O pi number, represented by the Greek letter π, is one of the best known and most important constants in mathematics. how is a irrational number, it is a non-repeating decimal and has infinitely many decimal places, so it is common to use an approximation of the value of π to solve problems.
This number is a constant, and the its value is approximately 3.141592653..., but the most commonly used approximation for the value of π is 3.14. The number π is used in calculations involving circular shapes, such as calculating the length of the circumference, calculating the area of the circle, and calculations involving spheres, cones, and cylinders.
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Summary about the number pi (π)
The number π (read: pi) is one of the best-known constants in Math.
It is used to calculate quantities involving circular shapes.
It is an irrational number, so it is a non-repeating decimal.
The value of π = 3.141592643...
It is quite common to use approximations for the value of π. The most used is\(\pi=3.14\).
History of the number pi (π)
The constant π appeared in the lives of our ancestors many years ago, as many mathematicians tried to find its value precisely. Historians report that the search for approximations to the value of πstarted with the Egyptians and Babylonians.
Years later, based on studies carried out by Euclid, the Greek mathematician Archimedes got an approximation to the value of π starting by calculating the perimeter of a hexagon and looking at what would happen to that perimeter by increasing the number of sides of the hexagon. polygon. Realizing that the longer the side of this polygon, the closer to the circumference this polygon came, Archimedes found the value 3.142 as an approximation to the value of π.
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Other mathematicians used the same method, increasing the side of the polygons, and then Ptolemy managed to find a more accurate approximation, π = 3.1416, using a 720-sided polygon. We also had later contributions from the Chinese, who found the value of π = 3.14159 with a polygon of 3072 sides.
With the passage of time and the development of technology, many mathematicians have been busy figuring out as many decimal places as possible for this number. Currently, a total of 62.8 trillion decimal places of the number π is known. This is the world record recognized by the Guinness Book calculated by the University of Applied Sciences at Grisons.
Read too: How are non-exact roots calculated?
What is the value of the number pi (π)?
We know, therefore, that π is a non-repeating decimal, that has infinite decimal places. In school exercises and entrance exams, we usually use an approximation for its value, such as 3 or 3.1 or 3.14. However, as we have seen, π has many decimal places, so mathematicians use more of them to do the math accurately.
See below the value of π considering the first 200 decimal places:
π = 3,14159265358979323846264338327950288419716939937510582097494459230781640628620899862803482534211706798214808651328230664709384460955058223172535940812848111745028410270193852110555964462294895493038196 |
How to calculate the number pi (π)?
The constant π was found when trying to calculate the ratio between the length of the circumference its diameter.
\(\pi=\frac{length}{diameter}=\frac{C}{d}\)
It turns out that a circle had never been measured with the necessary precision, so when doing this division, people realized that the value of calculus always approached a constant. This happens for any circle, with any radius.
What is pi (π) for?
The constant π is used to calculations involving round bodies, such as the area of a circle, the length of a circle, the volume, and the total area of cones, cylinders and spheres. When performing calculations with plane figures and geometric solids that have rounded faces, the number π is essential.
For example:
The formula for calculating the length of a circle is:
\(C=2\pi r\)
The formula for the area of a circle is:
\(A=\pi r^2\)
The formula to calculate the volume of the sphere is:
\(V=\frac{4}{3}\pi r^3\)
Therefore, only with the constant π is it possible to have precision in the value of quantities involving plane figures of circular shape and Geometric solids with circular faces.
By Raul Rodrigues de Oliveira
Maths teacher
Would you like to reference this text in a school or academic work? Look:
OLIVEIRA, Raul Rodrigues de. "Number pi (π)"; Brazil School. Available in: https://brasilescola.uol.com.br/matematica/numero-pi.htm. Accessed on March 30, 2022.
