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What is the proper definition of π
What is the proper definition of π
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Solution
Definition: Pi is a number - approximately 3.14..
it is the circumference of any circle divided by its diameter
That is 2πr/2r
The number Pi, denoted by the Greek letter π - pronounced 'pie', is one of the most common constants in all of mathematics. It is the circumference of any circle, divided by its diameter. Nobody knows its exact value, because no matter how many digits you calculate it to, the number never ends. For most practical uses, you can assume it is 3.142.
Some people have written computer programs and calculated it to an astonishing accuracy. For example some have calculated pi to 200 million digits.
Pi to a few dozen digits
3.1415926535897932384626433832795028841971693993751058209749445923078164062862089986280348253421170679 8214808651328230664709384460955058223172535940812848111745028410270193852110555964462294895493038196 4428810975665933446128475648233786783165271201909145648566923460348610454326648213393607260249141273 724587006606315588174881520920962829254091715364367892590360011330530548820466521384146951941511609...
On your calculator
Most calculators have a button to enter the value of Pi directly, so you don't usually have to remember all the digits. But it's handy to remember pi = 3.142 anyway. Using the calculator Pi button is better, because it inputs Pi to the most number of decimal places that the calculator is capable of.
Approximating Pi
If you just need a rough value for Pi you can assume it is 22/7, but this is only accurate to two decimal places. However it may be accurate enough for some uses when you don't have a calculator handy.
An even more accurate approximation is 355/113. This is corect to 6 decimal places.
Pi 3.1415927
22/7 3.1428571
355/113 3.1415929
it is the circumference of any circle divided by its diameter
That is 2πr/2r
The number Pi, denoted by the Greek letter π - pronounced 'pie', is one of the most common constants in all of mathematics. It is the circumference of any circle, divided by its diameter. Nobody knows its exact value, because no matter how many digits you calculate it to, the number never ends. For most practical uses, you can assume it is 3.142.
Some people have written computer programs and calculated it to an astonishing accuracy. For example some have calculated pi to 200 million digits.
Pi to a few dozen digits
3.1415926535897932384626433832795028841971693993751058209749445923078164062862089986280348253421170679 8214808651328230664709384460955058223172535940812848111745028410270193852110555964462294895493038196 4428810975665933446128475648233786783165271201909145648566923460348610454326648213393607260249141273 724587006606315588174881520920962829254091715364367892590360011330530548820466521384146951941511609...
On your calculator
Most calculators have a button to enter the value of Pi directly, so you don't usually have to remember all the digits. But it's handy to remember pi = 3.142 anyway. Using the calculator Pi button is better, because it inputs Pi to the most number of decimal places that the calculator is capable of.
Approximating Pi
If you just need a rough value for Pi you can assume it is 22/7, but this is only accurate to two decimal places. However it may be accurate enough for some uses when you don't have a calculator handy.
An even more accurate approximation is 355/113. This is corect to 6 decimal places.
Pi 3.1415927
22/7 3.1428571
355/113 3.1415929
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