The History of Pi
This is the most famous irrational and transcendental number in the world. Even people who don’t know what it means and don’t remember what they were taught in school know that there is such a number as “pi,” which is approximately equal to 3.14 and some digits further…
But the main thing is the essence, not the value. So why does this number have its own name and why is it considered almost magical?
What is the number pi in simple terms
Pi is the ratio of the circumference of a circle to its diameter. Any circle, every circle. This ratio is always constant, which means we can call pi a constant. 
Who discovered pi?
It is not exactly known who first discovered pi. Ancient mathematicians knew that if you divide the length of a circle by its diameter, you get something “around three.” They didn’t know the exact value, but they certainly knew where the number pi came from — from the ratio of the circumference of a circle to its diameter.
In Babylon, they thought that “pi” equaled 25/8, in Egypt, it was 256/81, and in India, it was 339/108. This level of accuracy was quite sufficient for the problems they were solving at the time. Most peoples rounded it to three.
The first person who seriously worked on determining the value of pi was Archimedes. So, with some stretch, we can “give the prize” to him and say that pi was discovered by Archimedes of Syracuse. Although, to be honest, he didn’t invent pi or discover it, he just established that it is somewhere there…
How to calculate pi
For Archimedes, such calculations had no practical meaning, as, like most of his contemporaries, he was interested in the process itself and the beauty of geometry.
He was solving the problem of squaring the circle, in simple terms, he was having fun trying to draw a circle with the same area as a square using only a compass and a ruler. One might think that the great Greek intended to calculate the area of a circle this way, but the point of the task wasn’t that; rather, it was to draw a circle equal to the square using these simple tools.
Nevertheless, Archimedes inscribed polygons in the circle and described them around the circumference. In this way, the described polygon is the upper bound of the area, and the inscribed one is the lower.
At 96 vertices — the 96-sided polygon, Archimedes apparently thought that it would be impossible to draw a more accurate figure.
The genius mathematician proposed the ratio of 22 to 7. Which is approximately 3.142857142857143. The value calculated by Archimedes differs from the one we know today by only 0.04%.
Of course, attempts to figure out the exact value of pi didn’t stop there. In Europe, India, and China. Chinese mathematician Li Hui calculated the area of a 3072-sided polygon, almost a circle, and developed a method for calculating pi.
He discovered that the areas of polygons form a geometric progression, which greatly simplified the calculation algorithm.
The precision of his calculations was much higher than anyone before him, with Li Hui’s calculated pi differing from the true value by 0.00028%.
Further calculations, surprisingly, were not related to circles at all. After all, you can’t measure the circumference with infinite accuracy.
Thus, mathematicians began to use infinite series to find pi. For example, the Leibniz series: π = 4/1 – 4/3 + 4/5 – 4/7….
When the number became a letter
Before 1706, the number was not referred to by a letter. William Jones proposed using the Greek letter “π”. This letter was chosen because it starts the words for circumference and perimeter in Greek. It’s logical and easy to remember.
After the famous mathematician Leonard Euler started using the letter “π” in his publications, this Greek letter became forever associated with the ratio of the circumference of a circle to its diameter.
Before the number was assigned a letter, it had other names:
- Archimedes’ constant
- Circular constant
- Ludolph’s number*
*Mathematician Ludolph van Ceulen calculated pi to 32 decimal places
What is pi equal to?
Pi is the ratio of the circumference to its diameter. The correct answer to this question should be: π = C/D. If the questioner wants a specific number, it is enough to give two decimal places:
3.14… — this is pi
You can increase the number of decimal places to 10, which will give 3.1415926535, but it will differ from the “school” value by slightly more than 0.05%. In everyday life, 3.14 is usually sufficient. However, for some tasks, it is certainly necessary to increase the precision.
For example, to calculate the circumference of the known universe with accuracy down to the radius of a hydrogen atom, 39 decimal places are enough.
However, the world record for pi’s length is 62.8 trillion decimal places. This was calculated at the Swiss University of Applied Sciences. Now, we know the last 10 digits: 7817924264.
The previous record was 31.4 trillion decimal places, and it was set by Google.
Who and why might need such accuracy? No one! It’s unnecessary; the number is so famous that it’s simply used to attract attention to one’s scientific achievements.
