How did the irrational number pi come about

The circle number Pi (π)

The following article gives you a compact overview of the history of the Number pi, its mathematical properties and the cult that has developed around this mysterious number. And of course the most exciting question (for every student) will also be answered: What do you need Pi for?

To a first definition First of all: The Greek letter π, pronounced "Pi", denotes the number that represents the relationship between the circumference of the circle and the diameter of the circle. You will find out what that means in detail later.
In mathematics, Greek letters are used for the most important constants. This makes them much easier to use, especially when doing arithmetic. Otherwise the number would have to be written out again every time. An impossible undertaking with the infinitely long circle number Pi. So Greek letters in mathematical calculations always refer to something that has a high value in mathematics. Only the most important constants have a representative letter from the Greek alphabet.

Pi has found its way into science under many different terms over the centuries. These include with the "Ludolph's number" and the "Archimedes constant"Probably the most common synonyms. All three terms are therefore the same number of around 3.14159.

The number Pi written out (500 decimal places)


Pi (π) =

3.

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The history of the circle number pi


The circle number Pi has occupied mankind for several millennia. And there is a simple reason for this: the design of wheels inevitably involves a confrontation with the relationship between circumference and diameter.

For the first time, pi was actually mentioned in writing by the Greek mathematician Archimedes (287-212 BC) in the third century BC Since then mathematicians referred to the work of Archimedes, the number was called "Archimedes' constant". The letter pi from the Greek alphabet was not used for the first time until the late 18th century. In the meantime, the circle number was also called "Ludolph's number", named after Ludolph van Ceulen (1540-1610), who spent most of his life calculating the exact number of pi digits after the decimal point.
While Archimedes mainly provided the theoretical basis for the infinite calculation of the decimal places, van Ceulen calculated the circle number Pi to 35 places after the decimal point. It took him more than two decades for this purely manual calculation.
However, assumptions suggest that the ancient egyptians knew the number Pi at least approximately. The dimensions of the Cheops pyramid (about 4500 years old) were brought into connection with the circle number. So far, however, this has not been scientifically confirmed convincingly.

Many well-known mathematicians have lined up in the history of the study of circle numbers. John Wallis, Gottfried Wilhelm Leibniz and Leonard Euler also dealt with the calculation and the search for new formulas for faster determination of the decimal places. Without the help of computers, it was only possible to determine about 400 decimal places until the early 20th century.
With the help of powerful computer systems, a new record is broken practically every year. The current record (as of 2014) is held by Shigeru Kondo and Alexander Yee with more than 12,000,000,000,000 (twelve trillion) specific digits after the decimal point.

Where does the number pi come from?


Central statement: Each circle with diameter 1 has the circumference of pi (3.14159).
You can visualize it like this: You create a circle of any size with a cord. The diameter of this circle is now size 1 (see illustration). If you break up the circle and lay the cord lengthways, you get the length of the circumference, which corresponds to 3.14159 times the diameter. This applies without exception to all circles of all sizes.

Some of you may now object: "But not every circle has a diameter = 1". However, this is not a fixed unit of measurement, the circle could also have a diameter of 10cm, 20cm or 76.52cm. (Only the relation, i.e. the ratio, between diameter and circumference is meant.) If you multiply these numbers by pi, you always get the circumference of the circle (10cm * π = 31.41cm; 20cm * π = 62.83cm; 76.52cm * π = 240.39cm). The larger the diameter of a circle, the larger (logically) the circumference and always in a fixed ratio of 3.14159 (π). For this reason, the circle number is a universally valid natural constant.

Note: Every circle with the diameter = 1 has the circumference of Pi. The ratio between diameter and circumference of 3.14 always remains the same, no matter how big the circle may be.

What do you need Pi for? What can you calculate with pi? Formulas!

For the grammar school middle and upper level, the circle number is primarily relevant in connection with the sub-area of ​​geometry. With Pi the circular area, the circumference, the diameter and the radius can be determined. The most important formulas are shown below:

Circular area = (π * diameter2) / 4
Circular area = π * radius2
scope = π * diameter
scope = 2 * π * radius
diameter = √ ((area * 4) / π)
diameter = Circumference / π
radius = √ (area / π)
radius = Circumference / 2 * π

Facts and knowledge about the district number:


  • Pi is a mathematical constant
  • Pi is defined as the ratio of the circumference to the diameter of a circle
  • Pi is an irrational number (Pi cannot be represented as a fraction -> conclusion: Pi is infinite)
  • Pi is a transcendent number (means that Pi cannot be represented by a polynomial without a remainder)
  • The number Pi is independent of the diameter / circumference of the circle
  • The numbers of pi do not follow any particular scheme
  • With the fraction 355/113 you can approximate the circle number with six correct decimal places