a very high-powered computer. You're not likely to break the record at home.

Memorization is your only hope. Mathematicians believe that the digits of pi are essentially random (with no pattern).

Set the calculator to either degree, radian or gradian mode and then press the "sin" which may alternatively also be called the "sin()" button. Put the value of the angle in between the parenthesis and press "=". The answer will be the sine of that angle.

Ask your teacher what number is acceptable. 3.14 or 22/7 are often used.

It is an alternative way of highlighting that it is multiplication, usually hand-written as x.

Pi is always equal to the circumference of a perfect circle divided by its own diameter. In mathematical terms: π = C/d.

Put .5 at the end. For example: Find the radius of a circle that has a diameter of 7 cm. Do 7 divided by 2= 3 1/2 and convert 1/2 into .5 and 3+.5 =3.5.

No, changing the base wouldn't help.

You can't because there is no way to write is 2 numbers on each side of / . You would simply do a decimal like (3.14285....) using division might be the easiest way for most people in this case.

Because you divided by zero. You have to use a positive integer for the denominator.

Pi is a numerical comparison between a circle's diameter and its circumference. It is a constant relationship regardless of the size of the circle. Pi is a commonly used tool in various branches of mathematics, as well as many other scientific pursuits.

It doesn't; sin(180) is a constant, and when multiplied by x, results in a straight line function. As x increases, xsin(180) tends toward positive infinity.

The Gregory-Leibniz series uses infinite 4/(odd number) fractions and still gives an approximate result. Remember that pi consists of infinite numbers in decimals that do not repeat in a pattern.

No. Pi is an endless string of unpredictable digits. The digits are not random, they are determined precisely by the formula c/d where c is the circumference and d is the diameter of a given perfect circle. Pi is said to be a normal number, meaning that every possible sequence of digits is equally likely to appear in it.

The Chudnovsky algorithm can really get you places. It is, however, quite complex.

Yes, however the approximation often uses more digits than the calculator can display. Also, after a few dozen digits of tau (2pi), even on a cosmological scale no more digits are needed to accurately measure nearly anything.

The only way C could equal π/2, which is (π)(½), is if the diameter was half a unit in length (that is, half a meter, half a foot, etc.). That means the radius would be one-quarter of a unit in length, and the area would be πr², or (π)(¼)² = (π)(1/16), = π/16 square units (square meters, square feet, etc.).

When compared to one billion iterations of Gregory-Leibniz series, the discrepancy is little bit under 1.5861 * (10^-8) %, which is pretty accurate for most applications. If you would have used 22/7, the discrepancy would have been around 0.04 %.

It depends on if you round up or down. If PI = 3.1415926... and you round to 3.1416 then your ratio of C to R is .00000734641... too big because you rounded up. In the real world, a circle of 1m circumference would be off by .007mm which is about 1/10th the diameter of a human hair.

These days pi is calculated by computers and can now be expressed in more than a trillion digits. It's an irrational number, which means that it literally has no end. The reason in this case is that the circumference of a circle and its diameter are related to each other numerically in such a way that there is no number (no matter how small) that will divide evenly into both quantities.

If you have a scientific calculator, you can just press the pi button, or you can estimate with this equation: 9999*sin(180/9999). To get a higher accuracy use more 9's, but remember to keep both numbers the same. Pi cannot be calculated exactly because it is irrational.

Approximation by inscribed polygon. You found n points on the perimeter of a unit circle. If n is big enough, the perimeter of the polygon is a good enough approximation of the perimeter of the circle. This method approximates 2pi from below meaning you'll always be a little bit less than 2pi, but by choosing enough points can make the error as small as you like.

Although there isn't any practical use to calculate pi out to so many places, people enjoy doing it to break records or look for a pattern.