The trend for records in such calculations began in the 1980s when the first computers appeared.
People also compete to see who can remember the most digits of pi. The most recent record is 70,000 digits. One can only admire the perseverance of Indian Rajveer Mina, who spent more than 10 hours setting this record.
What is pi used for in life?
Besides the obvious calculations of the area of a circle and the circumference in school problems, pi is used to calculate the trajectories of spacecraft. Since, in real life (not in science fiction films), spacecraft do not fly in a straight line. Only circles and ellipses are part of the trajectories.
For such calculations, pi is used to 15 decimal places. This is quite enough.
This is the trajectory to Mars, and this is an arc, not a straight line
For example, if we calculate the Earth’s equator length with such precision, the error will be roughly the size of a molecule.
Engineers and builders use the most famous number for calculations very often. Builders deal with columns, while mechanics work with shafts, bolts, axles, bearings, and other objects with a circular cross-section.
The simplest example is the need to calculate the pressure exerted by something round. For that, you need to calculate the area of the circle.
Pi is often found in formulas for calculating the intensity of electric fields. It’s also essential for vibration calculations…. In general, pi is used not only in solving school problems.
What is pi really equal to?
Everyone knows that pi equals 3.14… But what is its actual length?
Pi is an irrational number, which means it never ends. Currently, we know the first 68.2 trillion digits after the decimal point. It’s a very long number, infinitely long. But not infinitely large, it’s just slightly greater than three.
You can continue calculating digits after the decimal point, but what’s the point, except for breaking records?
If we recall Archimedes, who approximated the area of a circle using polygons, we can say that a circle is a polygon with an infinite number of vertices. But a polygon is still not a circle, which means the area of such figures can’t be exactly the same.
But from a mathematical standpoint, only the fractional part is long. The number itself is clearly less than 4. So, pi isn’t infinite, it’s just long, because dividing the circumference by the diameter of a whole number doesn’t give an integer. Therefore, you just need to choose the precision that’s sufficient for the particular task.
Interesting facts about pi
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- Pi is an irrational number. This means it can’t be written as m/n, where m and n are integers, and n is a positive integer. When it comes to a circle, simply put, π = C/D means “how many diameters D fit into the circumference C.” The answer to this question: if you unroll the circle into a line, the whole number of diameters doesn’t fit in its length; three fit, but there is still something left. So, an integer can’t be obtained, no matter what you do. Very irrational.
- The sequence of numbers in the “tail” of pi is random. And since the number of digits after the decimal point is infinite, you can find any combinations, for example, your birthdate or your phone number.
- Pi is a transcendental number. This means it cannot be the root of an algebraic equation. This was proven only in 1882.
- The idea that pi was discovered in the Egyptian pyramids (the ratio of height to semi-perimeter) is a myth. This ratio is 22 to 7, which is 3.1428. In the famous Rhind papyrus, “pi” is derived as 3.16. So, it’s neither the Egyptian nor the modern value, just a coincidence that appeared in just one pyramid.
- Pi hides the number 666. Both a myth and a fact at the same time. Yes, after the 3151st digit, the combination 666 appears, but it continues appearing later and not just once. Additionally, there are combinations of 777 and 999. There’s even 999999, and it appears after the 361st digit, which is four times closer to the beginning. So, you can find any combination in pi if you search.
- There are two pi days. The first is on April 14. In the American date format, it is written as 3.14. The celebration must happen at exactly 01:59:26, so it reads 3.14 1:59:26, which is 3.1415926. The second one is on July 22, in European format — 22/7. This holiday is called Pi Approximation Day, as 22 to 7 is the approximate value proposed by Archimedes.
- Your birthdate in pi. Since the set of numbers is random, non-repeating, and infinite, you can find your birthday and any other date in it. There’s a special website for this: mypiday.com
- In binary system, pi is written as 11.00100100001111110… Even in binary, it’s an infinite fraction.
What does pi mean?
Pi has no special or secret meaning; most of the mysteries of the oldest constant have already been solved. There’s nothing magical about it, but there’s a lot of charm hidden in it.
Pi truly deserves to be denoted by a letter, not a digit. First, it has rare properties, and second, it’s simply more convenient to write formulas with constants.
